The Human Mind As General Problem Solver
Gurr, Henry
2011-10-01
Since leaving U Cal Irvine Neutrino Research, I have been a University Physics Teacher, and an Informal Researcher Of Human Functionality. My talk will share what I discovered about the best ways to learn, many of which are regularities that are to be expected from the Neuronal Network Properties announced in the publications of physicist John Joseph Hopfield. Hopfield's Model of mammalian brain-body, provides solid instructive understanding of how best Learn, Solve Problems, Live! With it we understand many otherwise puzzling features of our intellect! Examples Why 1) Analogies and metaphors powerful in class instruction, ditto poems. 2) Best learning done in physical (Hands-On) situations with tight immediate dynamical feedback such as seen in learning to ride bike, drive car, speak language, etc. 3) Some of the best learning happens in seeming random exploration, bump around, trial and error. 4) Scientific discoveries happen, with no apparent effort, at odd moments. 5) Important discoveries DEPEND on considerable frustrating effort, then Flash of Insight AHA EURIKA.
Navier-Stokes Solvers and Generalizations for Reacting Flow Problems
Energy Technology Data Exchange (ETDEWEB)
Elman, Howard C
2013-01-27
This is an overview of our accomplishments during the final term of this grant (1 September 2008 -- 30 June 2012). These fall mainly into three categories: fast algorithms for linear eigenvalue problems; solution algorithms and modeling methods for partial differential equations with uncertain coefficients; and preconditioning methods and solvers for models of computational fluid dynamics (CFD).
Directory of Open Access Journals (Sweden)
Jürgen eSchmidhuber
2013-06-01
Full Text Available Most of computer science focuses on automatically solving given computational problems. I focus on automatically inventing or discovering problems in a way inspired by the playful behavior of animals and humans, to train a more and more general problem solver from scratch in an unsupervised fashion. Consider the infinite set of all computable descriptions of tasks with possibly computable solutions. The novel algorithmic framework POWERPLAY (2011 continually searches the space of possible pairs of new tasks and modifications of the current problem solver, until it finds a more powerful problem solver that provably solves all previously learned tasks plus the new one, while the unmodified predecessor does not. Wow-effects are achieved by continually making previously learned skills more efficient such that they require less time and space. New skills may (partially re-use previously learned skills. POWERPLAY's search orders candidate pairs of tasks and solver modifications by their conditional computational (time & space complexity, given the stored experience so far. The new task and its corresponding task-solving skill are those first found and validated. The computational costs of validating new tasks need not grow with task repertoire size. POWERPLAY's ongoing search for novelty keeps breaking the generalization abilities of its present solver. This is related to Goedel's sequence of increasingly powerful formal theories based on adding formerly unprovable statements to the axioms without affecting previously provable theorems. The continually increasing repertoire of problem solving procedures can be exploited by a parallel search for solutions to additional externally posed tasks. POWERPLAY may be viewed as a greedy but practical implementation of basic principles of creativity. A first experimental analysis can be found in separate papers [58, 56, 57].
Differential equations problem solver
Arterburn, David R
2012-01-01
REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and
Modified and fuzzified general problem solver for the 'monkey and banana' problem, 1
International Nuclear Information System (INIS)
Sano, Norihide; Takahashi, Ryoichi.
1991-01-01
The master-and-slave control system should be extensively implemented for the in-service inspection of operating nuclear power stations or the decommission of retired plants. The performance of this system depends on the intelligent slave. In this paper the degree of intelligence is approximated by the given amount of prior knowledge or suggestions. This paper aims at improving the general problem solver (GPS) by incorporating the learning process in order to solve the puzzle of the 'monkey and banana'. The monkey in this puzzle may be a reasonable alternative to represent the intelligent slave. Also, this paper deals with fuzzified problem solving since the master's command is not always crisp to the slave. (author)
Modified and fuzzified general problem solver for 'monkey and banana' problem
International Nuclear Information System (INIS)
Sano, Norihide; Takahashi, Ryoichi.
1994-01-01
Automatic operation is important for the in-service inspection of nuclear power stations of the decommission of retired plants. Master and slave control will be introduced for work-robot control. It is desirable that the slave possess problem-solving capabilities. In this paper we assume that the slave incorporates the general problem solver (GPS) algorithm. In view of having solved the 'monkey and banana' problem, the slave system is regarded as reasonable alternative which incorporates the capability of problem-solving. Basically, the GPS solves a problem by reducing the difference between the initial state and goal state, and hence the performance of GPS depends on selection of the difference to be reduced. The conventional GPS is given the order of importance of the differences in advance. In this study, the GPS was improved by making use of the rules which determine the order. When several choices are available for the given difference, a fuzzified decision to determine the necessary action is made, as demonstrated in this paper. (author)
Modified and fuzzified general problem solver for 'monkey and banana' problem, 2
International Nuclear Information System (INIS)
Sano, Norihide; Takahashi, Ryoichi.
1991-01-01
The automatic operation is important for the in-service inspection of the operating nuclear power station or the decommission of retired plants. The master and slave control will be introduced for work-robot control. It is desirable that the slave involves the capability of problem solving. This paper assumed that the slave involved the general problem solver algorithm. In view of having solved the puzzle of the 'monkey and banana', the slave system is regarded as the reasonable alternative which incorporates the capability of problem solving. Basically, the GPS solves a problem by reducing the difference between an initial state and a goal state, and hence the performance of GPS depends on selecting the difference to be reduced. The usual GPS is given in advance the ordering which indicates the importance of the differences. In this paper, the GPS was improved by making use of the rules which decide the order. When several choices are found on the given difference, the fuzzified decision to determine the action is demonstrated in this paper. (author)
Schmidhuber, Jürgen
2013-01-01
Most of computer science focuses on automatically solving given computational problems. I focus on automatically inventing or discovering problems in a way inspired by the playful behavior of animals and humans, to train a more and more general problem solver from scratch in an unsupervised fashion. Consider the infinite set of all computable descriptions of tasks with possibly computable solutions. Given a general problem-solving architecture, at any given time, the novel algorithmic framework PowerPlay (Schmidhuber, 2011) searches the space of possible pairs of new tasks and modifications of the current problem solver, until it finds a more powerful problem solver that provably solves all previously learned tasks plus the new one, while the unmodified predecessor does not. Newly invented tasks may require to achieve a wow-effect by making previously learned skills more efficient such that they require less time and space. New skills may (partially) re-use previously learned skills. The greedy search of typical PowerPlay variants uses time-optimal program search to order candidate pairs of tasks and solver modifications by their conditional computational (time and space) complexity, given the stored experience so far. The new task and its corresponding task-solving skill are those first found and validated. This biases the search toward pairs that can be described compactly and validated quickly. The computational costs of validating new tasks need not grow with task repertoire size. Standard problem solver architectures of personal computers or neural networks tend to generalize by solving numerous tasks outside the self-invented training set; PowerPlay's ongoing search for novelty keeps breaking the generalization abilities of its present solver. This is related to Gödel's sequence of increasingly powerful formal theories based on adding formerly unprovable statements to the axioms without affecting previously provable theorems. The continually increasing
Electric circuits problem solver
REA, Editors of
2012-01-01
Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.Here in this highly useful reference is the finest overview of electric circuits currently av
Advanced calculus problem solver
REA, Editors of
2012-01-01
Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.Here in this highly useful reference is the finest overview of advanced calculus currently av
Modern solvers for Helmholtz problems
Tang, Jok; Vuik, Kees
2017-01-01
This edited volume offers a state of the art overview of fast and robust solvers for the Helmholtz equation. The book consists of three parts: new developments and analysis in Helmholtz solvers, practical methods and implementations of Helmholtz solvers, and industrial applications. The Helmholtz equation appears in a wide range of science and engineering disciplines in which wave propagation is modeled. Examples are: seismic inversion, ultrasone medical imaging, sonar detection of submarines, waves in harbours and many more. The partial differential equation looks simple but is hard to solve. In order to approximate the solution of the problem numerical methods are needed. First a discretization is done. Various methods can be used: (high order) Finite Difference Method, Finite Element Method, Discontinuous Galerkin Method and Boundary Element Method. The resulting linear system is large, where the size of the problem increases with increasing frequency. Due to higher frequencies the seismic images need to b...
Creativity for Problem Solvers
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
2009-01-01
This paper presents some modern and interdisciplinary concepts about creativity and creative processes specially related to problem solving. Central publications related to the theme are briefly reviewed. Creative tools and approaches suitable to support problem solving are also presented. Finally......, the paper outlines the author’s experiences using creative tools and approaches to: Facilitation of problem solving processes, strategy development in organisations, design of optimisation systems for large scale and complex logistic systems, and creative design of software optimisation for complex non...
Edmondson, Amy C
2016-06-01
Companies today increasingly rely on teams that span many industries for radical innovation, especially to solve "wicked problems." So leaders have to understand how to promote collaboration when roles are uncertain, goals are shifting, expertise and organizational cultures are varied, and participants have clashing or even antagonistic perspectives. HBS professor Amy Edmondson has studied more than a dozen cross-industry innovation projects, among them the creation of a new city, a mango supply-chain transformation, and the design and construction of leading-edge buildings. She has identified the leadership practices that make successful cross-industry teams work: fostering an adaptable vision, promoting psychological safety, enabling knowledge sharing, and encouraging collaborative innovation. Though these practices are broadly familiar, their application within cross-industry teams calls for unique leadership approaches that combine flexibility, open-mindedness, humility, and fierce resolve.
Test set for initial value problem solvers
W.M. Lioen (Walter); J.J.B. de Swart (Jacques)
1998-01-01
textabstractThe CWI test set for IVP solvers presents a collection of Initial Value Problems to test solvers for implicit differential equations. This test set can both decrease the effort for the code developer to test his software in a reliable way, and cross the bridge between the application
The Scientist as Problem Solver.
1989-01-01
history. or imagined history. no magic and no mystery Each step appears to proceed. if not inexorably at least plausibly from the preceding one If the...discovery process appears quite unremarkable. The problem was found in the literatue (Goodwin S paper). and it can be represented in a quite standard way by
Problem Solvers' Conceptions about Osmosis.
Zuckerman, June T.
1994-01-01
Discusses the scheme and findings of a study designed to identify the conceptual knowledge used by high school students to solve a significant problem related to osmosis. Useful tips are provided to teachers to aid students in developing constructs that maximize understanding. (ZWH)
From 'troublemakers' to problem solvers
DEFF Research Database (Denmark)
Frandsen, Martin Severin; Pfeiffer Petersen, Lene
2012-01-01
in a disadvantaged neighbourhood in the suburbs of Copenhagen, designed and constructed colourful and imaginative dustbins to handle problems with local littering. The project was successful in creating an increased local awareness of waste management and reducing the amount of litter. However, the more important...
Fostering Creative Problem Solvers in Higher Education
DEFF Research Database (Denmark)
Zhou, Chunfang
2016-01-01
Recent studies have emphasized issues of social emergence based on thinking of societies as complex systems. The complexity of professional practice has been recognized as the root of challenges for higher education. To foster creative problem solvers is a key response of higher education in order...... to meet such challenges. This chapter aims to illustrate how to understand: 1) complexity as the nature of professional practice; 2) creative problem solving as the core skill in professional practice; 3) creativity as interplay between persons and their environment; 4) higher education as the context...... of fostering creative problem solvers; and 5) some innovative strategies such as Problem-Based Learning (PBL) and building a learning environment by Information Communication Technology (ICT) as potential strategies of creativity development. Accordingly, this chapter contributes to bridge the complexity...
Aleph Field Solver Challenge Problem Results Summary
Energy Technology Data Exchange (ETDEWEB)
Hooper, Russell [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Moore, Stan Gerald [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-01-01
Aleph models continuum electrostatic and steady and transient thermal fields using a finite-element method. Much work has gone into expanding the core solver capability to support enriched modeling consisting of multiple interacting fields, special boundary conditions and two-way interfacial coupling with particles modeled using Aleph's complementary particle-in-cell capability. This report provides quantitative evidence for correct implementation of Aleph's field solver via order- of-convergence assessments on a collection of problems of increasing complexity. It is intended to provide Aleph with a pedigree and to establish a basis for confidence in results for more challenging problems important to Sandia's mission that Aleph was specifically designed to address.
Parallel Solver for H(div) Problems Using Hybridization and AMG
Energy Technology Data Exchange (ETDEWEB)
Lee, Chak S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-01-15
In this paper, a scalable parallel solver is proposed for H(div) problems discretized by arbitrary order finite elements on general unstructured meshes. The solver is based on hybridization and algebraic multigrid (AMG). Unlike some previously studied H(div) solvers, the hybridization solver does not require discrete curl and gradient operators as additional input from the user. Instead, only some element information is needed in the construction of the solver. The hybridization results in a H1-equivalent symmetric positive definite system, which is then rescaled and solved by AMG solvers designed for H1 problems. Weak and strong scaling of the method are examined through several numerical tests. Our numerical results show that the proposed solver provides a promising alternative to ADS, a state-of-the-art solver [12], for H(div) problems. In fact, it outperforms ADS for higher order elements.
Thinking Process of Naive Problem Solvers to Solve Mathematical Problems
Mairing, Jackson Pasini
2017-01-01
Solving problems is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe…
Metaheuristics progress as real problem solvers
Nonobe, Koji; Yagiura, Mutsunori
2005-01-01
Metaheuristics: Progress as Real Problem Solvers is a peer-reviewed volume of eighteen current, cutting-edge papers by leading researchers in the field. Included are an invited paper by F. Glover and G. Kochenberger, which discusses the concept of Metaheuristic agent processes, and a tutorial paper by M.G.C. Resende and C.C. Ribeiro discussing GRASP with path-relinking. Other papers discuss problem-solving approaches to timetabling, automated planograms, elevators, space allocation, shift design, cutting stock, flexible shop scheduling, colorectal cancer and cartography. A final group of methodology papers clarify various aspects of Metaheuristics from the computational view point.
Cognitive Structures of Good and Poor Novice Problem Solvers in Physics
de Jong, Anthonius J.M.; Ferguson-Hessler, Monica G.M.
1986-01-01
The way knowledge is organized in memory is generally expected to relate to the degree of success in problem solving. In the present study, we investigated whether good novice problem solvers have their knowledge arranged around problem types to a greater extent than poor problem solvers have. In
Integrating Problem Solvers from Analogous Markets in New Product Ideation
DEFF Research Database (Denmark)
Franke, Nikolaus; Poetz, Marion; Schreier, Martin
2014-01-01
Who provides better inputs to new product ideation tasks, problem solvers with expertise in the area for which new products are to be developed or problem solvers from “analogous” markets that are distant but share an analogous problem or need? Conventional wisdom appears to suggest that target...
Linear solver performance in elastoplastic problem solution on GPU cluster
Khalevitsky, Yu. V.; Konovalov, A. V.; Burmasheva, N. V.; Partin, A. S.
2017-12-01
Applying the finite element method to severe plastic deformation problems involves solving linear equation systems. While the solution procedure is relatively hard to parallelize and computationally intensive by itself, a long series of large scale systems need to be solved for each problem. When dealing with fine computational meshes, such as in the simulations of three-dimensional metal matrix composite microvolume deformation, tens and hundreds of hours may be needed to complete the whole solution procedure, even using modern supercomputers. In general, one of the preconditioned Krylov subspace methods is used in a linear solver for such problems. The method convergence highly depends on the operator spectrum of a problem stiffness matrix. In order to choose the appropriate method, a series of computational experiments is used. Different methods may be preferable for different computational systems for the same problem. In this paper we present experimental data obtained by solving linear equation systems from an elastoplastic problem on a GPU cluster. The data can be used to substantiate the choice of the appropriate method for a linear solver to use in severe plastic deformation simulations.
Experiences with linear solvers for oil reservoir simulation problems
Energy Technology Data Exchange (ETDEWEB)
Joubert, W.; Janardhan, R. [Los Alamos National Lab., NM (United States); Biswas, D.; Carey, G.
1996-12-31
This talk will focus on practical experiences with iterative linear solver algorithms used in conjunction with Amoco Production Company`s Falcon oil reservoir simulation code. The goal of this study is to determine the best linear solver algorithms for these types of problems. The results of numerical experiments will be presented.
From Answer-Getters to Problem Solvers
Flynn, Mike
2017-01-01
In some math classrooms, students are taught to follow and memorize procedures to arrive at the correct solution to problems. In this article, author Mike Flynn suggests a way to move beyond answer-getting to true problem solving. He describes an instructional approach called three-act tasks in which students solve an engaging math problem in…
SolveDB: Integrating Optimization Problem Solvers Into SQL Databases
DEFF Research Database (Denmark)
Siksnys, Laurynas; Pedersen, Torben Bach
2016-01-01
for optimization problems, (2) an extensible infrastructure for integrating different solvers, and (3) query optimization techniques to achieve the best execution performance and/or result quality. Extensive experiments with the PostgreSQL-based implementation show that SolveDB is a versatile tool offering much...
A Creativity Course for Problem Solvers
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
This paper presents the principles of active learning and the contents of a creativity course entitled: Creativity and Problem Solving. The main purpose of this course is to create a space to discuss, reflect and experiment with creativity, creative processes and creative tools of relevance...
Problem Solvers: Solutions--Playing Basketball
Smith, Jeffrey
2014-01-01
In this article, fourth grade Upper Allen Elementary School (Mechanicsburg, Pennsylvania) teacher Jeffrey Smith describes his exploration of the Playing Basketball activity. Herein he describes how he found the problem to be an effective way to review concepts associated with the measurement of elapsed time with his students. Additionally, it…
Scalable Adaptive Multilevel Solvers for Multiphysics Problems
Energy Technology Data Exchange (ETDEWEB)
Xu, Jinchao [Pennsylvania State Univ., University Park, PA (United States). Dept. of Mathematics
2014-11-26
In this project, we carried out many studies on adaptive and parallel multilevel methods for numerical modeling for various applications, including Magnetohydrodynamics (MHD) and complex fluids. We have made significant efforts and advances in adaptive multilevel methods of the multiphysics problems: multigrid methods, adaptive finite element methods, and applications.
A distributed-memory hierarchical solver for general sparse linear systems
Energy Technology Data Exchange (ETDEWEB)
Chen, Chao [Stanford Univ., CA (United States). Inst. for Computational and Mathematical Engineering; Pouransari, Hadi [Stanford Univ., CA (United States). Dept. of Mechanical Engineering; Rajamanickam, Sivasankaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research; Boman, Erik G. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research; Darve, Eric [Stanford Univ., CA (United States). Inst. for Computational and Mathematical Engineering and Dept. of Mechanical Engineering
2017-12-20
We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it exploits the low-rank structure of fill-in blocks. Depending on the accuracy of low-rank approximations, the hierarchical solver can be used either as a direct solver or as a preconditioner. The parallel algorithm is based on data decomposition and requires only local communication for updating boundary data on every processor. Moreover, the computation-to-communication ratio of the parallel algorithm is approximately the volume-to-surface-area ratio of the subdomain owned by every processor. We also provide various numerical results to demonstrate the versatility and scalability of the parallel algorithm.
A generalized Poisson solver for first-principles device simulations
Energy Technology Data Exchange (ETDEWEB)
Bani-Hashemian, Mohammad Hossein; VandeVondele, Joost, E-mail: joost.vandevondele@mat.ethz.ch [Nanoscale Simulations, ETH Zürich, 8093 Zürich (Switzerland); Brück, Sascha; Luisier, Mathieu [Integrated Systems Laboratory, ETH Zürich, 8092 Zürich (Switzerland)
2016-01-28
Electronic structure calculations of atomistic systems based on density functional theory involve solving the Poisson equation. In this paper, we present a plane-wave based algorithm for solving the generalized Poisson equation subject to periodic or homogeneous Neumann conditions on the boundaries of the simulation cell and Dirichlet type conditions imposed at arbitrary subdomains. In this way, source, drain, and gate voltages can be imposed across atomistic models of electronic devices. Dirichlet conditions are enforced as constraints in a variational framework giving rise to a saddle point problem. The resulting system of equations is then solved using a stationary iterative method in which the generalized Poisson operator is preconditioned with the standard Laplace operator. The solver can make use of any sufficiently smooth function modelling the dielectric constant, including density dependent dielectric continuum models. For all the boundary conditions, consistent derivatives are available and molecular dynamics simulations can be performed. The convergence behaviour of the scheme is investigated and its capabilities are demonstrated.
Parallel Auxiliary Space AMG Solver for $H(div)$ Problems
Energy Technology Data Exchange (ETDEWEB)
Kolev, Tzanio V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2012-12-18
We present a family of scalable preconditioners for matrices arising in the discretization of $H(div)$ problems using the lowest order Raviart--Thomas finite elements. Our approach belongs to the class of “auxiliary space''--based methods and requires only the finite element stiffness matrix plus some minimal additional discretization information about the topology and orientation of mesh entities. Also, we provide a detailed algebraic description of the theory, parallel implementation, and different variants of this parallel auxiliary space divergence solver (ADS) and discuss its relations to the Hiptmair--Xu (HX) auxiliary space decomposition of $H(div)$ [SIAM J. Numer. Anal., 45 (2007), pp. 2483--2509] and to the auxiliary space Maxwell solver AMS [J. Comput. Math., 27 (2009), pp. 604--623]. Finally, an extensive set of numerical experiments demonstrates the robustness and scalability of our implementation on large-scale $H(div)$ problems with large jumps in the material coefficients.
Comparison of Einstein-Boltzmann solvers for testing general relativity
Bellini, E.; Barreira, A.; Frusciante, N.; Hu, B.; Peirone, S.; Raveri, M.; Zumalacárregui, M.; Avilez-Lopez, A.; Ballardini, M.; Battye, R. A.; Bolliet, B.; Calabrese, E.; Dirian, Y.; Ferreira, P. G.; Finelli, F.; Huang, Z.; Ivanov, M. M.; Lesgourgues, J.; Li, B.; Lima, N. A.; Pace, F.; Paoletti, D.; Sawicki, I.; Silvestri, A.; Skordis, C.; Umiltà, C.; Vernizzi, F.
2018-01-01
We compare Einstein-Boltzmann solvers that include modifications to general relativity and find that, for a wide range of models and parameters, they agree to a high level of precision. We look at three general purpose codes that primarily model general scalar-tensor theories, three codes that model Jordan-Brans-Dicke (JBD) gravity, a code that models f (R ) gravity, a code that models covariant Galileons, a code that models Hořava-Lifschitz gravity, and two codes that model nonlocal models of gravity. Comparing predictions of the angular power spectrum of the cosmic microwave background and the power spectrum of dark matter for a suite of different models, we find agreement at the subpercent level. This means that this suite of Einstein-Boltzmann solvers is now sufficiently accurate for precision constraints on cosmological and gravitational parameters.
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
Energy Technology Data Exchange (ETDEWEB)
Fisicaro, G., E-mail: giuseppe.fisicaro@unibas.ch; Goedecker, S. [Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel (Switzerland); Genovese, L. [University of Grenoble Alpes, CEA, INAC-SP2M, L-Sim, F-38000 Grenoble (France); Andreussi, O. [Institute of Computational Science, Università della Svizzera Italiana, Via Giuseppe Buffi 13, CH-6904 Lugano (Switzerland); Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland); Marzari, N. [Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland)
2016-01-07
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
International Nuclear Information System (INIS)
Fisicaro, G.; Goedecker, S.; Genovese, L.; Andreussi, O.; Marzari, N.
2016-01-01
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes
Mathematical Tasks without Words and Word Problems: Perceptions of Reluctant Problem Solvers
Holbert, Sydney Margaret
2013-01-01
This qualitative research study used a multiple, holistic case study approach (Yin, 2009) to explore the perceptions of reluctant problem solvers related to mathematical tasks without words and word problems. Participants were given a choice of working a mathematical task without words or a word problem during four problem-solving sessions. Data…
Teaching problem solving: Don't forget the problem solver(s)
Ranade, Saidas M.; Corrales, Angela
2013-05-01
The importance of intrapersonal and interpersonal intelligences has long been known but educators have debated whether to and how to incorporate those topics in an already crowded engineering curriculum. In 2010, the authors used the classroom as a laboratory to observe the usefulness of including selected case studies and exercises from the fields of neurology, artificial intelligence, cognitive sciences and social psychology in a new problem-solving course. To further validate their initial findings, in 2012, the authors conducted an online survey of engineering students and engineers. The main conclusion is that engineering students will benefit from learning more about the impact of emotions, culture, diversity and cognitive biases when solving problems. Specifically, the work shows that an augmented problem-solving curriculum needs to include lessons on labelling emotions and cognitive biases, 'evidence-based' data on the importance of culture and diversity and additional practice on estimating conditional probability.
A General Symbolic PDE Solver Generator: Beyond Explicit Schemes
Directory of Open Access Journals (Sweden)
K. Sheshadri
2003-01-01
Full Text Available This paper presents an extension of our Mathematica- and MathCode-based symbolic-numeric framework for solving a variety of partial differential equation (PDE problems. The main features of our earlier work, which implemented explicit finite-difference schemes, include the ability to handle (1 arbitrary number of dependent variables, (2 arbitrary dimensionality, and (3 arbitrary geometry, as well as (4 developing finite-difference schemes to any desired order of approximation. In the present paper, extensions of this framework to implicit schemes and the method of lines are discussed. While C++ code is generated, using the MathCode system for the implicit method, Modelica code is generated for the method of lines. The latter provides a preliminary PDE support for the Modelica language. Examples illustrating the various aspects of the solver generator are presented.
Parallel time domain solvers for electrically large transient scattering problems
Liu, Yang
2014-09-26
Marching on in time (MOT)-based integral equation solvers represent an increasingly appealing avenue for analyzing transient electromagnetic interactions with large and complex structures. MOT integral equation solvers for analyzing electromagnetic scattering from perfect electrically conducting objects are obtained by enforcing electric field boundary conditions and implicitly time advance electric surface current densities by iteratively solving sparse systems of equations at all time steps. Contrary to finite difference and element competitors, these solvers apply to nonlinear and multi-scale structures comprising geometrically intricate and deep sub-wavelength features residing atop electrically large platforms. Moreover, they are high-order accurate, stable in the low- and high-frequency limits, and applicable to conducting and penetrable structures represented by highly irregular meshes. This presentation reviews some recent advances in the parallel implementations of time domain integral equation solvers, specifically those that leverage multilevel plane-wave time-domain algorithm (PWTD) on modern manycore computer architectures including graphics processing units (GPUs) and distributed memory supercomputers. The GPU-based implementation achieves at least one order of magnitude speedups compared to serial implementations while the distributed parallel implementation are highly scalable to thousands of compute-nodes. A distributed parallel PWTD kernel has been adopted to solve time domain surface/volume integral equations (TDSIE/TDVIE) for analyzing transient scattering from large and complex-shaped perfectly electrically conducting (PEC)/dielectric objects involving ten million/tens of millions of spatial unknowns.
Composing Problem Solvers for Simulation Experimentation: A Case Study on Steady State Estimation
Leye, Stefan; Ewald, Roland; Uhrmacher, Adelinde M.
2014-01-01
Simulation experiments involve various sub-tasks, e.g., parameter optimization, simulation execution, or output data analysis. Many algorithms can be applied to such tasks, but their performance depends on the given problem. Steady state estimation in systems biology is a typical example for this: several estimators have been proposed, each with its own (dis-)advantages. Experimenters, therefore, must choose from the available options, even though they may not be aware of the consequences. To support those users, we propose a general scheme to aggregate such algorithms to so-called synthetic problem solvers, which exploit algorithm differences to improve overall performance. Our approach subsumes various aggregation mechanisms, supports automatic configuration from training data (e.g., via ensemble learning or portfolio selection), and extends the plugin system of the open source modeling and simulation framework James II. We show the benefits of our approach by applying it to steady state estimation for cell-biological models. PMID:24705453
GASPACHO: a generic automatic solver using proximal algorithms for convex huge optimization problems
Goossens, Bart; Luong, Hiêp; Philips, Wilfried
2017-08-01
Many inverse problems (e.g., demosaicking, deblurring, denoising, image fusion, HDR synthesis) share various similarities: degradation operators are often modeled by a specific data fitting function while image prior knowledge (e.g., sparsity) is incorporated by additional regularization terms. In this paper, we investigate automatic algorithmic techniques for evaluating proximal operators. These algorithmic techniques also enable efficient calculation of adjoints from linear operators in a general matrix-free setting. In particular, we study the simultaneous-direction method of multipliers (SDMM) and the parallel proximal algorithm (PPXA) solvers and show that the automatically derived implementations are well suited for both single-GPU and multi-GPU processing. We demonstrate this approach for an Electron Microscopy (EM) deconvolution problem.
A fast direct solver for boundary value problems on locally perturbed geometries
Zhang, Yabin; Gillman, Adrianna
2018-03-01
Many applications including optimal design and adaptive discretization techniques involve solving several boundary value problems on geometries that are local perturbations of an original geometry. This manuscript presents a fast direct solver for boundary value problems that are recast as boundary integral equations. The idea is to write the discretized boundary integral equation on a new geometry as a low rank update to the discretized problem on the original geometry. Using the Sherman-Morrison formula, the inverse can be expressed in terms of the inverse of the original system applied to the low rank factors and the right hand side. Numerical results illustrate for problems where perturbation is localized the fast direct solver is three times faster than building a new solver from scratch.
Fast immersed interface Poisson solver for 3D unbounded problems around arbitrary geometries
Gillis, T.; Winckelmans, G.; Chatelain, P.
2018-02-01
We present a fast and efficient Fourier-based solver for the Poisson problem around an arbitrary geometry in an unbounded 3D domain. This solver merges two rewarding approaches, the lattice Green's function method and the immersed interface method, using the Sherman-Morrison-Woodbury decomposition formula. The method is intended to be second order up to the boundary. This is verified on two potential flow benchmarks. We also further analyse the iterative process and the convergence behavior of the proposed algorithm. The method is applicable to a wide range of problems involving a Poisson equation around inner bodies, which goes well beyond the present validation on potential flows.
Applying EXCEL Solver to a watershed management goal-programming problem
J. E. de Steiguer
2000-01-01
This article demonstrates the application of EXCELÂ® spreadsheet linear programming (LP) solver to a watershed management multiple use goal programming (GP) problem. The data used to demonstrate the application are from a published study for a watershed in northern Colorado. GP has been used by natural resource managers for many years. However, the GP solution by means...
Critical Thinking and the Development of Innovative Problem Solvers
National Research Council Canada - National Science Library
Drew, Christopher T
2005-01-01
.... This capability can be trained by making Critical Thinking the focus of officer education. Critical Thinking is the general cognitive skill of developing the best solution when there is not a single correct answer...
A multilevel in space and energy solver for multigroup diffusion eigenvalue problems
Directory of Open Access Journals (Sweden)
Ben C. Yee
2017-09-01
Full Text Available In this paper, we present a new multilevel in space and energy diffusion (MSED method for solving multigroup diffusion eigenvalue problems. The MSED method can be described as a PI scheme with three additional features: (1 a grey (one-group diffusion equation used to efficiently converge the fission source and eigenvalue, (2 a space-dependent Wielandt shift technique used to reduce the number of PIs required, and (3 a multigrid-in-space linear solver for the linear solves required by each PI step. In MSED, the convergence of the solution of the multigroup diffusion eigenvalue problem is accelerated by performing work on lower-order equations with only one group and/or coarser spatial grids. Results from several Fourier analyses and a one-dimensional test code are provided to verify the efficiency of the MSED method and to justify the incorporation of the grey diffusion equation and the multigrid linear solver. These results highlight the potential efficiency of the MSED method as a solver for multidimensional multigroup diffusion eigenvalue problems, and they serve as a proof of principle for future work. Our ultimate goal is to implement the MSED method as an efficient solver for the two-dimensional/three-dimensional coarse mesh finite difference diffusion system in the Michigan parallel characteristics transport code. The work in this paper represents a necessary step towards that goal.
Implicit solvers for large-scale nonlinear problems
International Nuclear Information System (INIS)
Keyes, D E; Reynolds, D; Woodward, C S
2006-01-01
Computational scientists are grappling with increasingly complex, multi-rate applications that couple such physical phenomena as fluid dynamics, electromagnetics, radiation transport, chemical and nuclear reactions, and wave and material propagation in inhomogeneous media. Parallel computers with large storage capacities are paving the way for high-resolution simulations of coupled problems; however, hardware improvements alone will not prove enough to enable simulations based on brute-force algorithmic approaches. To accurately capture nonlinear couplings between dynamically relevant phenomena, often while stepping over rapid adjustments to quasi-equilibria, simulation scientists are increasingly turning to implicit formulations that require a discrete nonlinear system to be solved for each time step or steady state solution. Recent advances in iterative methods have made fully implicit formulations a viable option for solution of these large-scale problems. In this paper, we overview one of the most effective iterative methods, Newton-Krylov, for nonlinear systems and point to software packages with its implementation. We illustrate the method with an example from magnetically confined plasma fusion and briefly survey other areas in which implicit methods have bestowed important advantages, such as allowing high-order temporal integration and providing a pathway to sensitivity analyses and optimization. Lastly, we overview algorithm extensions under development motivated by current SciDAC applications
A TFETI domain decomposition solver for elastoplastic problems
Czech Academy of Sciences Publication Activity Database
Čermák, M.; Kozubek, T.; Sysala, Stanislav; Valdman, J.
2014-01-01
Roč. 231, č. 1 (2014), s. 634-653 ISSN 0096-3003 Institutional support: RVO:68145535 Keywords : elastoplasticity * Total FETI domain decomposition method * Finite element method * Semismooth Newton method Subject RIV: BA - General Mathematics Impact factor: 1.551, year: 2014 http://ac.els-cdn.com/S0096300314000253/1-s2.0-S0096300314000253-main.pdf?_tid=33a29cf4-996a-11e3-8c5a-00000aacb360&acdnat=1392816896_4584697dc26cf934dcf590c63f0dbab7
Applications of an implicit HLLC-based Godunov solver for steady state hypersonic problems
International Nuclear Information System (INIS)
Link, R.A.; Sharman, B.
2005-01-01
Over the past few years, there has been considerable activity developing research vehicles for studying hypersonic propulsion. Successful launches of the Australian Hyshot and the US Hyper-X vehicles have added a significant amount of flight test data to a field that had previously been limited to numerical simulation. A number of approaches have been proposed for hypersonics propulsion, including attached detonation wave, supersonics combustion, and shock induced combustion. Due to the high cost of developing flight hardware, CFD simulations will continue to be a key tool for investigating the feasibility of these concepts. Capturing the interactions of the vehicle body with the boundary layer and chemical reactions pushes the limits of available modelling tools and computer hardware. Explicit formulations are extremely slow in converging to a steady state; therefore, the use of implicit methods are warranted. An implicit LLC-based Godunov solver has been developed at Martec in collaboration with DRDC Valcartier to solve hypersonic problems with a minimum of CPU time and RAM storage. The solver, Chinook Implicit, is based upon the implicit formulation adopted by Batten et. al. The solver is based on a point implicit Gauss-Seidel method for unstructured grids, and includes fully implicit boundary conditions. Preliminary results for small and large scale inviscid hypersonics problems will be presented. (author)
Liu, Yang
2013-07-01
The computational complexity and memory requirements of multilevel plane wave time domain (PWTD)-accelerated marching-on-in-time (MOT)-based surface integral equation (SIE) solvers scale as O(NtNs(log 2)Ns) and O(Ns 1.5); here N t and Ns denote numbers of temporal and spatial basis functions discretizing the current [Shanker et al., IEEE Trans. Antennas Propag., 51, 628-641, 2003]. In the past, serial versions of these solvers have been successfully applied to the analysis of scattering from perfect electrically conducting as well as homogeneous penetrable targets involving up to Ns ≈ 0.5 × 106 and Nt ≈ 10 3. To solve larger problems, parallel PWTD-enhanced MOT solvers are called for. Even though a simple parallelization strategy was demonstrated in the context of electromagnetic compatibility analysis [M. Lu et al., in Proc. IEEE Int. Symp. AP-S, 4, 4212-4215, 2004], by and large, progress in this area has been slow. The lack of progress can be attributed wholesale to difficulties associated with the construction of a scalable PWTD kernel. © 2013 IEEE.
Cartesian Mesh Linearized Euler Equations Solver for Aeroacoustic Problems around Full Aircraft
Directory of Open Access Journals (Sweden)
Yuma Fukushima
2015-01-01
Full Text Available The linearized Euler equations (LEEs solver for aeroacoustic problems has been developed on block-structured Cartesian mesh to address complex geometry. Taking advantage of the benefits of Cartesian mesh, we employ high-order schemes for spatial derivatives and for time integration. On the other hand, the difficulty of accommodating curved wall boundaries is addressed by the immersed boundary method. The resulting LEEs solver is robust to complex geometry and numerically efficient in a parallel environment. The accuracy and effectiveness of the present solver are validated by one-dimensional and three-dimensional test cases. Acoustic scattering around a sphere and noise propagation from the JT15D nacelle are computed. The results show good agreement with analytical, computational, and experimental results. Finally, noise propagation around fuselage-wing-nacelle configurations is computed as a practical example. The results show that the sound pressure level below the over-the-wing nacelle (OWN configuration is much lower than that of the conventional DLR-F6 aircraft configuration due to the shielding effect of the OWN configuration.
Gurr, Henry
2014-03-01
Princeton Physicist J. J. Hopfield's Mathematical Model of the Mammalian Brain, (Similar To Ising Glass Model of a crystal of magnetic spin particles) says our Brain-Work for Memory, Perception, Language, Thinking, etc, (Even the AHA-EUREKA-Flash Of Insight Type Problem Solving), is achieved by our massively inter-connected CNS Neurons ... working together ... MINIMIZING an analog of physical energy ... thus yielding Optimal Solutions: These ``best'' answers, correspond to highest mental coherence, for most facets organism response, beit mental (eg: perception, memory, ideas, thinking, etc) or physical-muscular-actions (eg speaking, tool using, trail following, etc). Our brain is this way, because living creature, MUST be evolved, so they will find & use the best actions, for survival!!! Our human heritage, is to instantly compute near optimal future plans, (mental & physical-muscular), and be able to accomplish plans reliably & efficiently. If you know of book or articles in these topic areas, please email to HenryG--USCA.edu How to work well, with your own ``self'', called mind-body, will follow!! Conjectures: Who is the ``I'' that appears to make decisions? Am ``I'' the master of my domain? Is there an ``I'' or am ``I'' merely an illusion of reality.
Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities
Paszyńska, Anna
2015-06-01
This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver.
Continuous Genetic Algorithm as a Novel Solver for Stokes and Nonlinear Navier Stokes Problems
Directory of Open Access Journals (Sweden)
Z. S. Abo-Hammour
2014-01-01
Full Text Available The one-dimensional continuous genetic algorithm (CGA previously developed by the principal author is extended and enhanced to deal with two-dimensional spaces in this paper. The enhanced CGA converts the partial differential equations into algebraic equations by replacing the derivatives appearing in the differential equation with their proper finite difference formula in 2D spaces. This optimization methodology is then applied for the solution of steady-state two-dimensional Stokes and nonlinear Navier Stokes problems. The main advantage of using CGA for the solution of partial differential equations is that the algorithm can be applied to linear and nonlinear equations without any modification in its structure. A comparison between the results obtained using the 2D CGA and the known Galerkin finite element method using COMSOL is presented in this paper. The results showed that CGA has an excellent accuracy as compared to other numerical solvers.
High-resolution coupled physics solvers for analysing fine-scale nuclear reactor design problems
Mahadevan, Vijay S.; Merzari, Elia; Tautges, Timothy; Jain, Rajeev; Obabko, Aleksandr; Smith, Michael; Fischer, Paul
2014-01-01
An integrated multi-physics simulation capability for the design and analysis of current and future nuclear reactor models is being investigated, to tightly couple neutron transport and thermal-hydraulics physics under the SHARP framework. Over several years, high-fidelity, validated mono-physics solvers with proven scalability on petascale architectures have been developed independently. Based on a unified component-based architecture, these existing codes can be coupled with a mesh-data backplane and a flexible coupling-strategy-based driver suite to produce a viable tool for analysts. The goal of the SHARP framework is to perform fully resolved coupled physics analysis of a reactor on heterogeneous geometry, in order to reduce the overall numerical uncertainty while leveraging available computational resources. The coupling methodology and software interfaces of the framework are presented, along with verification studies on two representative fast sodium-cooled reactor demonstration problems to prove the usability of the SHARP framework. PMID:24982250
Collier, Nathan
2014-09-17
SUMMARY: We compare the computational efficiency of isogeometric Galerkin and collocation methods for partial differential equations in the asymptotic regime. We define a metric to identify when numerical experiments have reached this regime. We then apply these ideas to analyze the performance of different isogeometric discretizations, which encompass C0 finite element spaces and higher-continuous spaces. We derive convergence and cost estimates in terms of the total number of degrees of freedom and then perform an asymptotic numerical comparison of the efficiency of these methods applied to an elliptic problem. These estimates are derived assuming that the underlying solution is smooth, the full Gauss quadrature is used in each non-zero knot span and the numerical solution of the discrete system is found using a direct multi-frontal solver. We conclude that under the assumptions detailed in this paper, higher-continuous basis functions provide marginal benefits.
dftatom: A robust and general Schrödinger and Dirac solver for atomic structure calculations
Čertík, Ondřej; Pask, John E.; Vackář, Jiří
2013-07-01
A robust and general solver for the radial Schrödinger, Dirac, and Kohn-Sham equations is presented. The formulation admits general potentials and meshes: uniform, exponential, or other defined by nodal distribution and derivative functions. For a given mesh type, convergence can be controlled systematically by increasing the number of grid points. Radial integrations are carried out using a combination of asymptotic forms, Runge-Kutta, and implicit Adams methods. Eigenfunctions are determined by a combination of bisection and perturbation methods for robustness and speed. An outward Poisson integration is employed to increase accuracy in the core region, allowing absolute accuracies of 10-8 Hartree to be attained for total energies of heavy atoms such as uranium. Detailed convergence studies are presented and computational parameters are provided to achieve accuracies commonly required in practice. Comparisons to analytic and current-benchmark density-functional results for atomic number Z=1-92 are presented, verifying and providing a refinement to current benchmarks. An efficient, modular Fortran 95 implementation, dftatom, is provided as open source, including examples, tests, and wrappers for interface to other languages; wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines. Program summaryProgram title:dftatom Catalogue identifier: AEPA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPA_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: MIT license No. of lines in distributed program, including test data, etc.: 14122 No. of bytes in distributed program, including test data, etc.: 157453 Distribution format: tar.gz Programming language: Fortran 95 with interfaces to Python and C. Computer: Any computer with a Fortran 95 compiler. Operating system: Any OS with a Fortran 95 compiler. RAM: 500 MB
Harvey, Jason; Moore, Michael
2013-01-01
The General-Use Nodal Network Solver (GUNNS) is a modeling software package that combines nodal analysis and the hydraulic-electric analogy to simulate fluid, electrical, and thermal flow systems. GUNNS is developed by L-3 Communications under the TS21 (Training Systems for the 21st Century) project for NASA Johnson Space Center (JSC), primarily for use in space vehicle training simulators at JSC. It has sufficient compactness and fidelity to model the fluid, electrical, and thermal aspects of space vehicles in real-time simulations running on commodity workstations, for vehicle crew and flight controller training. It has a reusable and flexible component and system design, and a Graphical User Interface (GUI), providing capability for rapid GUI-based simulator development, ease of maintenance, and associated cost savings. GUNNS is optimized for NASA's Trick simulation environment, but can be run independently of Trick.
Debreu, Laurent; Neveu, Emilie; Simon, Ehouarn; Le Dimet, Francois Xavier; Vidard, Arthur
2014-05-01
In order to lower the computational cost of the variational data assimilation process, we investigate the use of multigrid methods to solve the associated optimal control system. On a linear advection equation, we study the impact of the regularization term on the optimal control and the impact of discretization errors on the efficiency of the coarse grid correction step. We show that even if the optimal control problem leads to the solution of an elliptic system, numerical errors introduced by the discretization can alter the success of the multigrid methods. The view of the multigrid iteration as a preconditioner for a Krylov optimization method leads to a more robust algorithm. A scale dependent weighting of the multigrid preconditioner and the usual background error covariance matrix based preconditioner is proposed and brings significant improvements. [1] Laurent Debreu, Emilie Neveu, Ehouarn Simon, François-Xavier Le Dimet and Arthur Vidard, 2014: Multigrid solvers and multigrid preconditioners for the solution of variational data assimilation problems, submitted to QJRMS, http://hal.inria.fr/hal-00874643 [2] Emilie Neveu, Laurent Debreu and François-Xavier Le Dimet, 2011: Multigrid methods and data assimilation - Convergence study and first experiments on non-linear equations, ARIMA, 14, 63-80, http://intranet.inria.fr/international/arima/014/014005.html
Energy Technology Data Exchange (ETDEWEB)
Schunert, Sebastian; Wang, Congjian; Wang, Yaqi; Kong, Fande; Ortensi, Javier; Baker, Benjamin; Gleicher, Frederick; DeHart, Mark; Martineau, Richard
2017-04-01
Rattlesnake and MAMMOTH are the designated TREAT analysis tools currently being developed at the Idaho National Laboratory. Concurrent with development of the multi-physics, multi-scale capabilities, sensitivity analysis and uncertainty quantification (SA/UQ) capabilities are required for predicitive modeling of the TREAT reactor. For steady-state SA/UQ, that is essential for setting initial conditions for the transients, generalized perturbation theory (GPT) will be used. This work describes the implementation of a PETSc based solver for the generalized adjoint equations that constitute a inhomogeneous, rank deficient problem. The standard approach is to use an outer iteration strategy with repeated removal of the fundamental mode contamination. The described GPT algorithm directly solves the GPT equations without the need of an outer iteration procedure by using Krylov subspaces that are orthogonal to the operator’s nullspace. Three test problems are solved and provide sufficient verification for the Rattlesnake’s GPT capability. We conclude with a preliminary example evaluating the impact of the Boron distribution in the TREAT reactor using perturbation theory.
Balsara, Dinshaw S.; Nkonga, Boniface
2017-10-01
Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional Riemann solver is also similarly improved. Such multidimensional Riemann problems arise when multiple states come together at the vertex of a mesh. The interaction of the resulting one-dimensional Riemann problems gives rise to a strongly-interacting state. We wish to endow this strongly-interacting state with physically-motivated sub-structure. The fastest way of endowing such sub-structure consists of making a multidimensional extension of the HLLI Riemann solver for hyperbolic conservation laws. Presenting such a multidimensional analogue of the HLLI Riemann solver with linear sub-structure for use on structured meshes is the goal of this work. The multidimensional MuSIC Riemann solver documented here is universal in the sense that it can be applied to any hyperbolic conservation law. The multidimensional Riemann solver is made to be consistent with constraints that emerge naturally from the Galerkin projection of the self-similar states within the wave model. When the full eigenstructure in both directions is used in the present Riemann solver, it becomes a complete Riemann solver in a multidimensional sense. I.e., all the intermediate waves are represented in the multidimensional wave model. The work also presents, for the very first time, an important analysis of the dissipation characteristics of multidimensional Riemann solvers. The present Riemann solver results in the most efficient implementation of a multidimensional Riemann solver with sub-structure. Because it preserves stationary linearly degenerate waves, it might also help with well-balancing. Implementation-related details are presented in pointwise fashion for the one-dimensional HLLI Riemann solver as well as the multidimensional MuSIC Riemann solver.
Problem Solvers: Problem--Light It up! and Solutions--Flags by the Numbers
Hall, Shaun
2009-01-01
A simple circuit is created by the continuous flow of electricity through conductors (copper wires) from a source of electrical energy (batteries). "Completing a circuit" means that electricity flows from the energy source through the circuit and, in the case described in this month's problem, causes the light bulb tolight up. The presence of…
DEFF Research Database (Denmark)
Helsgaun, Keld
This report describes the implementation of an extension of the Lin-Kernighan-Helsgaun TSP solver for solving constrained traveling salesman and vehicle routing problems. The extension, which is called LKH-3, is able to solve a variety of well-known problems, including the sequential ordering...... problem (SOP), the traveling repairman problem (TRP), variants of the multiple travel-ing salesman problem (mTSP), as well as vehicle routing problems (VRPs) with capacity, time windows, pickup-and-delivery and distance constraints. The implementation of LKH-3 builds on the idea of transforming...... the problems into standard symmetric traveling salesman problems and handling constraints by means of penalty functions. Extensive testing on benchmark instances from the literature has shown that LKH-3 is effective. Best known solutions are often obtained, and in some cases, new best solutions are found...
DEFF Research Database (Denmark)
Andersen, Michael; Abel, Sarah Maria Niebe; Erleben, Kenny
2017-01-01
-vector products as computational building blocks. We block the matrix-vector products in a way that allows us to evaluate the products, without having to assemble the full systems. Any iterative sub-solver can be used. Our work shows speedup factors ranging up to 500 for larger grid sizes....
Benchmarking optimization solvers for structural topology optimization
DEFF Research Database (Denmark)
Rojas Labanda, Susana; Stolpe, Mathias
2015-01-01
sizes is developed for this benchmarking. The problems are based on a material interpolation scheme combined with a density filter. Different optimization solvers including Optimality Criteria (OC), the Method of Moving Asymptotes (MMA) and its globally convergent version GCMMA, the interior point...... solvers in IPOPT and FMINCON, and the sequential quadratic programming method in SNOPT, are benchmarked on the library using performance profiles. Whenever possible the methods are applied to both the nested and the Simultaneous Analysis and Design (SAND) formulations of the problem. The performance...... profiles conclude that general solvers are as efficient and reliable as classical structural topology optimization solvers. Moreover, the use of the exact Hessians in SAND formulations, generally produce designs with better objective function values. However, with the benchmarked implementations solving...
Zhao, Xujun; Li, Jiyuan; Jiang, Xikai; Karpeev, Dmitry; Heinonen, Olle; Smith, Barry; Hernandez-Ortiz, Juan P.; de Pablo, Juan J.
2017-06-01
An efficient parallel Stokes' solver has been developed for complete description of hydrodynamic interactions between Brownian particles in bulk and confined geometries. A Langevin description of the particle dynamics is adopted, where the long-range interactions are included using a Green's function formalism. A scalable parallel computational approach is presented, where the general geometry Stokeslet is calculated following a matrix-free algorithm using the general geometry Ewald-like method. Our approach employs a highly efficient iterative finite-element Stokes' solver for the accurate treatment of long-range hydrodynamic interactions in arbitrary confined geometries. A combination of mid-point time integration of the Brownian stochastic differential equation, the parallel Stokes' solver, and a Chebyshev polynomial approximation for the fluctuation-dissipation theorem leads to an O(N) parallel algorithm. We illustrate the new algorithm in the context of the dynamics of confined polymer solutions under equilibrium and non-equilibrium conditions. The method is then extended to treat suspended finite size particles of arbitrary shape in any geometry using an immersed boundary approach.
An Exact, Compressible One-Dimensional Riemann Solver for General, Convex Equations of State
Energy Technology Data Exchange (ETDEWEB)
Kamm, James Russell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-03-05
This note describes an algorithm with which to compute numerical solutions to the one- dimensional, Cartesian Riemann problem for compressible flow with general, convex equations of state. While high-level descriptions of this approach are to be found in the literature, this note contains most of the necessary details required to write software for this problem. This explanation corresponds to the approach used in the source code that evaluates solutions for the 1D, Cartesian Riemann problem with a JWL equation of state in the ExactPack package [16, 29]. Numerical examples are given with the proposed computational approach for a polytropic equation of state and for the JWL equation of state.
An evaluation of parallel multigrid as a solver and a preconditioner for singular perturbed problems
Energy Technology Data Exchange (ETDEWEB)
Oosterlee, C.W. [Inst. for Algorithms and Scientific Computing, Sankt Augustin (Germany); Washio, T. [C& C Research Lab., Sankt Augustin (Germany)
1996-12-31
In this paper we try to achieve h-independent convergence with preconditioned GMRES and BiCGSTAB for 2D singular perturbed equations. Three recently developed multigrid methods are adopted as a preconditioner. They are also used as solution methods in order to compare the performance of the methods as solvers and as preconditioners. Two of the multigrid methods differ only in the transfer operators. One uses standard matrix- dependent prolongation operators from. The second uses {open_quotes}upwind{close_quotes} prolongation operators, developed. Both employ the Galerkin coarse grid approximation and an alternating zebra line Gauss-Seidel smoother. The third method is based on the block LU decomposition of a matrix and on an approximate Schur complement. This multigrid variant is presented in. All three multigrid algorithms are algebraic methods.
Realization of the chess mate solver application
Vučković Vladan V.
2004-01-01
This paper presents details of the chess mate solver application, which is a part of the author’s Geniss general chess application. The problem chess is an important domain connected with solving of the chess problems. The Geniss Mate Solver (G.M.S.) application solves Mate-in-N-move problems. Main techniques used for the implementation of the application are full-width searching with Alpha-Beta pruning technique and zero evaluation function. The application is written in Delphi for Windows p...
Burtyka, Filipp
2018-03-01
The paper firstly considers the problem of finding solvents for arbitrary unilateral polynomial matrix equations with second-order matrices over prime finite fields from the practical point of view: we implement the solver for this problem. The solver’s algorithm has two step: the first is finding solvents, having Jordan Normal Form (JNF), the second is finding solvents among the rest matrices. The first step reduces to the finding roots of usual polynomials over finite fields, the second is essentially exhaustive search. The first step’s algorithms essentially use the polynomial matrices theory. We estimate the practical duration of computations using our software implementation (for example that one can’t construct unilateral matrix polynomial over finite field, having any predefined number of solvents) and answer some theoretically-valued questions.
On a construction of fast direct solvers
Czech Academy of Sciences Publication Activity Database
Práger, Milan
2003-01-01
Roč. 48, č. 3 (2003), s. 225-236 ISSN 0862-7940 Institutional research plan: CEZ:AV0Z1019905; CEZ:AV0Z1019905 Keywords : Poisson equation * boundary value problem * fast direct solver Subject RIV: BA - General Mathematics
Constraint-based solver for the Military unit path finding problem
CSIR Research Space (South Africa)
Leenen, L
2010-04-01
Full Text Available -based approach because it requires flexibility in modelling. The authors formulate the MUPFP as a constraint satisfaction problem and a constraint-based extension of the search algorithm. The concept demonstrator uses a provided map, for example taken from Google...
Debreu, Laurent; Neveu, Emilie; Simon, Ehouarn; Le Dimet, François-Xavier; Vidard, Arthur
2013-01-01
In order to lower the computational cost of the variational data assimilation process, we investigate the use of multigrid methods to solve the associated optimal control system. On a linear advection equation, we study the impact of the regularization term of the optimal control and the impact of discretization errors on the efficiency of the coarse grid correction step. We show that even if the optimal control problem leads to the solution of an elliptic system, numerical errors introduced ...
International Nuclear Information System (INIS)
Li Jiequan; Li Qibing; Xu Kun
2011-01-01
The generalized Riemann problem (GRP) scheme for the Euler equations and gas-kinetic scheme (GKS) for the Boltzmann equation are two high resolution shock capturing schemes for fluid simulations. The difference is that one is based on the characteristics of the inviscid Euler equations and their wave interactions, and the other is based on the particle transport and collisions. The similarity between them is that both methods can use identical MUSCL-type initial reconstructions around a cell interface, and the spatial slopes on both sides of a cell interface involve in the gas evolution process and the construction of a time-dependent flux function. Although both methods have been applied successfully to the inviscid compressible flow computations, their performances have never been compared. Since both methods use the same initial reconstruction, any difference is solely coming from different underlying mechanism in their flux evaluation. Therefore, such a comparison is important to help us to understand the correspondence between physical modeling and numerical performances. Since GRP is so faithfully solving the inviscid Euler equations, the comparison can be also used to show the validity of solving the Euler equations itself. The numerical comparison shows that the GRP exhibits a slightly better computational efficiency, and has comparable accuracy with GKS for the Euler solutions in 1D case, but the GKS is more robust than GRP. For the 2D high Mach number flow simulations, the GKS is absent from the shock instability and converges to the steady state solutions faster than the GRP. The GRP has carbuncle phenomena, likes a cloud hanging over exact Riemann solvers. The GRP and GKS use different physical processes to describe the flow motion starting from a discontinuity. One is based on the assumption of equilibrium state with infinite number of particle collisions, and the other starts from the non-equilibrium free transport process to evolve into an
Network Method Critical Path as a Search Problem Solvers Critical Path
Fachrudin Fachrudin
2005-01-01
Activity is a lot of work takes time, energy and capital. Many companies do a lot of unplanned activities with a working method so that his workers are not finished just because time. This is much work other jobs to do and finished at the same time while a job with another job different in kind. Of the things mentioned above then the writing will be presented a solution that can solve problems with a method, the method known as Network or Network Method, The Critical Path Method as a search p...
CIP - a new numerical solver for general nonlinear hyperbolic equations in multi-dimension
International Nuclear Information System (INIS)
Yabe, Takashi; Takewaki, Hideaki.
1986-12-01
A new method CIP (Cubic-Interpolated Pseudo-particle) to solve hyperbolic equations is proposed. The method gives a stable and less diffusive result for square wave propagation compared with FCT (Flux-Corrected Transport) and a better result for propagation of a sine wave with a discontinuity. The scheme is extended to nonlinear and multi-dimensional problems. (orig.) [de
Numerical and computational efficiency of solvers for two-phase problems
Czech Academy of Sciences Publication Activity Database
Axelsson, Owe; Boyanova, P.; Kronbichler, M.; Neytcheva, M.; Wu, X.
2013-01-01
Roč. 65, č. 3 (2013), s. 301-314 ISSN 0898-1221 Institutional support: RVO:68145535 Keywords : Cahn–Hilliard equation * preconditioning * Inexact Newton method * Quasi-Newton method * parallel tests Subject RIV: BA - General Mathematics Impact factor: 1.996, year: 2013 http://ac.els-cdn.com/S0898122112004191/1-s2.0-S0898122112004191-main.pdf?_tid=e77dd742-63a2-11e2-9070-00000aab0f02&acdnat=1358756389_e11eaef264d0bac8123c4a00be3f6efa
On generalized operator quasi-equilibrium problems
Kum, Sangho; Kim, Won Kyu
2008-09-01
In this paper, we will introduce the generalized operator equilibrium problem and generalized operator quasi-equilibrium problem which generalize the operator equilibrium problem due to Kazmi and Raouf [K.R. Kazmi, A. Raouf, A class of operator equilibrium problems, J. Math. Anal. Appl. 308 (2005) 554-564] into multi-valued and quasi-equilibrium problems. Using a Fan-Browder type fixed point theorem in [S. Park, Foundations of the KKM theory via coincidences of composites of upper semicontinuous maps, J. Korean Math. Soc. 31 (1994) 493-519] and an existence theorem of equilibrium for 1-person game in [X.-P. Ding, W.K. Kim, K.-K. Tan, Equilibria of non-compact generalized games with L*-majorized preferences, J. Math. Anal. Appl. 164 (1992) 508-517] as basic tools, we prove new existence theorems on generalized operator equilibrium problem and generalized operator quasi-equilibrium problem which includes operator equilibrium problems.
Generalizations of the Brachistochrone Problem
Gemmer, J.; Umble, R.; Nolan, M.
2006-01-01
Consider a frictionless surface S in a gravitational field that need not be uniform. Given two points A and B on S, what curve is traced out by a particle that starts at A and reaches B in the shortest time? This paper considers this problem on simple surfaces such as surfaces of revolution and solves the problem two ways: First, we use conservation of mechanical energy and the Euler-Lagange equation; second, we use geometrical optics and the eikonal equation. We conclude with a discussion of...
Realization of the chess mate solver application
Directory of Open Access Journals (Sweden)
Vučković Vladan V.
2004-01-01
Full Text Available This paper presents details of the chess mate solver application, which is a part of the author’s Geniss general chess application. The problem chess is an important domain connected with solving of the chess problems. The Geniss Mate Solver (G.M.S. application solves Mate-in-N-move problems. Main techniques used for the implementation of the application are full-width searching with Alpha-Beta pruning technique and zero evaluation function. The application is written in Delphi for Windows programming environment and the searching engine is completely coded in assembly language (about 10000 lines. This hybrid software structure enables efficient program development by using high-level programming environment and the realization of a very fast searching engine at the same time. The machine code is manually coded and could achieve above 7 million generated positions per second on the 1Ghz Celeron PC.
Dimensional reduction of a generalized flux problem
International Nuclear Information System (INIS)
Moroz, A.
1992-01-01
In this paper, a generalized flux problem with Abelian and non-Abelian fluxes is considered. In the Abelian case we shall show that the generalized flux problem for tight-binding models of noninteracting electrons on either 2n- or (2n + 1)-dimensional lattice can always be reduced to an n-dimensional hopping problem. A residual freedom in this reduction enables one to identify equivalence classes of hopping Hamiltonians which have the same spectrum. In the non-Abelian case, the reduction is not possible in general unless the flux tensor factorizes into an Abelian one times are element of the corresponding algebra
A survey of deterministic solvers for rarefied flows (Invited)
Mieussens, Luc
2014-12-01
Numerical simulations of rarefied gas flows are generally made with DSMC methods. Up to a recent period, deterministic numerical methods based on a discretization of the Boltzmann equation were restricted to simple problems (1D, linearized flows, or simple geometries, for instance). In the last decade, several deterministic solvers have been developed in different teams to tackle more complex problems like 2D and 3D flows. Some of them are based on the full Boltzmann equation. Solving this equation numerically is still very challenging, and 3D solvers are still restricted to monoatomic gases, even if recent works have proved it was possible to simulate simple flows for polyatomic gases. Other solvers are based on simpler BGK like models: they allow for much more intensive simulations on 3D flows for realistic geometries, but treating complex gases requires extended BGK models that are still under development. In this paper, we discuss the main features of these existing solvers, and we focus on their strengths and inefficiencies. We will also review some recent results that show how these solvers can be improved: - higher accuracy (higher order finite volume methods, discontinuous Galerkin approaches) - lower memory and CPU costs with special velocity discretization (adaptive grids, spectral methods) - multi-scale simulations by using hybrid and asymptotic preserving schemes - efficient implementation on high performance computers (parallel computing, hybrid parallelization) Finally, we propose some perspectives to make these solvers more efficient and more popular.
The generalized minimum spanning tree problem
Pop, P.C.; Kern, Walter; Still, Georg J.
2000-01-01
We consider the Generalized Minimum Spanning Tree Problem denoted by GMSTP. It is known that GMSTP is NP-hard and even finding a near optimal solution is NP-hard. We introduce a new mixed integer programming formulation of the problem which contains a polynomial number of constraints and a
Generalized network improvement and packing problems
Holzhauser, Michael
2016-01-01
Michael Holzhauser discusses generalizations of well-known network flow and packing problems by additional or modified side constraints. By exploiting the inherent connection between the two problem classes, the author investigates the complexity and approximability of several novel network flow and packing problems and presents combinatorial solution and approximation algorithms. Contents Fractional Packing and Parametric Search Frameworks Budget-Constrained Minimum Cost Flows: The Continuous Case Budget-Constrained Minimum Cost Flows: The Discrete Case Generalized Processing Networks Convex Generalized Flows Target Groups Researchers and students in the fields of mathematics, computer science, and economics Practitioners in operations research and logistics The Author Dr. Michael Holzhauser studied computer science at the University of Kaiserslautern and is now a research fellow in the Optimization Research Group at the Department of Mathematics of the University of Kaiserslautern.
Generalized production planning problem under interval uncertainty
Directory of Open Access Journals (Sweden)
Samir A. Abass
2010-06-01
Full Text Available Data in many real life engineering and economical problems suffer from inexactness. Herein we assume that we are given some intervals in which the data can simultaneously and independently perturb. We consider the generalized production planning problem with interval data. The interval data are in both of the objective function and constraints. The existing results concerning the qualitative and quantitative analysis of basic notions in parametric production planning problem. These notions are the set of feasible parameters, the solvability set and the stability set of the first kind.
Initial Value Problem in General Relativity
Isenberg, James
2013-01-01
This article, written to appear as a chapter in "The Springer Handbook of Spacetime", is a review of the initial value problem for Einstein's gravitational field theory in general relativity. Designed to be accessible to graduate students who have taken a first course in general relativity, the article first discusses how to reformulate the spacetime fields and spacetime covariant field equations of Einstein's theory in terms of fields and field equations compatible with a 3+1 foliation of sp...
Generalized Darcy–Oseen resolvent problem
Czech Academy of Sciences Publication Activity Database
Medková, Dagmar; Ptashnyk, M.; Varnhorn, W.
2016-01-01
Roč. 39, č. 6 (2016), s. 1621-1630 ISSN 0170-4214 Institutional support: RVO:67985840 Keywords : Darcy -Oseen resolvent problem * semipermeable membrane * Brinkman- Darcy equations * fluid flow between free-fluid domains and porous media Subject RIV: BA - General Mathematics Impact factor: 1.017, year: 2016 http://onlinelibrary.wiley.com/doi/10.1002/mma.3872/abstract
Generalized Benders’ Decomposition for topology optimization problems
DEFF Research Database (Denmark)
Munoz Queupumil, Eduardo Javier; Stolpe, Mathias
2011-01-01
) problems with discrete design variables to global optimality. We present the theoretical aspects of the method, including a proof of finite convergence and conditions for obtaining global optimal solutions. The method is also linked to, and compared with, an Outer-Approximation approach and a mixed 0......–1 semi definite programming formulation of the considered problem. Several ways to accelerate the method are suggested and an implementation is described. Finally, a set of truss topology optimization problems are numerically solved to global optimality.......This article considers the non-linear mixed 0–1 optimization problems that appear in topology optimization of load carrying structures. The main objective is to present a Generalized Benders’ Decomposition (GBD) method for solving single and multiple load minimum compliance (maximum stiffness...
Prevalence of alcohol problems in general practice
DEFF Research Database (Denmark)
Rambaldi, A; Todisco, N; Gluud, C
1996-01-01
The Michigan Alcoholism Screening Test (MAST) and the response to a question about heavy alcohol consumption were used to assess the prevalence of alcohol problems in consecutive patients (77 males and 46 females) consulting a general practitioner in an urban area in the South of Italy...... (Castellammare di Stabia). Alcohol problems, which were defined by a cut-off score of 5 on the MAST and/or by heavy alcohol consumption (corresponding to at least 60 g of ethanol daily for males and 36 g of ethanol daily for females for at least 2 years), were identified in 54 patients [43.9%; 95% confidence...... heavy alcohol consumption had a predictive negative value of 97.2% (95% CI 90.2-99.7%) and a predictive positive value of 73.1% (95% CI 59.0-84.4%) in relation to MAST positive patients. It is suggested that general practitioners should incorporate this question about heavy alcohol consumption...
Gambling Problems in the General Danish Population
DEFF Research Database (Denmark)
Harrison, Glenn W.; Jessen, Lasse J.; Lau, Morten
and estimate prevalence of gambling problems using sample weights and controlling for sample selection. We find that 95.4% of the population has no detectable risk, 2.9% has an early risk, 0.8% has an intermediate risk, 0.7% has an advanced risk, and 0.2% can be classified as problem gamblers...... ratesof detectable gambling risk groups, since gambling behavior is positively correlated with the decision to participate in gambling surveys. We also find that imposing a threshold gambling history leads to underestimation of the prevalence of gambling problems.......We compare several popular survey instruments for measuring gambling behavior and gambling propensity to assess if they differ in their classification of individuals in the general adult Danish population. We also examine correlations with standard survey instruments for alcohol use, anxiety...
A generalization of the convex Kakeya problem
Ahn, Heekap
2012-01-01
We consider the following geometric alignment problem: Given a set of line segments in the plane, find a convex region of smallest area that contains a translate of each input segment. This can be seen as a generalization of Kakeya\\'s problem of finding a convex region of smallest area such that a needle can be turned through 360 degrees within this region. Our main result is an optimal Θ(n log n)-time algorithm for our geometric alignment problem, when the input is a set of n line segments. We also show that, if the goal is to minimize the perimeter of the region instead of its area, then the optimum placement is when the midpoints of the segments coincide. Finally, we show that for any compact convex figure G, the smallest enclosing disk of G is a smallest-perimeter region containing a translate of any rotated copy of G. © 2012 Springer-Verlag Berlin Heidelberg.
PROBLEMS OF GENERAL PRACTICE IN RURAL CALIFORNIA
Carey, Hollis L.; Andrews, Carroll B.
1949-01-01
Medical care for rural populations is an important problem facing the medical profession nationally and locally. The mechanism for solution lies in the existing American Medical Association and California Medical Association committees on rural medical service and further development of “local health councils.” Additional emphasis on training of physicians for general practice is essential through medical school graduate and postgraduate periods. The problem of providing additional adequately equipped and staffed hospitals must receive much consideration. Recognizing that passiveness invites aggressive non-medical agencies to foster bureaucratic dictation inimical to the practice of medicine, the rural physician must act through medical and community organizations to correct weaknesses in the structure of medical practice. PMID:18116230
P. Zoeteweij (Peter)
2005-01-01
htmlabstractComposing constraint solvers based on tree search and constraint propagation through generic iteration leads to efficient and flexible constraint solvers. This was demonstrated using OpenSolver, an abstract branch-and-propagate tree search engine that supports a wide range of relevant
Foley, Greg
2014-01-01
A problem that illustrates two ways of computing the break-even radius of insulation is outlined. The problem is suitable for students who are taking an introductory module in heat transfer or transport phenomena and who have some previous knowledge of the numerical solution of non- linear algebraic equations. The potential for computer algebra,…
W.M. Lioen (Walter); J.J.B. de Swart (Jacques); W.A. van der Veen
1996-01-01
textabstractIn this paper a collection of Initial Value test Problems for systems of Ordinary Differential Equations, Implicit Differential Equations and Differential-Algebraic Equations is presented. This test set is maintained by the project group for Parallel IVP Solvers of CWI, department of
Anholonomic Cauchy problem in general relativity
International Nuclear Information System (INIS)
Stachel, J.
1980-01-01
The Lie derivative approach to the Cauchy problem in general relativity is applied to the evolution along an arbitrary timelike vector field for the case where the dynamical degrees of freedom are chosen as the (generally anholonomic) metric of the hypersurface elements orthogonal to the vector field. Generalizations of the shear, rotation, and acceleration are given for a nonunit timelike vector field, and applied to the three-plus-one breakup of the Riemann tensor into components parallel and orthogonal to the vector field, resulting in the anholonomic Gauss--Codazzi equations. A similar breakup of the Einstein field equations results in the form of the constraint and evolution equations for the anholonomic case. The results are applied to the case of a space--time with a timelike Killing vector field (stationary field) to demonstrate their utility. Other possible applications, such as in the numerical integration of the field equations, are mentioned. Definitions are given of three-index shear, rotation, and acceleration tensors, and their use in a two-plus-two decomposition of the Riemann tensor and field equations is indicated
Thevenot, Catherine; Castel, Caroline; Fanget, Muriel; Fayol, Michel
2010-01-01
The authors used the operand-recognition paradigm (C. Thevenot, M. Fanget, & M. Fayol, 2007) in order to study the strategies used by adults to solve subtraction problems. This paradigm capitalizes on the fact that algorithmic procedures degrade the memory traces of the operands. Therefore, greater difficulty in recognizing them is expected…
A Test Set for stiff Initial Value Problem Solvers in the open source software R: Package deTestSet
Mazzia, F.; Cash, J.R.; Soetaert, K.
2012-01-01
In this paper we present the R package deTestSet that includes challenging test problems written as ordinary differential equations (ODEs), differential algebraic equations (DAEs) of index up to 3 and implicit differential equations (IDES). In addition it includes 6 new codes to solve initial value
Myong-Hun Chang; Joseph E. Harrington
2013-01-01
The dynamic choice between individual and social learning is explored for a population of autonomous agents whose objective is to find solutions to a stream of related problems. The probability that an agent is in the individual learning mode, as opposed to the social learning mode, evolves over time through reinforcement learning. Furthermore, the communication network of an agent is also endogenous. Our main finding is that when agents are sufficiently effective at social learning, structur...
Czech Academy of Sciences Publication Activity Database
Kočvara, Michal; Stingl, M.
2009-01-01
Roč. 120, č. 1 (2009), s. 285-287 ISSN 0025-5610 R&D Projects: GA AV ČR IAA1075402 Institutional research plan: CEZ:AV0Z10750506 Keywords : semidefinite programming * iterative methods Subject RIV: BA - General Mathematics Impact factor: 2.048, year: 2009
Nonlinear multigrid solvers exploiting AMGe coarse spaces with approximation properties
DEFF Research Database (Denmark)
Christensen, Max la Cour; Vassilevski, Panayot S.; Villa, Umberto
2017-01-01
This paper introduces a nonlinear multigrid solver for mixed finite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The AMGe coarse spaces with approximation properties used in this work enable us to overcome the difficulties...... discretizations on general unstructured grids for a large class of nonlinear partial differential equations, including saddle point problems. The approximation properties of the coarse spaces ensure that our FAS approach for general unstructured meshes leads to optimal mesh-independent convergence rates similar...... to those achieved by geometric FAS on a nested hierarchy of refined meshes. In the numerical results, Newton’s method and Picard iterations with state-of-the-art inner linear solvers are compared to our FAS algorithm for the solution of a nonlinear saddle point problem arising from porous media flow...
A generalization of the convex Kakeya problem
Ahn, Heekap
2013-09-19
Given a set of line segments in the plane, not necessarily finite, what is a convex region of smallest area that contains a translate of each input segment? This question can be seen as a generalization of Kakeya\\'s problem of finding a convex region of smallest area such that a needle can be rotated through 360 degrees within this region. We show that there is always an optimal region that is a triangle, and we give an optimal Θ(nlogn)-time algorithm to compute such a triangle for a given set of n segments. We also show that, if the goal is to minimize the perimeter of the region instead of its area, then placing the segments with their midpoint at the origin and taking their convex hull results in an optimal solution. Finally, we show that for any compact convex figure G, the smallest enclosing disk of G is a smallest-perimeter region containing a translate of every rotated copy of G. © 2013 Springer Science+Business Media New York.
The Generalized Fixed-Charge Network Design Problem
DEFF Research Database (Denmark)
Thomadsen, Tommy; Stidsen, Thomas K.
2007-01-01
In this paper we present the generalized fixed-charge network design (GFCND) problem. The GFCND problem is an instance of the so-called generalized network design problems. In such problems, clusters instead of nodes have to be interconnected by a network. The network interconnecting the clusters...... is a fixed-charge network, and thus the GFCND problem generalizes the fixed-charge network design problem. The GFCND problem is related to the more general problem of designing hierarchical telecommunication networks. A mixed integer programming model is described and a branch-cut-and-price algorithm...
Directory of Open Access Journals (Sweden)
Christian F. Janßen
2015-07-01
Full Text Available This contribution is dedicated to demonstrating the high potential and manifold applications of state-of-the-art computational fluid dynamics (CFD tools for free-surface flows in civil and environmental engineering. All simulations were performed with the academic research code ELBE (efficient lattice boltzmann environment, http://www.tuhh.de/elbe. The ELBE code follows the supercomputing-on-the-desktop paradigm and is especially designed for local supercomputing, without tedious accesses to supercomputers. ELBE uses graphics processing units (GPU to accelerate the computations and can be used in a single GPU-equipped workstation of, e.g., a design engineer. The code has been successfully validated in very different fields, mostly related to naval architecture and mechanical engineering. In this contribution, we give an overview of past and present applications with practical relevance for civil engineers. The presented applications are grouped into three major categories: (i tsunami simulations, considering wave propagation, wave runup, inundation and debris flows; (ii dam break simulations; and (iii numerical wave tanks for the calculation of hydrodynamic loads on fixed and moving bodies. This broad range of applications in combination with accurate numerical results and very competitive times to solution demonstrates that modern CFD tools in general, and the ELBE code in particular, can be a helpful design tool for civil and environmental engineers.
Sun, Rui; Xiao, Heng
2016-04-01
With the growth of available computational resource, CFD-DEM (computational fluid dynamics-discrete element method) becomes an increasingly promising and feasible approach for the study of sediment transport. Several existing CFD-DEM solvers are applied in chemical engineering and mining industry. However, a robust CFD-DEM solver for the simulation of sediment transport is still desirable. In this work, the development of a three-dimensional, massively parallel, and open-source CFD-DEM solver SediFoam is detailed. This solver is built based on open-source solvers OpenFOAM and LAMMPS. OpenFOAM is a CFD toolbox that can perform three-dimensional fluid flow simulations on unstructured meshes; LAMMPS is a massively parallel DEM solver for molecular dynamics. Several validation tests of SediFoam are performed using cases of a wide range of complexities. The results obtained in the present simulations are consistent with those in the literature, which demonstrates the capability of SediFoam for sediment transport applications. In addition to the validation test, the parallel efficiency of SediFoam is studied to test the performance of the code for large-scale and complex simulations. The parallel efficiency tests show that the scalability of SediFoam is satisfactory in the simulations using up to O(107) particles.
The dual of a generalized minimax location problem
DEFF Research Database (Denmark)
Juel, Henrik; Love, Robert F.
1992-01-01
This paper develops the dual formulation of a generalized minimax facility location problem which has distance and linear constraints......This paper develops the dual formulation of a generalized minimax facility location problem which has distance and linear constraints...
A direct parallel sparse matrix solver
International Nuclear Information System (INIS)
Tran, T.M.; Gruber, R.; Appert, K.; Wuthrich, S.
1995-08-01
The direct sparse matrix solver is based on a domain decomposition technique to achieve data and work parallelization. Geometries that have long and thin structures are specially efficiently tractable with this solver, provided that they can be decomposed mainly in one direction. Due to the separation of the algorithm into a factorization stage and a solution stage, time-dependent problems with a constant coefficient matrix are particularly well suited for this solver. The parallelization performances obtained on a Cray T3D show that the method scales up to at least 256 processors. (author) 5 figs., 2 tabs., 9 refs
Parallel Symmetric Eigenvalue Problem Solvers
2015-05-01
108 8.3.2 Nastran benchmark (order 1.5 million) . . . . . . . . . . . . 108 8.3.3 Nastran benchmark (order 7.2 million...110 8.4 TraceMin-Multisectioning . . . . . . . . . . . . . . . . . . . . . . . 113 8.4.1 Nastran benchmark (order 1.5 million...113 8.4.2 Nastran benchmark (order 7.2 million) . . . . . . . . . . . . 115 8.4.3 Anderson model of localization . . . . . . . . . . . . . . . . 120
Approximate Riemann solver for the two-fluid plasma model
International Nuclear Information System (INIS)
Shumlak, U.; Loverich, J.
2003-01-01
An algorithm is presented for the simulation of plasma dynamics using the two-fluid plasma model. The two-fluid plasma model is more general than the magnetohydrodynamic (MHD) model often used for plasma dynamic simulations. The two-fluid equations are derived in divergence form and an approximate Riemann solver is developed to compute the fluxes of the electron and ion fluids at the computational cell interfaces and an upwind characteristic-based solver to compute the electromagnetic fields. The source terms that couple the fluids and fields are treated implicitly to relax the stiffness. The algorithm is validated with the coplanar Riemann problem, Langmuir plasma oscillations, and the electromagnetic shock problem that has been simulated with the MHD plasma model. A numerical dispersion relation is also presented that demonstrates agreement with analytical plasma waves
Directory of Open Access Journals (Sweden)
Granville Sewell
2013-01-01
Full Text Available PDE2D is a general-purpose partial differential equation solver which solves very general systems of nonlinear, steady-state, time-dependent and eigenvalue PDEs in 1D intervals, general 2D regions (see Figure 1, and a wide range of simple 3D regions (see Figure 2, with general boundary conditions. It uses a collocation finite element method [2] for 3D problems, and either a collocation or Galerkin finite element method can be used for 1D and 2D problems. It has been sold commercially for 30 years, but recently a version has been made available, which can be downloaded at no cost from www.pde2d.com.
General problems of modeling for accelerators
International Nuclear Information System (INIS)
Luccio, A.
1991-01-01
In this presentation the author only discusses problems of modeling for circular accelerators and bases the examples on the AGS Booster Synchrotron presently being commissioned at BNL. A model is a platonic representation of an accelerator. With algorithms, implemented through computer codes, the model is brought to life. At the start of a new accelerator project, the model and the real machine are taking shape somewhat apart. They get closer and closer as the project goes on. Ideally, the modeler is only satisfied when the model or the machine cannot be distinguished. Accelerator modeling for real time control has specific problems. If one wants fast responses, algorithms may be implemented in hardware or by parallel computation, perhaps by neural networks. Algorithms and modeling is not only for accelerator control. It is also for: accelerator parameter measurement; hardware problem debugging, perhaps with some help of artificial intelligence; operator training, much like a flight simulator
Exponential operators, generalized polynomials and evolution problems
International Nuclear Information System (INIS)
Dattoli, G.; Mancho, A.M.; Quattromini, M.; Torre, A.
2001-01-01
The operator (d/dx) χ d/dx plays a central role in the theory of operational calculus. Its exponential form is crucial in problems relevant to solutions of Fokker-Planck and Schroedinger equations. We explore the formal properties of the evolution operators associated to (d/dx) χ d/dx, discuss its link to special forms of Laguerre polynomials and Laguerre-based functions. The obtained results are finally applied to specific problems concerning the solution of Fokker-Planck equations relevant to the beam lifetime in storage rings
A General Solution for Troesch's Problem
Directory of Open Access Journals (Sweden)
Hector Vazquez-Leal
2012-01-01
Full Text Available The homotopy perturbation method (HPM is employed to obtain an approximate solution for the nonlinear differential equation which describes Troesch’s problem. In contrast to other reported solutions obtained by using variational iteration method, decomposition method approximation, homotopy analysis method, Laplace transform decomposition method, and HPM method, the proposed solution shows the highest degree of accuracy in the results for a remarkable wide range of values of Troesch’s parameter.
Prevalence of alcohol problems in general practice
DEFF Research Database (Denmark)
Rambaldi, A; Todisco, N; Gluud, C
1996-01-01
heavy alcohol consumption had a predictive negative value of 97.2% (95% CI 90.2-99.7%) and a predictive positive value of 73.1% (95% CI 59.0-84.4%) in relation to MAST positive patients. It is suggested that general practitioners should incorporate this question about heavy alcohol consumption...
NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES
Energy Technology Data Exchange (ETDEWEB)
Christensen, Max La Cour [Technical Univ. of Denmark, Lyngby (Denmark); Villa, Umberto E. [Univ. of Texas, Austin, TX (United States); Engsig-Karup, Allan P. [Technical Univ. of Denmark, Lyngby (Denmark); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-01-22
The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.
A systematic approach to numerical dispersion in Maxwell solvers
Blinne, Alexander; Schinkel, David; Kuschel, Stephan; Elkina, Nina; Rykovanov, Sergey G.; Zepf, Matt
2018-03-01
The finite-difference time-domain (FDTD) method is a well established method for solving the time evolution of Maxwell's equations. Unfortunately the scheme introduces numerical dispersion and therefore phase and group velocities which deviate from the correct values. The solution to Maxwell's equations in more than one dimension results in non-physical predictions such as numerical dispersion or numerical Cherenkov radiation emitted by a relativistic electron beam propagating in vacuum. Improved solvers, which keep the staggered Yee-type grid for electric and magnetic fields, generally modify the spatial derivative operator in the Maxwell-Faraday equation by increasing the computational stencil. These modified solvers can be characterized by different sets of coefficients, leading to different dispersion properties. In this work we introduce a norm function to rewrite the choice of coefficients into a minimization problem. We solve this problem numerically and show that the minimization procedure leads to phase and group velocities that are considerably closer to c as compared to schemes with manually set coefficients available in the literature. Depending on a specific problem at hand (e.g. electron beam propagation in plasma, high-order harmonic generation from plasma surfaces, etc.), the norm function can be chosen accordingly, for example, to minimize the numerical dispersion in a certain given propagation direction. Particle-in-cell simulations of an electron beam propagating in vacuum using our solver are provided.
A Novel Interactive MINLP Solver for CAPE Applications
DEFF Research Database (Denmark)
Henriksen, Jens Peter; Støy, S.; Russel, Boris Mariboe
2000-01-01
This paper presents an interactive MINLP solver that is particularly suitable for solution of process synthesis, design and analysis problems. The interactive MINLP solver is based on the decomposition based MINLP algorithms, where a NLP sub-problem is solved in the innerloop and a MILP master...
A parallel PCG solver for MODFLOW.
Dong, Yanhui; Li, Guomin
2009-01-01
In order to simulate large-scale ground water flow problems more efficiently with MODFLOW, the OpenMP programming paradigm was used to parallelize the preconditioned conjugate-gradient (PCG) solver with in this study. Incremental parallelization, the significant advantage supported by OpenMP on a shared-memory computer, made the solver transit to a parallel program smoothly one block of code at a time. The parallel PCG solver, suitable for both MODFLOW-2000 and MODFLOW-2005, is verified using an 8-processor computer. Both the impact of compilers and different model domain sizes were considered in the numerical experiments. Based on the timing results, execution times using the parallel PCG solver are typically about 1.40 to 5.31 times faster than those using the serial one. In addition, the simulation results are the exact same as the original PCG solver, because the majority of serial codes were not changed. It is worth noting that this parallelizing approach reduces cost in terms of software maintenance because only a single source PCG solver code needs to be maintained in the MODFLOW source tree. Copyright © 2009 The Author(s). Journal Compilation © 2009 National Ground Water Association.
Strong Duality and Optimality Conditions for Generalized Equilibrium Problems
Directory of Open Access Journals (Sweden)
D. H. Fang
2013-01-01
Full Text Available We consider a generalized equilibrium problem involving DC functions. By using the properties of the epigraph of the conjugate functions, some sufficient and/or necessary conditions for the weak and strong duality results and optimality conditions for generalized equilibrium problems are provided.
Ltaief, Hatem
2012-01-01
This paper proposes an efficient implementation of the generalized symmetric eigenvalue problem on multicore architecture. Based on a four-stage approach and tile algorithms, the original problem is first transformed into a standard symmetric eigenvalue problem by computing the Cholesky factorization of the right hand side symmetric definite positive matrix (first stage), and applying the inverse of the freshly computed triangular Cholesky factors to the original dense symmetric matrix of the problem (second stage). Calculating the eigenpairs of the resulting problem is then equivalent to the eigenpairs of the original problem. The computation proceeds by reducing the updated dense symmetric matrix to symmetric band form (third stage). The band structure is further reduced by applying a bulge chasing procedure, which annihilates the extra off-diagonal entries using orthogonal transformations (fourth stage). More details on the third and fourth stage can be found in Haidar et al. [Accepted at SC\\'11, November 2011]. The eigenvalues are then calculated from the tridiagonal form using the standard LAPACK QR algorithm (i.e., DTSEQR routine), while the complex and challenging eigenvector computations will be addressed in a companion paper. The tasks from the various stages can concurrently run in an out-of-order fashion. The data dependencies are cautiously tracked by the dynamic runtime system environment QUARK, which ensures the dependencies are not violated for numerical correctness purposes. The obtained tile four-stage generalized symmetric eigenvalue solver significantly outperforms the state-of-the-art numerical libraries (up to 21-fold speed up against multithreaded LAPACK with optimized multithreaded MKL BLAS and up to 4-fold speed up against the corresponding routine from the commercial numerical software Intel MKL) on four sockets twelve cores AMD system with a 24000×24000 matrix size. © 2012 The authors and IOS Press. All rights reserved.
Minimal connections: the classical Steiner problem and generalizations
Directory of Open Access Journals (Sweden)
Emanuele Paolini
2012-12-01
Full Text Available The classical Steiner problem is the problem of finding the shortest graph connecting a given finite set of points. In this seminar we review the classical problem and introduce a new, generalized formulation, which extends the original one to infinite sets in metric spaces.
Ergül, Özgür
2014-04-01
Graphics processing units (GPUs) are gradually becoming mainstream in high-performance computing, as their capabilities for enhancing performance of a large spectrum of scientific applications to many fold when compared to multi-core CPUs have been clearly identified and proven. In this paper, implementation and performance-tuning details for porting an explicit marching-on-in-time (MOT)-based time-domain volume-integral-equation (TDVIE) solver onto GPUs are described in detail. To this end, a high-level approach, utilizing the OpenACC directive-based parallel programming model, is used to minimize two often-faced challenges in GPU programming: developer productivity and code portability. The MOT-TDVIE solver code, originally developed for CPUs, is annotated with compiler directives to port it to GPUs in a fashion similar to how OpenMP targets multi-core CPUs. In contrast to CUDA and OpenCL, where significant modifications to CPU-based codes are required, this high-level approach therefore requires minimal changes to the codes. In this work, we make use of two available OpenACC compilers, CAPS and PGI. Our experience reveals that different annotations of the code are required for each of the compilers, due to different interpretations of the fairly new standard by the compiler developers. Both versions of the OpenACC accelerated code achieved significant performance improvements, with up to 30× speedup against the sequential CPU code using recent hardware technology. Moreover, we demonstrated that the GPU-accelerated fully explicit MOT-TDVIE solver leveraged energy-consumption gains of the order of 3× against its CPU counterpart. © 2014 IEEE.
DEFF Research Database (Denmark)
Hossain, Mokter
2018-01-01
The objective of this study is to identify motivations, challenges, and opportunities of successful solvers participating in virtual teams of innovation contests (ICs) organized by an innovation intermediary. Based on 82 interviews of successful solvers, this study provides novel insights into ICs....... The main motivational factors of successful solvers engaged in problem solving are money, learning, fun, sense of achievement, passion, and networking. Major challenges solvers face include unclear or insufficient problem description, lack of option for communication, language barrier, time zone...
Wavelet-Based Poisson Solver for Use in Particle-in-Cell Simulations
Terzic, Balsa; Mihalcea, Daniel; Pogorelov, Ilya V
2005-01-01
We report on a successful implementation of a wavelet-based Poisson solver for use in 3D particle-in-cell simulations. One new aspect of our algorithm is its ability to treat the general (inhomogeneous) Dirichlet boundary conditions. The solver harnesses advantages afforded by the wavelet formulation, such as sparsity of operators and data sets, existence of effective preconditioners, and the ability simultaneously to remove numerical noise and further compress relevant data sets. Having tested our method as a stand-alone solver on two model problems, we merged it into IMPACT-T to obtain a fully functional serial PIC code. We present and discuss preliminary results of application of the new code to the modelling of the Fermilab/NICADD and AES/JLab photoinjectors.
Recent results on a general financial equilibrium problem
Barbagallo, Annamaria; Daniele, Patrizia; Lorino, Mariagrazia; Maugeri, Antonino; Mirabella, Cristina
2013-10-01
The paper is devoted to the study of a general financial equilibrium problem which is modeled by means of a variational inequality. The main theoretical results obtained in these last years are presented.
Book Review: Solving Language Problems: From General to ...
African Journals Online (AJOL)
Abstract. Book Title: Solving Language Problems: From General to Applied Linguistics. Book Author: R.R.K. Hartmann (Ed.) 1st edition 1996, vi + 298 pp. ISBN 0-85989-484-3. Exeter: University of Exeter Press.
The analysis of singletons in generalized birthday problems
Koot, M.R.; Mandjes, M.R.H.
2012-01-01
This paper describes techniques to characterize the number of singletons in the setting of the generalized birthday problem, that is, the birthday problem in which the birthdays are non-uniformly distributed over the year. Approximations for the mean and variance presented which explicitly indicate
Bounds in the generalized Weber problem under locational uncertainty
DEFF Research Database (Denmark)
Juel, Henrik
1981-01-01
An existing analysis of the bounds on the Weber problem solution under uncertainty is incorrect. For the generalized problem with arbitrary measures of distance, we give easily computable ranges on the bounds and state the conditions under which the exact values of the bounds can be found...... with little computational effort. Numerical examples illustrate the analysis....
Child dental fear and general emotional problems: a pilot study
Krikken, J.B.; ten Cate, J.M.; Veerkamp, J.S.J.
2010-01-01
AIM: This was to investigate the relation between general emotional and behavioural problems of the child and dental anxiety and dental behavioural management problems. BACKGROUND: Dental treatment involves many potentially unpleasant stimuli, which all may lead to the development of dental anxiety
Procrustes Problems for General, Triangular, and Symmetric Toeplitz Matrices
Directory of Open Access Journals (Sweden)
Juan Yang
2013-01-01
Full Text Available The Toeplitz Procrustes problems are the least squares problems for the matrix equation AX=B over some Toeplitz matrix sets. In this paper the necessary and sufficient conditions are obtained about the existence and uniqueness for the solutions of the Toeplitz Procrustes problems when the unknown matrices are constrained to the general, the triangular, and the symmetric Toeplitz matrices, respectively. The algorithms are designed and the numerical examples show that these algorithms are feasible.
Higher-Order Generalized Invexity in Control Problems
Directory of Open Access Journals (Sweden)
S. K. Padhan
2011-01-01
Full Text Available We introduce a higher-order duality (Mangasarian type and Mond-Weir type for the control problem. Under the higher-order generalized invexity assumptions on the functions that compose the primal problems, higher-order duality results (weak duality, strong duality, and converse duality are derived for these pair of problems. Also, we establish few examples in support of our investigation.
Local Conjecturing Process in the Solving of Pattern Generalization Problem
Sutarto; Nusantara, Toto; Subanji; Sisworo
2016-01-01
This aim of this study is to describe the process of local conjecturing in generalizing patterns based on Action, Process, Object, Schema (APOS) theory. The subjects were 16 grade 8 students from a junior high school. Data collection used Pattern Generalization Problem (PGP) and interviews. In the first stage, students completed PGP; in the second…
A general approach to posterior contraction in nonparametric inverse problems
Knapik, Bartek; Salomond, Jean Bernard
In this paper, we propose a general method to derive an upper bound for the contraction rate of the posterior distribution for nonparametric inverse problems. We present a general theorem that allows us to derive contraction rates for the parameter of interest from contraction rates of the related
Two-dimensional time dependent Riemann solvers for neutron transport
International Nuclear Information System (INIS)
Brunner, Thomas A.; Holloway, James Paul
2005-01-01
A two-dimensional Riemann solver is developed for the spherical harmonics approximation to the time dependent neutron transport equation. The eigenstructure of the resulting equations is explored, giving insight into both the spherical harmonics approximation and the Riemann solver. The classic Roe-type Riemann solver used here was developed for one-dimensional problems, but can be used in multidimensional problems by treating each face of a two-dimensional computation cell in a locally one-dimensional way. Several test problems are used to explore the capabilities of both the Riemann solver and the spherical harmonics approximation. The numerical solution for a simple line source problem is compared to the analytic solution to both the P 1 equation and the full transport solution. A lattice problem is used to test the method on a more challenging problem
Generalized Nash equilibrium problems, bilevel programming and mpec
Lalitha, CS
2017-01-01
The book discusses three classes of problems: the generalized Nash equilibrium problems, the bilevel problems and the mathematical programming with equilibrium constraints (MPEC). These problems interact through their mathematical analysis as well as their applications. The primary aim of the book is to present the modern tool of variational analysis and optimization, which are used to analyze these three classes of problems. All contributing authors are respected academicians, scientists and researchers from around the globe. These contributions are based on the lectures delivered by experts at CIMPA School, held at the University of Delhi, India, from 25 November–6 December 2013, and peer-reviewed by international experts. The book contains five chapters. Chapter 1 deals with nonsmooth, nonconvex bilevel optimization problems whose feasible set is described by using the graph of the solution set mapping of a parametric optimization problem. Chapter 2 describes a constraint qualification to MPECs considere...
Numerical solution of pipe flow problems for generalized Newtonian fluids
International Nuclear Information System (INIS)
Samuelsson, K.
1993-01-01
In this work we study the stationary laminar flow of incompressible generalized Newtonian fluids in a pipe with constant arbitrary cross-section. The resulting nonlinear boundary value problems can be written in a variational formulation and solved using finite elements and the augmented Lagrangian method. The solution of the boundary value problem is obtained by finding a saddle point of the augmented Lagrangian. In the algorithm the nonlinear part of the equations is treated locally and the solution is obtained by iteration between this nonlinear problem and a global linear problem. For the solution of the linear problem we use the SSOR preconditioned conjugate gradient method. The approximating problem is solved on a sequence of adaptively refined grids. A scheme for adjusting the value of the crucial penalization parameter of the augmented Lagrangian is proposed. Applications to pipe flow and a problem from the theory of capacities are given. (author) (34 refs.)
A General Theory of Markovian Time Inconsistent Stochastic Control Problems
DEFF Research Database (Denmark)
Björk, Tomas; Murgochi, Agatha
We develop a theory for stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a Bellman optimality principle. We attach these problems by viewing them within a game theoretic framework, and we look for Nash subgame perfect equilibrium points....... For a general controlled Markov process and a fairly general objective functional we derive an extension of the standard Hamilton-Jacobi-Bellman equation, in the form of a system of on-linear equations, for the determination for the equilibrium strategy as well as the equilibrium value function. All known...... examples of time inconsistency in the literature are easily seen to be special cases of the present theory. We also prove that for every time inconsistent problem, there exists an associated time consistent problem such that the optimal control and the optimal value function for the consistent problem...
Black-box solvers for partial differential equations
International Nuclear Information System (INIS)
Weiss, R.; Schoenauer, W.
1993-01-01
The design principles of the black-box solvers FIDISOL/CADSOL and VECFEM are presented for the solution of system of elliptic and parabolic partial differential equations by the finite difference and the finite element method. Special focus is directed to a high flexibility of the programs in order to solve a large range of problems. The solvers use state-of-the-art algorithms and are adapted to advanced computer architectures in order to achieve a high performance. As quality control an error estimate is implemented. The resulting numerical problems focus in the iterative linear solvers. It is a real challenge to select robust and efficient iterative solvers for an extremely wide class of problems. The strong relation between application problem and mathematical problems is pointed out. (orig.)
Varying domains in a general class of sublinear elliptic problems
Directory of Open Access Journals (Sweden)
Santiago Cano-Casanova
2004-05-01
Full Text Available In this paper we use the linear theory developed in [8] and [9] to show the continuous dependence of the positive solutions of a general class of sublinear elliptic boundary value problems of mixed type with respect to the underlying domain. Our main theorem completes the results of Daners and Dancer [12] -and the references there in-, where the classical Robin problem was dealt with. Besides the fact that we are working with mixed non-classical boundary conditions, it must be mentioned that this paper is considering problems where bifurcation from infinity occurs; now a days, analyzing these general problems, where the coefficients are allowed to vary and eventually vanishing or changing sign, is focusing a great deal of attention -as they give rise to metasolutions (e.g., [20]-.
Parallel sparse direct solver for integrated circuit simulation
Chen, Xiaoming; Yang, Huazhong
2017-01-01
This book describes algorithmic methods and parallelization techniques to design a parallel sparse direct solver which is specifically targeted at integrated circuit simulation problems. The authors describe a complete flow and detailed parallel algorithms of the sparse direct solver. They also show how to improve the performance by simple but effective numerical techniques. The sparse direct solver techniques described can be applied to any SPICE-like integrated circuit simulator and have been proven to be high-performance in actual circuit simulation. Readers will benefit from the state-of-the-art parallel integrated circuit simulation techniques described in this book, especially the latest parallel sparse matrix solution techniques. · Introduces complicated algorithms of sparse linear solvers, using concise principles and simple examples, without complex theory or lengthy derivations; · Describes a parallel sparse direct solver that can be adopted to accelerate any SPICE-like integrated circuit simulato...
Municipal solid waste management problems: an applied general equilibrium analysis
Bartelings, H.
2003-01-01
Keywords: Environmental policy; General equilibrium modeling; Negishi format; Waste management policies; Market distortions.
About 40% of the entire budget spent on environmental problems in the
A generalization of the finiteness problem in local cohomology ...
Indian Academy of Sciences (India)
(Math. Sci.) Vol. 119, No. 2, April 2009, pp. 159–164. © Printed in India. A generalization of the finiteness problem in local cohomology modules. AMIR MAFI. Department of Mathematics, University of Kurdistan, P.O. Box 416, Sanandaj, Iran. Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-5746,.
Digital Competence: general problems and experimental practices concerning highschools
Directory of Open Access Journals (Sweden)
Roberto Gris
2015-10-01
Full Text Available In the current social context Information and Communication Technologies (ICT are more and more present and pervasive and the European institutions enter the Digital Competence in the Key Competences for Lifelong Learning. In this focus we are deepened the general problems of Digital Competence and competence-based education and to describe experimental practices concerning highschools.
Generalized birthday problems in the large-deviations regime
Mandjes, M.
2014-01-01
This paper considers generalized birthday problems, in which there are d classes of possible outcomes. A fraction f i of the N possible outcomes has probability α i /N, where $\\sum_{i=1}^{d} f_{i} =\\sum_{i=1}^{d} f_{i}\\alpha_{i}=1$. Sampling k times (with replacements), the objective is to determine
Refinements, Generalizations, and Applications of Jordan's Inequality and Related Problems
Directory of Open Access Journals (Sweden)
Feng Qi
2009-01-01
Full Text Available This is a survey and expository article. Some new developments on refinements, generalizations, and applications of Jordan's inequality and related problems, including some results about Wilker-Anglesio's inequality, some estimates for three kinds of complete elliptic integrals, and several inequalities for the remainder of power series expansion of the exponential function, are summarized.
Problem-Based Learning in a General Psychology Course.
Willis, Sandra A.
2002-01-01
Describes the adoption of problem-based learning (PBL) techniques in a general psychology course. States that the instructor used a combination of techniques, including think-pair-share, lecture/discussion, and PBL. Notes means and standard deviations for graded components of PBL format versus lecture/discussion format. (Contains 18 references.)…
The Neumann Problem for the Laplace Equation on General Domains
Czech Academy of Sciences Publication Activity Database
Medková, Dagmar
2007-01-01
Roč. 57, č. 4 (2007), s. 1107-1139 ISSN 0011-4642 Institutional research plan: CEZ:AV0Z10190503 Keywords : Laplace equation * Neumann problem * potential Subject RIV: BA - General Mathematics Impact factor: 0.155, year: 2007
Polymorphic Uncertain Linear Programming for Generalized Production Planning Problems
Directory of Open Access Journals (Sweden)
Xinbo Zhang
2014-01-01
Full Text Available A polymorphic uncertain linear programming (PULP model is constructed to formulate a class of generalized production planning problems. In accordance with the practical environment, some factors such as the consumption of raw material, the limitation of resource and the demand of product are incorporated into the model as parameters of interval and fuzzy subsets, respectively. Based on the theory of fuzzy interval program and the modified possibility degree for the order of interval numbers, a deterministic equivalent formulation for this model is derived such that a robust solution for the uncertain optimization problem is obtained. Case study indicates that the constructed model and the proposed solution are useful to search for an optimal production plan for the polymorphic uncertain generalized production planning problems.
Application of Neutrosophic Set Theory in Generalized Assignment Problem
Directory of Open Access Journals (Sweden)
Supriya Kar
2015-09-01
Full Text Available This paper presents the application of Neutrosophic Set Theory (NST in solving Generalized Assignment Problem (GAP. GAP has been solved earlier under fuzzy environment. NST is a generalization of the concept of classical set, fuzzy set, interval-valued fuzzy set, intuitionistic fuzzy set. Elements of Neutrosophic set are characterized by a truth-membership function, falsity and also indeterminacy which is a more realistic way of expressing the parameters in real life problem. Here the elements of the cost matrix for the GAP are considered as neutrosophic elements which have not been considered earlier by any other author. The problem has been solved by evaluating score function matrix and then solving it by Extremum Difference Method (EDM [1] to get the optimal assignment. The method has been demonstrated by a suitable numerical example.
Czech Academy of Sciences Publication Activity Database
Hnětynková, Iveta; Plešinger, M.; Strakoš, Z.
2015-01-01
Roč. 36, č. 2 (2015), s. 417-434 ISSN 0895-4798 R&D Projects: GA ČR GA13-06684S Grant - others:GA MŠk(CZ) EE2.3.30.0065; GA MŠk(CZ) LL1202 Keywords : total least squares problem * multiple right-hand sides * core problem * Golub-Kahan bidiagonalization * generalized Jacobi matrices Subject RIV: BA - General Mathematics Impact factor: 1.883, year: 2015
Fast Multipole-Based Preconditioner for Sparse Iterative Solvers
Ibeid, Huda
2014-05-04
Among optimal hierarchical algorithms for the computational solution of elliptic problems, the Fast Multipole Method (FMM) stands out for its adaptability to emerging architectures, having high arithmetic intensity, tunable accuracy, and relaxed global synchronization requirements. We demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Compared with multilevel methods, it is capable of comparable algebraic convergence rates down to the truncation error of the discretized PDE, and it has superior multicore and distributed memory scalability properties on commodity architecture supercomputers.
International Nuclear Information System (INIS)
Hofer, E.
1981-01-01
Simulations in thermo- and fluiddynamics often require the numerical solution of large initial value problems with stiffness caused by eigenvalues close to the imaginary axis. The regions of absolute stability of the most widely used ordinary differential equation (ODE) solvers, for stiff problems, do not properly account for this. The paper introduces a general purpose ODE-solver with considerably larger stability regions. Its reliability is illustrated by test problems, with complex eigenvalues, from a well known test package. Applications in large codes, for simulations in thermo- and fluiddynamics, demonstrate its practical usability. (orig.) [de
Redesigning problem solving component in General Physics course.
Shakov, Jerry; McGuire, Jim
2007-04-01
Problem-based learning has been widely used in teaching introductory/general physics courses for a long time. The role of problem-solving sessions in the learning process is absolutely critical: they give the students an opportunity to learn how to apply both newly and previously acquired knowledge to practical situations, how to put together different strategies and portions of material, and much more. Unfortunately, the traditional format used for the problem solving sessions is not very accommodative for the goal: large class sizes and limited time often force instructors to spend most of the time solving sample problems in front of the class, which leaves the students with the role of passive observers. In this work, we will discuss how one can involve the students in the process of active learning using collaborative strategies and principles of cognitive apprenticeship.
General terms and rigidity: another solution to the trivialization problem
Directory of Open Access Journals (Sweden)
Eleonora Orlando
2014-06-01
Full Text Available In this paper I am concerned with the problem of applying the notion of rigidity to general terms. In Naming and Necessity, Kripke has clearly suggested that we should include some general terms among the rigid ones, namely, those common nouns semantically correlated with natural substances, species and phenomena, in general, natural kinds -'water', 'tiger', 'heat'- and some adjectives -'red', 'hot', 'loud'. However, the notion of rigidity has been defined for singular terms; after all, the notion that Kripke has provided us with is the notion of a rigid designator. But general terms do not designate single individuals: rather, they apply to many of them. In sum, the original concept of rigidity cannot be straightforwardly applied to general terms: it has to be somehow redefined in order to make it cover them. As is known, two main positions have been put forward to accomplish that task: the identity of designation conception, according to which a rigid general term is one that designates the same property or kind in all possible worlds, and the essentialist conception, which conceives of a rigid general term as an essentialist one, namely, a term that expresses an essential property of an object. My purpose in the present paper is to defend a particular version of the identity of designation conception: on the proposed approach, a rigid general term will be one that expresses the same property in all possible worlds and names the property it expresses. In my opinion, the position can be established on the basis of an inference to the best explanation of our intuitive interpretation and evaluation, relative to counterfactual circumstances, of statements containing different kinds of general terms, which is strictly analogous to our intuitive interpretation and evaluation, relative to such circumstances, of statements containing different kinds of singular ones. I will argue that it is possible to offer a new solution to the trivialization
A general solution to some plane problems of micropolar elasticity
DEFF Research Database (Denmark)
Warren, William E.; Byskov, Esben
2008-01-01
that micropolar effects are most significant in material regions subjected to large deformation gradients. Specific results are presented for the classical crack problem, the half plane loaded uniformly on the surface, Flamant's problem, and the circular cylinder compressed by equal and opposite oncentrated......We obtain a general solution to the field equations of plane micropolar elasticity for materials characterized by a hexagonal or equilateral triangular structure. These materials exhibit 3-fold symmetry in the plane and the elastic response is isotropic. Utilizing two displacement potential...
Stochastic programming problems with generalized integrated chance constraints
Czech Academy of Sciences Publication Activity Database
Branda, Martin
2012-01-01
Roč. 61, č. 8 (2012), s. 949-968 ISSN 0233-1934 R&D Projects: GA ČR GAP402/10/1610 Grant - others:SVV(CZ) 261315/2010 Institutional support: RVO:67985556 Keywords : chance constraints * integrated chance constraints * penalty functions * sample approximations * blending problem Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.707, year: 2012 http://library.utia.cas.cz/separaty/2012/E/branda-stochastic programming problems with generalized integrated.pdf
A New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems
Directory of Open Access Journals (Sweden)
Fatemeh Mohammad
2014-05-01
Full Text Available In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem $Ax = \\lambda Bx$[Q.~Ye and P.~Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011 1697-1715]. In particular, the linear convergence property of the inverse subspace iteration is preserved.
Mathematical programming solver based on local search
Gardi, Frédéric; Darlay, Julien; Estellon, Bertrand; Megel, Romain
2014-01-01
This book covers local search for combinatorial optimization and its extension to mixed-variable optimization. Although not yet understood from the theoretical point of view, local search is the paradigm of choice for tackling large-scale real-life optimization problems. Today's end-users demand interactivity with decision support systems. For optimization software, this means obtaining good-quality solutions quickly. Fast iterative improvement methods, like local search, are suited to satisfying such needs. Here the authors show local search in a new light, in particular presenting a new kind of mathematical programming solver, namely LocalSolver, based on neighborhood search. First, an iconoclast methodology is presented to design and engineer local search algorithms. The authors' concern about industrializing local search approaches is of particular interest for practitioners. This methodology is applied to solve two industrial problems with high economic stakes. Software based on local search induces ex...
Fast Multipole-Based Elliptic PDE Solver and Preconditioner
Ibeid, Huda
2016-12-07
Exascale systems are predicted to have approximately one billion cores, assuming Gigahertz cores. Limitations on affordable network topologies for distributed memory systems of such massive scale bring new challenges to the currently dominant parallel programing model. Currently, there are many efforts to evaluate the hardware and software bottlenecks of exascale designs. It is therefore of interest to model application performance and to understand what changes need to be made to ensure extrapolated scalability. Fast multipole methods (FMM) were originally developed for accelerating N-body problems for particle-based methods in astrophysics and molecular dynamics. FMM is more than an N-body solver, however. Recent efforts to view the FMM as an elliptic PDE solver have opened the possibility to use it as a preconditioner for even a broader range of applications. In this thesis, we (i) discuss the challenges for FMM on current parallel computers and future exascale architectures, with a focus on inter-node communication, and develop a performance model that considers the communication patterns of the FMM for spatially quasi-uniform distributions, (ii) employ this performance model to guide performance and scaling improvement of FMM for all-atom molecular dynamics simulations of uniformly distributed particles, and (iii) demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for satisfying conditions at finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Compared with multilevel methods, FMM is capable of comparable algebraic convergence rates down to the truncation error of the discretized PDE, and it has superior multicore and distributed memory scalability properties on commodity
Use of Tabu Search in a Solver to Map Complex Networks onto Emulab Testbeds
National Research Council Canada - National Science Library
MacDonald, Jason E
2007-01-01
The University of Utah's solver for the testbed mapping problem uses a simulated annealing metaheuristic algorithm to map a researcher's experimental network topology onto available testbed resources...
Evolving effective incremental SAT solvers with GP
Bader, Mohamed; Poli, R.
2008-01-01
Hyper-Heuristics could simply be defined as heuristics to choose other heuristics, and it is a way of combining existing heuristics to generate new ones. In a Hyper-Heuristic framework, the framework is used for evolving effective incremental (Inc*) solvers for SAT. We test the evolved heuristics (IncHH) against other known local search heuristics on a variety of benchmark SAT problems.
Lonigan, Christopher J; Spiegel, Jamie A; Goodrich, J Marc; Morris, Brittany M; Osborne, Colleen M; Lerner, Matthew D; Phillips, Beth M
2017-11-01
Findings from prior research have consistently indicated significant associations between self-regulation and externalizing behaviors. Significant associations have also been reported between children's language skills and both externalizing behaviors and self-regulation. Few studies to date, however, have examined these relations longitudinally, simultaneously, or with respect to unique clusters of externalizing problems. The current study examined the influence of preschool self-regulation on general and specific externalizing behavior problems in early elementary school and whether these relations were independent of associations between language, self-regulation, and externalizing behaviors in a sample of 815 children (44% female). Additionally, given a general pattern of sex differences in the presentations of externalizing behavior problems, self-regulation, and language skills, sex differences for these associations were examined. Results indicated unique relations of preschool self-regulation and language with both general externalizing behavior problems and specific problems of inattention. In general, self-regulation was a stronger longitudinal correlate of externalizing behavior for boys than it was for girls, and language was a stronger longitudinal predictor of hyperactive/impulsive behavior for girls than it was for boys.
An Enhanced Genetic Algorithm for the Generalized Traveling Salesman Problem
Directory of Open Access Journals (Sweden)
H. Jafarzadeh
2017-12-01
Full Text Available The generalized traveling salesman problem (GTSP deals with finding the minimum-cost tour in a clustered set of cities. In this problem, the traveler is interested in finding the best path that goes through all clusters. As this problem is NP-hard, implementing a metaheuristic algorithm to solve the large scale problems is inevitable. The performance of these algorithms can be intensively promoted by other heuristic algorithms. In this study, a search method is developed that improves the quality of the solutions and competition time considerably in comparison with Genetic Algorithm. In the proposed algorithm, the genetic algorithms with the Nearest Neighbor Search (NNS are combined and a heuristic mutation operator is applied. According to the experimental results on a set of standard test problems with symmetric distances, the proposed algorithm finds the best solutions in most cases with the least computational time. The proposed algorithm is highly competitive with the published until now algorithms in both solution quality and running time.
General Problem Solving Strategies Employed in the Mexican Mathematical Olympiad
Directory of Open Access Journals (Sweden)
María del Consuelo Valle Espinosa
2007-11-01
Full Text Available This article describes the general strategies applied to problem solving in the State Math Olympiad selection test, in Puebla, Mexico. It analyzes the answers of 91 participants, ages 14 to 17, from junior high school and high school. Whether participants reached a problem solution or not, they rendered their results in one answer sheet and the arguments for those results in other. These answer sheets were used to form a database with 546 results. The sheets selected for the database were those in which participants identified the unknown factor, data and condition of the problem, in addition to have offered one or several solution strategies. Then, strategies were verbally described, their usage frequency calculated, and their effect on the different branches of mathematics depending on the problem analyzed. The strategy or strategies provided by participants were examined to identify stages of problem solving. The results showed that only 5% of the answer sheets had complete solutions. That emphasizes the need to systematize the State training courses for the National Olympiad. The importance of the training course is directly related to its purpose: to prepare young people for the National Olympiad and to enrich the Higher Education System of Puebla with students interested in doing science careers, with the ability to develop their hypothetical–deductive reasoning successfully.
Directory of Open Access Journals (Sweden)
Sergei Turovets
2014-01-01
Full Text Available The Electrical Impedance Tomography (EIT and electroencephalography (EEG forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG- type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique.
A Comparison of Monte Carlo and Deterministic Solvers for keff and Sensitivity Calculations
Energy Technology Data Exchange (ETDEWEB)
Haeck, Wim [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Parsons, Donald Kent [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); White, Morgan Curtis [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Saller, Thomas [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Favorite, Jeffrey A. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-12-12
Verification and validation of our solutions for calculating the neutron reactivity for nuclear materials is a key issue to address for many applications, including criticality safety, research reactors, power reactors, and nuclear security. Neutronics codes solve variations of the Boltzmann transport equation. The two main variants are Monte Carlo versus deterministic solutions, e.g. the MCNP [1] versus PARTISN [2] codes, respectively. There have been many studies over the decades that examined the accuracy of such solvers and the general conclusion is that when the problems are well-posed, either solver can produce accurate results. However, the devil is always in the details. The current study examines the issue of self-shielding and the stress it puts on deterministic solvers. Most Monte Carlo neutronics codes use continuous-energy descriptions of the neutron interaction data that are not subject to this effect. The issue of self-shielding occurs because of the discretisation of data used by the deterministic solutions. Multigroup data used in these solvers are the average cross section and scattering parameters over an energy range. Resonances in cross sections can occur that change the likelihood of interaction by one to three orders of magnitude over a small energy range. Self-shielding is the numerical effect that the average cross section in groups with strong resonances can be strongly affected as neutrons within that material are preferentially absorbed or scattered out of the resonance energies. This affects both the average cross section and the scattering matrix.
ELSI: A unified software interface for Kohn-Sham electronic structure solvers
Yu, Victor Wen-zhe; Corsetti, Fabiano; García, Alberto; Huhn, William P.; Jacquelin, Mathias; Jia, Weile; Lange, Björn; Lin, Lin; Lu, Jianfeng; Mi, Wenhui; Seifitokaldani, Ali; Vázquez-Mayagoitia, Álvaro; Yang, Chao; Yang, Haizhao; Blum, Volker
2018-01-01
Solving the electronic structure from a generalized or standard eigenproblem is often the bottleneck in large scale calculations based on Kohn-Sham density-functional theory. This problem must be addressed by essentially all current electronic structure codes, based on similar matrix expressions, and by high-performance computation. We here present a unified software interface, ELSI, to access different strategies that address the Kohn-Sham eigenvalue problem. Currently supported algorithms include the dense generalized eigensolver library ELPA, the orbital minimization method implemented in libOMM, and the pole expansion and selected inversion (PEXSI) approach with lower computational complexity for semilocal density functionals. The ELSI interface aims to simplify the implementation and optimal use of the different strategies, by offering (a) a unified software framework designed for the electronic structure solvers in Kohn-Sham density-functional theory; (b) reasonable default parameters for a chosen solver; (c) automatic conversion between input and internal working matrix formats, and in the future (d) recommendation of the optimal solver depending on the specific problem. Comparative benchmarks are shown for system sizes up to 11,520 atoms (172,800 basis functions) on distributed memory supercomputing architectures.
International Nuclear Information System (INIS)
Turinsky, P.J.; Al-Chalabi, R.M.K.; Engrand, P.; Sarsour, H.N.; Faure, F.X.; Guo, W.
1994-06-01
NESTLE is a FORTRAN77 code that solves the few-group neutron diffusion equation utilizing the Nodal Expansion Method (NEM). NESTLE can solve the eigenvalue (criticality); eigenvalue adjoint; external fixed-source steady-state; or external fixed-source. or eigenvalue initiated transient problems. The code name NESTLE originates from the multi-problem solution capability, abbreviating Nodal Eigenvalue, Steady-state, Transient, Le core Evaluator. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two or four energy groups can be utilized, with all energy groups being thermal groups (i.e. upscatter exits) if desired. Core geometries modelled include Cartesian and Hexagonal. Three, two and one dimensional models can be utilized with various symmetries. The non-linear iterative strategy associated with the NEM method is employed. An advantage of the non-linear iterative strategy is that NSTLE can be utilized to solve either the nodal or Finite Difference Method representation of the few-group neutron diffusion equation
A General Solution Framework for Component-Commonality Problems
Directory of Open Access Journals (Sweden)
Nils Boysen
2009-05-01
Full Text Available Component commonality - the use of the same version of a component across multiple products - is being increasingly considered as a promising way to offer high external variety while retaining low internal variety in operations. However, increasing commonality has both positive and negative cost effects, so that optimization approaches are required to identify an optimal commonality level. As components influence to a greater or lesser extent nearly every process step along the supply chain, it is not surprising that a multitude of diverging commonality problems is being investigated in literature, each of which are developing a specific algorithm designed for the respective commonality problem being considered. The paper on hand aims at a general framework which is flexible and efficient enough to be applied to a wide range of commonality problems. Such a procedure based on a two-stage graph approach is presented and tested. Finally, flexibility of the procedure is shown by customizing the framework to account for different types of commonality problems.
The problem of time quantum mechanics versus general relativity
Anderson, Edward
2017-01-01
This book is a treatise on time and on background independence in physics. It first considers how time is conceived of in each accepted paradigm of physics: Newtonian, special relativity, quantum mechanics (QM) and general relativity (GR). Substantial differences are moreover uncovered between what is meant by time in QM and in GR. These differences jointly source the Problem of Time: Nine interlinked facets which arise upon attempting concurrent treatment of the QM and GR paradigms, as is required in particular for a background independent theory of quantum gravity. A sizeable proportion of current quantum gravity programs - e.g. geometrodynamical and loop quantum gravity approaches to quantum GR, quantum cosmology, supergravity and M-theory - are background independent in this sense. This book's foundational topic is thus furthermore of practical relevance in the ongoing development of quantum gravity programs. This book shows moreover that eight of the nine facets of the Problem of Time already occur upon ...
Spectrum of general surgical problems in the developmentally disabled adults
International Nuclear Information System (INIS)
Khalid, K.; Al-Salamah, Saleh M.
2006-01-01
This study highlights the spectrum of general surgical problems necessitating admission on intellectually disabled adult patients. Problems encountered in the management and the ways to overcome various difficulties are highlighted. Prospective collection of data on 63 consecutive developmentally disabled adult patients admitted to the Department of General Surgery, Riyadh Medical Complex (RMC), Riyadh, Kingdom of Saudi Arabia for various indications from January 2000 through December 2004. Demographic details, clinical presentation, diagnostic modalities, associated physical and neurological disabilities, coexisting medical condition, treatment options, morbidity and mortality were analyzed. Various difficulties encountered during the management and mean to overcome these problems are addressed. Sixty-three patients accounted for 71 admissions. Mean age was 26.7 years with a male preponderance (4.25:1). Fifty-four patients were admitted for various emergency conditions. History of pica could be obtained in 33% of the cases. Twenty-seven patients were admitted for acute abdomen. Volvulus of the colon (22.2%) and pseudo-obstruction (18.5%) were the most common causes of acute abdomen. Twenty-one patients were admitted with upper gastrointestinal bleeding. Reflux esophagitis was the most common cause of bleeding (62%). Overall morbidity was 41% for emergency admissions and 22% for elective surgery. Hospital mortality was 21.4% for emergency surgery. There was no death in elective cases. Developmentally disabled patients comprise a special class of patients with peculiar management problems. The treating clinician should be aware of various unexpected conditions not found as frequently in the normal patient population. Apparent lack of pain does not exclude an acute emergency. Possible surgical condition should be suspected if there is vomiting, abdominal distension, fever, increased irritability of recent onset. Male gender and history of pica are added risk factors
Directory of Open Access Journals (Sweden)
X. Zhao
2012-01-01
Full Text Available A combined interior point homotopy continuation method is proposed for solving general multiobjective programming problem. We prove the existence and convergence of a smooth homotopy path from almost any interior initial interior point to a solution of the KKT system under some basic assumptions.
Non-integrability of the generalized spring-pendulum problem
International Nuclear Information System (INIS)
Maciejewski, Andrzej J; Przybylska, Maria; Weil, Jacques-Arthur
2004-01-01
We investigate a generalization of the three-dimensional spring-pendulum system. The problem depends on two real parameters (k, a), where k is the Young modulus of the spring and a describes the nonlinearity of elastic forces. We show that this system is not integrable when k ≠ -a. We carefully investigated the case k = -a when the necessary condition for integrability given by the Morales-Ruiz-Ramis theory is satisfied. We discuss an application of the higher order variational equations for proving the non-integrability in this case
Generalized Mixed Equilibria, Variational Inclusions, and Fixed Point Problems
Directory of Open Access Journals (Sweden)
A. E. Al-Mazrooei
2014-01-01
Full Text Available We propose two iterative algorithms for finding a common element of the set of solutions of finite generalized mixed equilibrium problems, the set of solutions of finite variational inclusions for maximal monotone and inverse strong monotone mappings, and the set of common fixed points of infinite nonexpansive mappings and an asymptotically κ-strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove some strong and weak convergence theorems for the proposed iterative algorithms under suitable conditions.
A robust multilevel simultaneous eigenvalue solver
Costiner, Sorin; Taasan, Shlomo
1993-01-01
Multilevel (ML) algorithms for eigenvalue problems are often faced with several types of difficulties such as: the mixing of approximated eigenvectors by the solution process, the approximation of incomplete clusters of eigenvectors, the poor representation of solution on coarse levels, and the existence of close or equal eigenvalues. Algorithms that do not treat appropriately these difficulties usually fail, or their performance degrades when facing them. These issues motivated the development of a robust adaptive ML algorithm which treats these difficulties, for the calculation of a few eigenvectors and their corresponding eigenvalues. The main techniques used in the new algorithm include: the adaptive completion and separation of the relevant clusters on different levels, the simultaneous treatment of solutions within each cluster, and the robustness tests which monitor the algorithm's efficiency and convergence. The eigenvectors' separation efficiency is based on a new ML projection technique generalizing the Rayleigh Ritz projection, combined with a technique, the backrotations. These separation techniques, when combined with an FMG formulation, in many cases lead to algorithms of O(qN) complexity, for q eigenvectors of size N on the finest level. Previously developed ML algorithms are less focused on the mentioned difficulties. Moreover, algorithms which employ fine level separation techniques are of O(q(sub 2)N) complexity and usually do not overcome all these difficulties. Computational examples are presented where Schrodinger type eigenvalue problems in 2-D and 3-D, having equal and closely clustered eigenvalues, are solved with the efficiency of the Poisson multigrid solver. A second order approximation is obtained in O(qN) work, where the total computational work is equivalent to only a few fine level relaxations per eigenvector.
Parallel iterative solvers and preconditioners using approximate hierarchical methods
Energy Technology Data Exchange (ETDEWEB)
Grama, A.; Kumar, V.; Sameh, A. [Univ. of Minnesota, Minneapolis, MN (United States)
1996-12-31
In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES solver for Boundary Element Methods. The solver uses a hierarchical approximate matrix-vector product based on a hybrid Barnes-Hut / Fast Multipole Method. We study the impact of various accuracy parameters on the convergence and show that with minimal loss in accuracy, our solver yields significant speedups. We demonstrate the excellent parallel efficiency and scalability of our solver. The combined speedups from approximation and parallelism represent an improvement of several orders in solution time. We also develop fast and paralellizable preconditioners for this problem. We report on the performance of an inner-outer scheme and a preconditioner based on truncated Green`s function. Experimental results on a 256 processor Cray T3D are presented.
DEFF Research Database (Denmark)
Bjørner, Nikolaj; Dung, Phan Anh; Fleckenstein, Lars
2015-01-01
Z provides a portfolio of approaches for solving linear optimization problems over SMT formulas, MaxSMT, and their combinations. Objective functions are combined as either Pareto fronts, lexicographically, or each objective is optimized independently. We describe usage scenarios of vZ, outline the tool......vZ is a part of the SMT solver Z3. It allows users to pose and solve optimization problems modulo theories. Many SMT applications use models to provide satisfying assignments, and a growing number of these build on top of Z3 to get optimal assignments with respect to objective functions. v...
Origins and development of the Cauchy problem in general relativity
Ringström, Hans
2015-06-01
The seminal work of Yvonne Choquet-Bruhat published in 1952 demonstrates that it is possible to formulate Einstein's equations as an initial value problem. The purpose of this article is to describe the background to and impact of this achievement, as well as the result itself. In some respects, the idea of viewing the field equations of general relativity as a system of evolution equations goes back to Einstein himself; in an argument justifying that gravitational waves propagate at the speed of light, Einstein used a special choice of coordinates to derive a system of wave equations for the linear perturbations on a Minkowski background. Over the following decades, Hilbert, de Donder, Lanczos, Darmois and many others worked to put Einstein's ideas on a more solid footing. In fact, the issue of local uniqueness (giving a rigorous justification for the statement that the speed of propagation of the gravitational field is bounded by that of light) was already settled in the 1930s by the work of Stellmacher. However, the first person to demonstrate both local existence and uniqueness in a setting in which the notion of finite speed of propagation makes sense was Yvonne Choquet-Bruhat. In this sense, her work lays the foundation for the formulation of Einstein's equations as an initial value problem. Following a description of the results of Choquet-Bruhat, we discuss the development of three research topics that have their origin in her work. The first one is local existence. One reason for addressing it is that it is at the heart of the original paper. Moreover, it is still an active and important research field, connected to the problem of characterizing the asymptotic behaviour of solutions that blow up in finite time. As a second topic, we turn to the questions of global uniqueness and strong cosmic censorship. These questions are of fundamental importance to anyone interested in justifying that the Cauchy problem makes sense globally. They are also closely
Good, L. H.; Erickson, A.
2016-02-01
Academic learning and research experiences alone cannot prepare our emerging ocean leaders to take on the challenges facing our oceans. Developing solutions that incorporate environmental and ocean sciences necessitates an interdisciplinary approach, requiring emerging leaders to be able to work in collaborative knowledge to action systems, rather than on micro-discipline islands. Professional and informal learning experiences can enhance graduate marine education by helping learners gain the communication, collaboration, and innovative problem-solving skills necessary for them to interact with peers at the interface of science and policy. These rich experiences can also provide case-based and hands-on opportunities for graduate learners to explore real-world examples of ocean science, policy, and management in action. However, academic programs are often limited in their capacity to offer such experiences as a part of a traditional curriculum. Rather than expecting learners to rely on their academic training, one approach is to encourage and support graduates to seek professional development beyond their university's walls, and think more holistically about their learning as it relates to their career interests. During this session we discuss current thinking around the professional learning needs of emerging ocean leaders, what this means for academic epistemologies, and examine initial evaluation outcomes from activities in our cross-campus consortium model in Monterey Bay, California. This innovative model includes seven regional academic institutions working together to develop an interdisciplinary ocean community and increase access to professional development opportunities to better prepare regional ocean-interested graduate students and early career researchers as future leaders.
A GPU-enabled Finite Volume solver for global magnetospheric simulations on unstructured grids
Lani, Andrea; Yalim, Mehmet Sarp; Poedts, Stefaan
2014-10-01
This paper describes an ideal Magnetohydrodynamics (MHD) solver for global magnetospheric simulations based on a B1 +B0 splitting approach, which has been implemented within the COOLFluiD platform and adapted to run on modern heterogeneous architectures featuring General Purpose Graphical Processing Units (GPGPUs). The code is based on a state-of-the-art Finite Volume discretization for unstructured grids and either explicit or implicit time integration, suitable for both steady and time accurate problems. Innovative object-oriented design and coding techniques mixing C++ and CUDA are discussed. Performance results of the modified code on single and multiple processors are presented and compared with those provided by the original solver.
An efficient iterative method for the generalized Stokes problem
Energy Technology Data Exchange (ETDEWEB)
Sameh, A. [Univ. of Minnesota, Twin Cities, MN (United States); Sarin, V. [Univ. of Illinois, Urbana, IL (United States)
1996-12-31
This paper presents an efficient iterative scheme for the generalized Stokes problem, which arises frequently in the simulation of time-dependent Navier-Stokes equations for incompressible fluid flow. The general form of the linear system is where A = {alpha}M + vT is an n x n symmetric positive definite matrix, in which M is the mass matrix, T is the discrete Laplace operator, {alpha} and {nu} are positive constants proportional to the inverses of the time-step {Delta}t and the Reynolds number Re respectively, and B is the discrete gradient operator of size n x k (k < n). Even though the matrix A is symmetric and positive definite, the system is indefinite due to the incompressibility constraint (B{sup T}u = 0). This causes difficulties both for iterative methods and commonly used preconditioners. Moreover, depending on the ratio {alpha}/{nu}, A behaves like the mass matrix M at one extreme and the Laplace operator T at the other, thus complicating the issue of preconditioning.
Topological approach to the generalized n-centre problem
Bolotin, S. V.; Kozlov, V. V.
2017-06-01
This paper considers a natural Hamiltonian system with two degrees of freedom and Hamiltonian H=\\Vert p\\Vert^2/2+V(q). The configuration space M is a closed surface (for non-compact M certain conditions at infinity are required). It is well known that if the potential energy V has n>2χ(M) Newtonian singularities, then the system is not integrable and has positive topological entropy on the energy level H=h>\\sup V. This result is generalized here to the case when the potential energy has several singular points a_j of type V(q)∼ -\\operatorname{dist}(q,a_j)-α_j. Let A_k=2-2k-1, k\\in{N}, and let n_k be the number of singular points with A_k≤slant α_jk+1. It is proved that if \\displaystyle \\sum2≤slant k≤slant∞n_kA_k>2χ(M), then the system has a compact chaotic invariant set of collision-free trajectories on any energy level H=h>\\sup V. This result is purely topological: no analytical properties of the potential energy are used except the presence of singularities. The proofs are based on the generalized Levi-Civita regularization and elementary topology of coverings. As an example, the plane n-centre problem is considered. Bibliography: 29 titles.
Directory of Open Access Journals (Sweden)
Álvaro Bernal
2014-01-01
Full Text Available Numerical methods are usually required to solve the neutron diffusion equation applied to nuclear reactors due to its heterogeneous nature. The most popular numerical techniques are the Finite Difference Method (FDM, the Coarse Mesh Finite Difference Method (CFMD, the Nodal Expansion Method (NEM, and the Nodal Collocation Method (NCM, used virtually in all neutronic diffusion codes, which give accurate results in structured meshes. However, the application of these methods in unstructured meshes to deal with complex geometries is not straightforward and it may cause problems of stability and convergence of the solution. By contrast, the Finite Element Method (FEM and the Finite Volume Method (FVM are easily applied to unstructured meshes. On the one hand, the FEM can be accurate for smoothly varying functions. On the other hand, the FVM is typically used in the transport equations due to the conservation of the transported quantity within the volume. In this paper, the FVM algorithm implemented in the ARB Partial Differential Equations solver has been used to discretize the neutron diffusion equation to obtain the matrices of the generalized eigenvalue problem, which has been solved by means of the SLEPc library.
Parallel linear solvers for simulations of reactor thermal hydraulics
International Nuclear Information System (INIS)
Yan, Y.; Antal, S.P.; Edge, B.; Keyes, D.E.; Shaver, D.; Bolotnov, I.A.; Podowski, M.Z.
2011-01-01
The state-of-the-art multiphase fluid dynamics code, NPHASE-CMFD, performs multiphase flow simulations in complex domains using implicit nonlinear treatment of the governing equations and in parallel, which is a very challenging environment for the linear solver. The present work illustrates how the Portable, Extensible Toolkit for Scientific Computation (PETSc) and scalable Algebraic Multigrid (AMG) preconditioner from Hypre can be utilized to construct robust and scalable linear solvers for the Newton correction equation obtained from the discretized system of governing conservation equations in NPHASE-CMFD. The overall long-tem objective of this work is to extend the NPHASE-CMFD code into a fully-scalable solver of multiphase flow and heat transfer problems, applicable to both steady-state and stiff time-dependent phenomena in complete fuel assemblies of nuclear reactors and, eventually, the entire reactor core (such as the Virtual Reactor concept envisioned by CASL). This campaign appropriately begins with the linear algebraic equation solver, which is traditionally a bottleneck to scalability in PDE-based codes. The computational complexity of the solver is usually superlinear in problem size, whereas the rest of the code, the “physics” portion, usually has its complexity linear in the problem size. (author)
Limited Data Problems for the Generalized Radon Transform in Rn
DEFF Research Database (Denmark)
Frikel, Jürgen; Quinto, Eric Todd
2016-01-01
We consider the generalized Radon transform (defined in terms of smooth weight functions) on hyperplanes in Rn. We analyze general filtered backprojection type reconstruction methods for limited data with filters given by general pseudodifferential operators. We provide microlocal characterizatio...
Molecular biology problem solver : a laboratory guide
National Research Council Canada - National Science Library
Gerstein, Alan S., 1957
2001-01-01
... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Chapter 1. Preparing for Success in the Laboratory Phillip P. Franciskovich . . . . . . . . . . . . . . . . . . . . . . . . 1 Chapter 2. Getting What You Need...
Molecular biology problem solver: a laboratory guide
National Research Council Canada - National Science Library
Gerstein, Alan S
2001-01-01
... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Chapter 1. Preparing for Success in the Laboratory Phillip P. Franciskovich . . . . . . . . . . . . . . . . . . . . . . . . 1 Chapter 2. Getting What You Need...
Equipping the enterprise interoperability problem solver
Oude Luttighuis, P.; Folmer, E.J.A.
2011-01-01
The maturity of the enterprise interoperability field does not match the importance attached to it by many, both in the public as well as the private community. A host of models, paradigms, designs, standards, methods, and instruments seems to be available, but many of them are only used in rather
Equipping the Enterprise Interoperability Problem Solver
Oude Luttighuis, Paul; Folmer, Erwin Johan Albert; Charalabidis, Yannis
2010-01-01
The maturity of the enterprise interoperability field does not match the importance attached to it by many, both in the public as well as the private community. A host of models, paradigms, designs, standards, methods, and instruments seems to be available, but many of them are only used in rather
Needed: A New Generation of Problem Solvers
McArthur, John W.; Sachs, Jeffrey
2009-01-01
Amid the global economic crisis dominating policy makers' recent attention, the world faces many other equal if not greater long-term challenges that will require concerted and highly skilled policy efforts in coming years. Those interwoven challenges include the mitigation of climate change, the control of emerging diseases, the reduction of…
Fast solvers for concentrated elastic contact problems
Zhao, J.
2015-01-01
Rail transportation plays an important role in our everyday life, and there is fast development and modernization in the railway industry to meet the growing demand for swifter, safer and more comfortable trains. At the same time, the security of train operation and the maintenance of rails have to
Refined isogeometric analysis for a preconditioned conjugate gradient solver
Garcia, Daniel
2018-02-12
Starting from a highly continuous Isogeometric Analysis (IGA) discretization, refined Isogeometric Analysis (rIGA) introduces C0 hyperplanes that act as separators for the direct LU factorization solver. As a result, the total computational cost required to solve the corresponding system of equations using a direct LU factorization solver dramatically reduces (up to a factor of 55) Garcia et al. (2017). At the same time, rIGA enriches the IGA spaces, thus improving the best approximation error. In this work, we extend the complexity analysis of rIGA to the case of iterative solvers. We build an iterative solver as follows: we first construct the Schur complements using a direct solver over small subdomains (macro-elements). We then assemble those Schur complements into a global skeleton system. Subsequently, we solve this system iteratively using Conjugate Gradients (CG) with an incomplete LU (ILU) preconditioner. For a 2D Poisson model problem with a structured mesh and a uniform polynomial degree of approximation, rIGA achieves moderate savings with respect to IGA in terms of the number of Floating Point Operations (FLOPs) and computational time (in seconds) required to solve the resulting system of linear equations. For instance, for a mesh with four million elements and polynomial degree p=3, the iterative solver is approximately 2.6 times faster (in time) when applied to the rIGA system than to the IGA one. These savings occur because the skeleton rIGA system contains fewer non-zero entries than the IGA one. The opposite situation occurs for 3D problems, and as a result, 3D rIGA discretizations provide no gains with respect to their IGA counterparts when considering iterative solvers.
Efficient Implementation of the Riccati Recursion for Solving Linear-Quadratic Control Problems
DEFF Research Database (Denmark)
Frison, Gianluca; Jørgensen, John Bagterp
2013-01-01
. In this paper, we compare a number of solvers for an extended formulation of the LQ control problem: a Riccati recursion based solver can be considered the best choice for the general problem with dense matrices. Furthermore, we present a novel version of the Riccati solver, that makes use of the Cholesky......In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is typically the main computational effort at each iteration...... factorization of the Pn matrices to reduce the number of flops. When combined with regularization and mixed precision, this algorithm can solve large instances of the LQ control problem up to 3 times faster than the classical Riccati solver....
Utility Generalization and Composability Problems in Explanation-Based Learning.
Gratch, Jonathan M.; DeJong, Gerald F.
The PRODIGY/EBL system [Minton88] was one of the first works to directly attack the problem of strategy utility. The problem of finding effective strategies was reduced to the problem of finding effective rules. However, this paper illustrates limitations of the approach. There are two basic difficulties. The first arises from the fact that the…
A moving-mesh hydrodynamic solver for ChaNGa
Chang, Philip; Wadsley, James; Quinn, Thomas R.
2017-11-01
We describe the structure and implementation of a moving-mesh (MM) hydrodynamics (HD) solver in the large-scale parallel code, Charm N-body GrAvity solver (ChaNGa). While largely based on the algorithm implemented in AREPO, our implementation differs a few aspects. We describe our use of the Voronoi tessellation library, VORO++, to compute the Voronoi tessellation directly. We also incorporate some recent advances in gradient estimation and reconstruction that gives better accuracy in HD solutions at minimal computational cost. We validate this module with a small battery of test problems against the smooth particle HD solver included in ChaNGa. Finally, we study one example of a scientific problem involving the mergers of two main-sequence stars and highlight the small quantitative differences between smooth particle and MM HD. We close with a discussion of anticipated future improvements and advancements.
Optimising a parallel conjugate gradient solver
Energy Technology Data Exchange (ETDEWEB)
Field, M.R. [O`Reilly Institute, Dublin (Ireland)
1996-12-31
This work arises from the introduction of a parallel iterative solver to a large structural analysis finite element code. The code is called FEX and it was developed at Hitachi`s Mechanical Engineering Laboratory. The FEX package can deal with a large range of structural analysis problems using a large number of finite element techniques. FEX can solve either stress or thermal analysis problems of a range of different types from plane stress to a full three-dimensional model. These problems can consist of a number of different materials which can be modelled by a range of material models. The structure being modelled can have the load applied at either a point or a surface, or by a pressure, a centrifugal force or just gravity. Alternatively a thermal load can be applied with a given initial temperature. The displacement of the structure can be constrained by having a fixed boundary or by prescribing the displacement at a boundary.
Fuzzy Generalized Variational Like Inequality problems in Topological Vector Spaces
Directory of Open Access Journals (Sweden)
M. K. Ahmad
2013-01-01
Full Text Available This paper is devoted to the existence of solutions for generalized variational like inequalities with fuzzy mappings in topological vector spaces by using a particular form of the generalized KKM-Theorem.
Institutional Problems and Solutions of General Education in Chinese Universities
Meng, Weiqing; Huang, Wei
2018-01-01
Embedding general education in the Chinese university education system is a considerably complex systemic project, and a lack of institutional arrangements beneficial to general education has always been a key barrier in implementation. Currently, the main institutional restricting factors for university general education include substantial…
Directory of Open Access Journals (Sweden)
Mohammed Zia
2018-03-01
Full Text Available The Equality-Generalized Travelling Salesman Problem (E-GTSP, which is an extension of the Travelling Salesman Problem (TSP, is stated as follows: given groups of points within a city, like banks, supermarkets, etc., find a minimum cost Hamiltonian cycle that visits each group exactly once. It can model many real-life combinatorial optimization scenarios more efficiently than TSP. This study presents five spatially driven search-algorithms for possible transformation of E-GTSP to TSP by considering the spatial spread of points in a given urban city. Presented algorithms are tested over 15 different cities, classified by their street-network’s fractal-dimension. Obtained results denote that the R-Search algorithm, which selects the points from each group based on their radial separation with respect to the start–end point, is the best search criterion for any E-GTSP to TSP conversion modelled for a city street network. An 8.8% length error has been reported for this algorithm.
Iterative solvers in forming process simulations
van den Boogaard, Antonius H.; Rietman, Bert; Huetink, Han
1998-01-01
The use of iterative solvers in implicit forming process simulations is studied. The time and memory requirements are compared with direct solvers and assessed in relation with the rest of the Newton-Raphson iteration process. It is shown that conjugate gradient{like solvers with a proper
A real-time Grad-Shafranov PDE solver and MIMO controller
Energy Technology Data Exchange (ETDEWEB)
Barp, A.; Cerna, M.; Concezzi, S. [National Instruments, Austin, TX 78759-3504 (United States); Giannone, L. [Max-Planck-Institute for Plasma Physics, EURATOM-IPP Association, D-85748 Garching (Germany); Morrow, G. [National Instruments, Austin, TX 78759-3504 (United States); Ruan, Q., E-mail: qing.ruan@ni.com [National Instruments, Austin, TX 78759-3504 (United States); Veeramani, A.; Wenzel, L. [National Instruments, Austin, TX 78759-3504 (United States)
2012-12-15
Highlights: Black-Right-Pointing-Pointer Introduce a spectral algorithm based Grad-Shafranov equation solver. Black-Right-Pointing-Pointer Implement the solver using LabVIEW with cycle time less than 1 ms. Black-Right-Pointing-Pointer Benchmark the redesign of a MIMO controller. - Abstract: Plasma control experiments require enormous computational power to solve large problems with critical time constraints. For tokamak control, the non-linear and constrained Grad-Shafranov equation needs to be solved in real-time with a cycle time of less than 1 ms. A new algorithm for the solution of this equation based on discrete sine transforms and a tridiagonal solver rather than the commonly used cyclic reduction algorithm is presented. Input signals from magnetic probes and flux loops are the constraints for the equation that must be continuously solved to calculate the magnetic equilibrium. A number of novel mathematical ideas were introduced and several generally applicable numerical strategies were developed using LabVIEW graphical dataflow programming to meet the critical timing goals. Benchmarks on CPUs are reported. Furthermore, the design of a MIMO (multiple input and output) controller to demonstrate the possibilities of tokamak position and shape control using graphical dataflow programming is discussed.
International Nuclear Information System (INIS)
Lozano, Juan-Andres; Garcia-Herranz, Nuria; Ahnert, Carol; Aragones, Jose-Maria
2008-01-01
In this work we address the development and implementation of the analytic coarse-mesh finite-difference (ACMFD) method in a nodal neutron diffusion solver called ANDES. The first version of the solver is implemented in any number of neutron energy groups, and in 3D Cartesian geometries; thus it mainly addresses PWR and BWR core simulations. The details about the generalization to multigroups and 3D, as well as the implementation of the method are given. The transverse integration procedure is the scheme chosen to extend the ACMFD formulation to multidimensional problems. The role of the transverse leakage treatment in the accuracy of the nodal solutions is analyzed in detail: the involved assumptions, the limitations of the method in terms of nodal width, the alternative approaches to implement the transverse leakage terms in nodal methods - implicit or explicit -, and the error assessment due to transverse integration. A new approach for solving the control rod 'cusping' problem, based on the direct application of the ACMFD method, is also developed and implemented in ANDES. The solver architecture turns ANDES into an user-friendly, modular and easily linkable tool, as required to be integrated into common software platforms for multi-scale and multi-physics simulations. ANDES can be used either as a stand-alone nodal code or as a solver to accelerate the convergence of whole core pin-by-pin code systems. The verification and performance of the solver are demonstrated using both proof-of-principle test cases and well-referenced international benchmarks
Szeto, Alan Ka-Fai
This study explored how undergraduate students in a new problem-centered General Chemistry Laboratory curriculum achieved cognitive growth. The new curriculum had three instructional segments: the highly-structured, semi-structured, and open-ended segments. The pedagogical approaches adopted were expository, guided-inquiry, and open-inquiry styles, respectively. Sixty-seven first-year undergraduate students who enrolled in the course in Spring semester, 2000, at Columbia University and three Ph.D.-level chemistry experts were included in the study. A qualitative approach was used including data collection through "think-aloud" problem solving; however, quantitative data such as test scores were also used. The findings from this study confirmed that chemistry experts possessed sophisticated and domain-specific conceptual knowledge structures; they mobilized and applied conceptual knowledge in conjunction with use of heuristics, tacit knowledge, and experience in authentic problem solving. They validated the new curriculum design in preparing students for inquiry-type of problem solving. For novices, solving of semi-structured before ill-structured problems had a positive effect on the solvers' chance of success in solving the latter type of problems as their abilities to mobilize and apply conceptual knowledge and use effective strategies appeared to be critical for successful problem solving. Students in the new course curriculum had grown cognitively as evidenced by their performance on the Case Study projects and Final Examination. High academic achievers were found to perform well independently while the medium and relatively low academic achievers should benefit from sustained and intensive instruction. It is proposed that ill-structured problems should be used to assess and identify the best from the better students. Finally, it was found that no significant change in students' attitudes had resulted from their curriculum experience. Gender and cognitive style
Multilevel solvers of first-order system least-squares for Stokes equations
Energy Technology Data Exchange (ETDEWEB)
Lai, Chen-Yao G. [National Chung Cheng Univ., Chia-Yi (Taiwan, Province of China)
1996-12-31
Recently, The use of first-order system least squares principle for the approximate solution of Stokes problems has been extensively studied by Cai, Manteuffel, and McCormick. In this paper, we study multilevel solvers of first-order system least-squares method for the generalized Stokes equations based on the velocity-vorticity-pressure formulation in three dimensions. The least-squares functionals is defined to be the sum of the L{sup 2}-norms of the residuals, which is weighted appropriately by the Reynolds number. We develop convergence analysis for additive and multiplicative multilevel methods applied to the resulting discrete equations.
LAPACKrc: Fast linear algebra kernels/solvers for FPGA accelerators
International Nuclear Information System (INIS)
Gonzalez, Juan; Nunez, Rafael C
2009-01-01
We present LAPACKrc, a family of FPGA-based linear algebra solvers able to achieve more than 100x speedup per commodity processor on certain problems. LAPACKrc subsumes some of the LAPACK and ScaLAPACK functionalities, and it also incorporates sparse direct and iterative matrix solvers. Current LAPACKrc prototypes demonstrate between 40x-150x speedup compared against top-of-the-line hardware/software systems. A technology roadmap is in place to validate current performance of LAPACKrc in HPC applications, and to increase the computational throughput by factors of hundreds within the next few years.
A RADIATION TRANSFER SOLVER FOR ATHENA USING SHORT CHARACTERISTICS
International Nuclear Information System (INIS)
Davis, Shane W.; Stone, James M.; Jiang Yanfei
2012-01-01
We describe the implementation of a module for the Athena magnetohydrodynamics (MHD) code that solves the time-independent, multi-frequency radiative transfer (RT) equation on multidimensional Cartesian simulation domains, including scattering and non-local thermodynamic equilibrium (LTE) effects. The module is based on well known and well tested algorithms developed for modeling stellar atmospheres, including the method of short characteristics to solve the RT equation, accelerated Lambda iteration to handle scattering and non-LTE effects, and parallelization via domain decomposition. The module serves several purposes: it can be used to generate spectra and images, to compute a variable Eddington tensor (VET) for full radiation MHD simulations, and to calculate the heating and cooling source terms in the MHD equations in flows where radiation pressure is small compared with gas pressure. For the latter case, the module is combined with the standard MHD integrators using operator splitting: we describe this approach in detail, including a new constraint on the time step for stability due to radiation diffusion modes. Implementation of the VET method for radiation pressure dominated flows is described in a companion paper. We present results from a suite of test problems for both the RT solver itself and for dynamical problems that include radiative heating and cooling. These tests demonstrate that the radiative transfer solution is accurate and confirm that the operator split method is stable, convergent, and efficient for problems of interest. We demonstrate there is no need to adopt ad hoc assumptions of questionable accuracy to solve RT problems in concert with MHD: the computational cost for our general-purpose module for simple (e.g., LTE gray) problems can be comparable to or less than a single time step of Athena's MHD integrators, and only few times more expensive than that for more general (non-LTE) problems.
Advanced Algebraic Multigrid Solvers for Subsurface Flow Simulation
Chen, Meng-Huo
2015-09-13
In this research we are particularly interested in extending the robustness of multigrid solvers to encounter complex systems related to subsurface reservoir applications for flow problems in porous media. In many cases, the step for solving the pressure filed in subsurface flow simulation becomes a bottleneck for the performance of the simulator. For solving large sparse linear system arising from MPFA discretization, we choose multigrid methods as the linear solver. The possible difficulties and issues will be addressed and the corresponding remedies will be studied. As the multigrid methods are used as the linear solver, the simulator can be parallelized (although not trivial) and the high-resolution simulation become feasible, the ultimately goal which we desire to achieve.
An efficient spectral crystal plasticity solver for GPU architectures
Malahe, Michael
2018-03-01
We present a spectral crystal plasticity (CP) solver for graphics processing unit (GPU) architectures that achieves a tenfold increase in efficiency over prior GPU solvers. The approach makes use of a database containing a spectral decomposition of CP simulations performed using a conventional iterative solver over a parameter space of crystal orientations and applied velocity gradients. The key improvements in efficiency come from reducing global memory transactions, exposing more instruction-level parallelism, reducing integer instructions and performing fast range reductions on trigonometric arguments. The scheme also makes more efficient use of memory than prior work, allowing for larger problems to be solved on a single GPU. We illustrate these improvements with a simulation of 390 million crystal grains on a consumer-grade GPU, which executes at a rate of 2.72 s per strain step.
Top Element Problem and Macneille Completions of Generalized Effect Algebras
RieČanová, Z.; Kalina, M.
2014-10-01
Effect algebras (EAs), introduced by D. J. Foulis and M. K. Bennett, as common generalizations of Boolean algebras, orthomodular lattices and MV-algebras, are nondistributive algebraic structures including unsharp elements. Their unbounded versions, called generalized effect algebras, are posets which may have or may have not an EA-MacNeille completion, or cannot be embedded into any complete effect algebra. We give a necessary and sufficient condition for a generalized effect algebra to have an EA-MacNeille completion. Some examples are provided.
MINOS: A simplified Pn solver for core calculation
International Nuclear Information System (INIS)
Baudron, A.M.; Lautard, J.J.
2007-01-01
This paper describes a new generation of the neutronic core solver MINOS resulting from developments done in the DESCARTES project. For performance reasons, the numerical method of the existing MINOS solver in the SAPHYR system has been reused in the new system. It is based on the mixed-dual finite element approximation of the simplified transport equation. We have extended the previous method to the treatment of unstructured geometries composed by quadrilaterals, allowing us to treat geometries where fuel pins are exactly represented. For Cartesian geometries, the solver takes into account assembly discontinuity coefficients in the simplified P n context. The solver has been rewritten in C + + programming language using an object-oriented design. Its general architecture was reconsidered in order to improve its capability of evolution and its maintainability. Moreover, the performance of the previous version has been improved mainly regarding the matrix construction time; this result improves significantly the performance of the solver in the context of industrial application requiring thermal-hydraulic feedback and depletion calculations. (authors)
Fast Euler solver for transonic airfoils. I - Theory. II - Applications
Dadone, Andrea; Moretti, Gino
1988-01-01
Equations written in terms of generalized Riemann variables are presently integrated by inverting six bidiagonal matrices and two tridiagonal matrices, using an implicit Euler solver that is based on the lambda-formulation. The solution is found on a C-grid whose boundaries are very close to the airfoil. The fast solver is then applied to the computation of several flowfields on a NACA 0012 airfoil at various Mach number and alpha values, yielding results that are primarily concerned with transonic flows. The effects of grid fineness and boundary distances are analyzed; the code is found to be robust and accurate, as well as fast.
Optimal portfolio selection for general provisioning and terminal wealth problems
van Weert, K.; Dhaene, J.; Goovaerts, M.
2010-01-01
In Dhaene et al. (2005), multiperiod portfolio selection problems are discussed, using an analytical approach to find optimal constant mix investment strategies in a provisioning or a savings context. In this paper we extend some of these results, investigating some specific, real-life situations.
Optimal portfolio selection for general provisioning and terminal wealth problems
van Weert, K.; Dhaene, J.; Goovaerts, M.
2009-01-01
In Dhaene et al. (2005), multiperiod portfolio selection problems are discussed, using an analytical approach to find optimal constant mix investment strategies in a provisioning or savings context. In this paper we extend some of these results, investigating some specific, real-life situations. The
Integer programming for the generalized high school timetabling problem
DEFF Research Database (Denmark)
Kristiansen, Simon; Sørensen, Matias; Stidsen, Thomas Riis
2015-01-01
Recently, the XHSTT format for high school timetabling was introduced. It provides a uniform way of modeling problem instances and corresponding solutions. The format supports a wide variety of constraints, and currently 38 real-life instances from 11 different countries are available. Thereby...
Linear system solvers based on space decompositions and parallel computations
Czech Academy of Sciences Publication Activity Database
Blaheta, Radim; Jakl, Ondřej; Starý, Jiří
2003-01-01
Roč. 10, č. 6 (2003), s. 439-454 ISSN 1210-2717 R&D Projects: GA AV ČR IBS3086102 Institutional research plan: CEZ:AV0Z3086906 Keywords : large scale modelling * FEM * iterative solvers Subject RIV: BA - General Mathematics
Contribution of radiobiology to the problem of general fitness
International Nuclear Information System (INIS)
Vacha, J.
1976-01-01
On the basis of the present scarce literary data it can be taken as proved that between the numerous properties of the organism usually considered as biologically valuable (high fertility, longevity, higher body weight, resistance to fasting, radiation, and infection agents, certain favorable parameters of CNS) there exist many single and multiple positive correlations. The existence of these correlations allows for the introduction of the working concept of general fitness, stimulating further interdisciplinary research in this field important both in practice and theory. Most correlated manifestations of fitness demonstrated a masked influence of the organism's genotype even though the manner of this manifestation on the phenotype level remains considerably obscure. The efficiency of the haematopoietic system is doubtless one of the mechanisms of general fitness; it is determined by the very complex coordination of several cytokinetic parameters. Important factors are the efficiency of regulation mechanisms at CNS level, the endocrine system, and the regulators of cell populations. Generally highest fitness is connected with a ''balanced'' regulation type, which is characterized by optimal activation of the homeostatic regulation mechanism. In studying the causes of general fitness a systems approach is inevitable which evaluates the levels of individual factors not ''mechanically'' or linearly but from the point of view of the needs of the whole organism and with the application of concepts established by the systems theory (e.g. by the theory of automatic regulation). The sensitivity of an organism to irradiation with ionizing radiation turns out to be a suitable criterion of its general fitness. (author)
Directory of Open Access Journals (Sweden)
Ahmad Mujahid Ahmad Zaidi
2013-01-01
Full Text Available Rolled homogeneous armor (RHA plate subjected to blast loading is a complex problem involving the nonlinear fluid-structure interaction. The numerical techniques using the spatial discretization scheme that has been provided as a solver in the AUTODYN computer code will be used in this study in order to predict the RHA response subjected to explosive (TNT blast loading. The final deflection will be used as a reference in order to identify the suitable solver for both materials RHA and TNT; then the plastic deformation will be chosen in the simulation process. Instead of using the same solver for RHA and TNT domains, the optimization of solver can be achieved if it is only used in an appropriate domain, or in other words, a different domain will be using different solver. The solvers, which were available in AUTODYN, were used in the analysis of impact and explosion or fluid-structure interaction. Therefore, in this paper, we will determine the suitable solver for both materials (TNT and RHA plate, and the appropriate interaction coupling solver will be obtained. Defining TNT and RHA plates using the Arbitrary Lagrangian Eulerian solver has found the best coupling solver for this case study when compared with existing experimental data. This coupling solver will be used for future analysis in simulating blast-loading phenomena.
Generalized mixed finite element method for 3D elasticity problems
Qing, Guanghui; Mao, Junhui; Liu, Yanhong
2017-06-01
Without applying any stable element techniques in the mixed methods, two simple generalized mixed element (GME) formulations were derived by combining the minimum potential energy principle and Hellinger-Reissner (H-R) variational principle. The main features of the GME formulations are that the common C0 -continuous polynomial shape functions for displacement methods are used to express both displacement and stress variables, and the coefficient matrix of these formulations is not only automatically symmetric but also invertible. Hence, the numerical results of the generalized mixed methods based on the GME formulations are stable. Displacement as well as stress results can be obtained directly from the algebraic system for finite element analysis after introducing stress and displacement boundary conditions simultaneously. Numerical examples show that displacement and stress results retain the same accuracy. The results of the noncompatible generalized mixed method proposed herein are more accurate than those of the standard noncompatible displacement method. The noncompatible generalized mixed element is less sensitive to element geometric distortions.
Nonlinear Analysis of the Generalized Thermo-Magnetodynamic Problem
Czech Academy of Sciences Publication Activity Database
Nedoma, Jiří
1995-01-01
Roč. 63, 1/3 (1995), s. 393-402 ISSN 0377-0427. [Modelling'94. Prague, 29.08.1994-02.09.1994] Grant - others:COPERNICUS(XE) 94-00820 Keywords : generalized magnetodynamics * partial differential equations * variational inequalities * viscoplasticity * geodynamics * magnetic field of planets * astrophysics Impact factor: 0.373, year: 1995
General Systems Theory Approaches to Organizations: Some Problems in Application
Peery, Newman S., Jr.
1975-01-01
Considers the limitations of General Systems Theory (GST) as a major paradigm within administrative theory and concludes that most systems formulations overemphasize growth and show little appreciation for intraorganizational conflict, diversity of values, and political action within organizations. Suggests that these limitations are mainly due to…
The problem of diagnostic variability in general practice.
Crombie, D L; Cross, K W; Fleming, D M
1992-08-01
The aim was to examine the scale, source, and relevance of variation between general practices in respect of the rates with which patients consulted with illnesses falling in each of several diagnostic groups. This study involved a general practice morbidity survey conducted over two years, 1970-72. All patients who consulted their general practitioners were identified and the number of these who consulted with diagnoses attributable to each of the 18 main chapters of the International classification of diseases were counted. Patients who consulted for more than one diagnosis within a chapter were counted once only; those who consulted for one or more diagnoses in each of several chapters were counted once for each chapter. This was a national survey involving general practitioners in England and Wales. The study involved 214,524 patients from 53 selected general practices (115 doctors) who were registered with their general practitioners for the whole of the year 1970-71 and for whom their morbidity data had been linked with their social data from the 1971 census. Using the numbers of patients on the practice lists as denominators, practice patient consulting rates (PPCR) were calculated for each practice and for each ICD chapter. Variability in chapter PPCR was examined by calculating coefficients of variation and, after allowance for random variation, coefficients of residual variation. There were large interpractice (doctor) variations in all chapter rates. These variations were only marginally attributable to: chance; different age, sex and social class mixes of practice populations; geographical locations; and practice organisation. The rates were, however, consistent from one year to the next for any one practice. Approximately half of the interpractice (doctor) diagnostic variability was associated with overall patient consulting behaviour. When the effects of this behaviour were discounted, any major residual diagnostic variability was confined largely to
A generalization of the Birthday problem and the chromatic polynomial
Fadnavis, Sukhada
2011-01-01
The birthday paradox states that there is at least a 50% chance that some two out of twenty-three randomly chosen people will share the same birth date. The calculation for this problem assumes that all birth dates are equally likely. We consider the following two modifications of this question. If the distribution of birthdays is non-uniform, does that increase or decrease the probability of matching birth dates? Further, what if we focus on birthdays shared by some particular pairs rather t...
Zantinge, E.M.; Verhaak, P.F.M.; Bakker, D.H. de; Kerssens, J.J.; Meer, K. van der; Bensing, J.M.
2007-01-01
OBJECTIVE: To investigate if general practitioners (GPs) with a higher workload are less inclined to encourage their patients to disclose psychological problems, and are less aware of their patients' psychological problems. METHODS: Data from 2095 videotaped consultations from a representative
DEFF Research Database (Denmark)
Pilegaard, Henrik
2003-01-01
general Normal clauses accepted by both solvers and run the experiments for all three possible combinations of input and solver. This allows the solvers to be tested on even ground and enables the reuse of existing analyses and their corresponding ALFP constraint generators. The performance...
High order Poisson Solver for unbounded flows
DEFF Research Database (Denmark)
Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe
2015-01-01
This paper presents a high order method for solving the unbounded Poisson equation on a regular mesh using a Green’s function solution. The high order convergence was achieved by formulating mollified integration kernels, that were derived from a filter regularisation of the solution field...... the equations of fluid mechanics as an example, but can be used in many physical problems to solve the Poisson equation on a rectangular unbounded domain. For the two-dimensional case we propose an infinitely smooth test function which allows for arbitrary high order convergence. Using Gaussian smoothing....... The method was implemented on a rectangular domain using fast Fourier transforms (FFT) to increase computational efficiency. The Poisson solver was extended to directly solve the derivatives of the solution. This is achieved either by including the differential operator in the integration kernel...
Introduction to the concept of thermal stability: expression of the general problem
International Nuclear Information System (INIS)
Llory, M.; Planchard, J.
1981-01-01
In the first part, an introduction is given to the concept of thermal stability, based firstly on experimental results and secondly on a simplified formulation of the problem. In the second part, the above considerations are generalized: the general problem of thermal stability is stated and it is shown that it can be considered as an eigenvalue problem. In the third part, a simple application of the general case is developed [fr
Generalized single-hidden layer feedforward networks for regression problems.
Wang, Ning; Er, Meng Joo; Han, Min
2015-06-01
In this paper, traditional single-hidden layer feedforward network (SLFN) is extended to novel generalized SLFN (GSLFN) by employing polynomial functions of inputs as output weights connecting randomly generated hidden units with corresponding output nodes. The significant contributions of this paper are as follows: 1) a primal GSLFN (P-GSLFN) is implemented using randomly generated hidden nodes and polynomial output weights whereby the regression matrix is augmented by full or partial input variables and only polynomial coefficients are to be estimated; 2) a simplified GSLFN (S-GSLFN) is realized by decomposing the polynomial output weights of the P-GSLFN into randomly generated polynomial nodes and tunable output weights; 3) both P- and S-GSLFN are able to achieve universal approximation if the output weights are tuned by ridge regression estimators; and 4) by virtue of the developed batch and online sequential ridge ELM (BR-ELM and OSR-ELM) learning algorithms, high performance of the proposed GSLFNs in terms of generalization and learning speed is guaranteed. Comprehensive simulation studies and comparisons with standard SLFNs are carried out on real-world regression benchmark data sets. Simulation results demonstrate that the innovative GSLFNs using BR-ELM and OSR-ELM are superior to standard SLFNs in terms of accuracy, training speed, and structure compactness.
Robust large-scale parallel nonlinear solvers for simulations.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Pawlowski, Roger Patrick; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)
2005-11-01
existing linear solver, which makes it simple to write and easily portable. However, the method usually takes twice as long to solve as Newton-GMRES on general problems because it solves two linear systems at each iteration. In this paper, we discuss modifications to Bouaricha's method for a practical implementation, including a special globalization technique and other modifications for greater efficiency. We present numerical results showing computational advantages over Newton-GMRES on some realistic problems. We further discuss a new approach for dealing with singular (or ill-conditioned) matrices. In particular, we modify an algorithm for identifying a turning point so that an increasingly ill-conditioned Jacobian does not prevent convergence.
On a covariant 2+2 formulation of the initial value problem in general relativity
International Nuclear Information System (INIS)
Smallwood, J.
1980-03-01
The initial value problems in general relativity are considered from a geometrical standpoint with especial reference to the development of a covariant 2+2 formalism in which space-time is foliated by space-like 2-surfaces under the headings; the Cauchy problem in general relativity, the covariant 3+1 formulation of the Cauchy problem, characteristic and mixed initial value problems, on locally imbedding a family of null hypersurfaces, the 2+2 formalism, the 2+2 formulation of the Cauchy problem, the 2+2 formulation of the characteristic and mixed initial value problems, and a covariant Lagrangian 2+2 formulation. (U.K.)
Efficient use of iterative solvers in nested topology optimization
DEFF Research Database (Denmark)
Amir, Oded; Stolpe, Mathias; Sigmund, Ole
2009-01-01
In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, it is suggested to reduce this computational cost by using an approximation to the solution of the nested problem, generated...... by a Krylov subspace iterative solver. By choosing convergence criteria for the iterative solver that are strongly related to the optimization objective and to the design sensitivities, it is possible to terminate the iterative solution of the nested equations earlier compared to traditional convergence...... measures. The approximation is shown to be sufficiently accurate for the practical purpose of optimization even though the nested equation system is not solved accurately. The approach is tested on several medium-scale topology optimization problems, including three dimensional minimum compliance problems...
Efficient use of iterative solvers in nested topology optimization
DEFF Research Database (Denmark)
Amir, Oded; Stolpe, Mathias; Sigmund, Ole
2010-01-01
In the nested approach to structural optimization, most of the computational effort is invested in the solution of the analysis equations. In this study, it is suggested to reduce this computational cost by using an approximation to the solution of the analysis problem, generated by a Krylov...... subspace iterative solver. By choosing convergence criteria for the iterative solver that are strongly related to the optimization objective and to the design sensitivities, it is possible to terminate the iterative solution of the nested equations earlier compared to traditional convergence measures....... The approximation is computationally shown to be sufficiently accurate for the purpose of optimization though the nested equation system is not necessarily solved accurately. The approach is tested on several large-scale topology optimization problems, including minimum compliance problems and compliant mechanism...
A finite element Poisson solver for gyrokinetic particle simulations in a global field aligned mesh
International Nuclear Information System (INIS)
Nishimura, Y.; Lin, Z.; Lewandowski, J.L.V.; Ethier, S.
2006-01-01
A new finite element Poisson solver is developed and applied to a global gyrokinetic toroidal code (GTC) which employs the field aligned mesh and thus a logically non-rectangular grid in a general geometry. Employing test cases where the analytical solutions are known, the finite element solver has been verified. The CPU time scaling versus the matrix size employing portable, extensible toolkit for scientific computation (PETSc) to solve the sparse matrix is promising. Taking the ion temperature gradient modes (ITG) as an example, the solution from the new finite element solver has been compared to the solution from the original GTC's iterative solver which is only efficient for adiabatic electrons. Linear and nonlinear simulation results from the two different forms of the gyrokinetic Poisson equation (integral form and the differential form) coincide each other. The new finite element solver enables the implementation of advanced kinetic electron models for global electromagnetic simulations
Generalized information theory: aims, results, and open problems
International Nuclear Information System (INIS)
Klir, George J.
2004-01-01
The principal purpose of this paper is to present a comprehensive overview of generalized information theory (GIT): a research program whose objective is to develop a broad treatment of uncertainty-based information, not restricted to classical notions of uncertainty. After a brief overview of classical information theories, a broad framework for formalizing uncertainty and the associated uncertainty-based information of a great spectrum of conceivable types is sketched. The various theories of imprecise probabilities that have already been developed within this framework are then surveyed, focusing primarily on some important unifying principles applying to all these theories. This is followed by introducing two higher levels of the theories of imprecise probabilities: (i) the level of measuring the amount of relevant uncertainty (predictive, retrodictive, prescriptive, diagnostic, etc.) in any situation formalizable in each given theory, and (ii) the level of some methodological principles of uncertainty, which are contingent upon the capability to measure uncertainty and the associated uncertainty-based information. Various issues regarding both the measurement of uncertainty and the uncertainty principles are discussed. Again, the focus is on unifying principles applicable to all the theories. Finally, the current status of GIT is assessed and future research in the area is discussed
PROPAGATION-BASED CONSTRAINT SOLVER IN IMS
Directory of Open Access Journals (Sweden)
I.Ol. Blynov
2012-03-01
Full Text Available Article compiling the main ideas of creating propagation-based constraint solver, theoretical basis of constraint programming and its implementation in IMS (Insertion Modeling System
Migration of vectorized iterative solvers to distributed memory architectures
Energy Technology Data Exchange (ETDEWEB)
Pommerell, C. [AT& T Bell Labs., Murray Hill, NJ (United States); Ruehl, R. [CSCS-ETH, Manno (Switzerland)
1994-12-31
Both necessity and opportunity motivate the use of high-performance computers for iterative linear solvers. Necessity results from the size of the problems being solved-smaller problems are often better handled by direct methods. Opportunity arises from the formulation of the iterative methods in terms of simple linear algebra operations, even if this {open_quote}natural{close_quotes} parallelism is not easy to exploit in irregularly structured sparse matrices and with good preconditioners. As a result, high-performance implementations of iterative solvers have attracted a lot of interest in recent years. Most efforts are geared to vectorize or parallelize the dominating operation-structured or unstructured sparse matrix-vector multiplication, or to increase locality and parallelism by reformulating the algorithm-reducing global synchronization in inner products or local data exchange in preconditioners. Target architectures for iterative solvers currently include mostly vector supercomputers and architectures with one or few optimized (e.g., super-scalar and/or super-pipelined RISC) processors and hierarchical memory systems. More recently, parallel computers with physically distributed memory and a better price/performance ratio have been offered by vendors as a very interesting alternative to vector supercomputers. However, programming comfort on such distributed memory parallel processors (DMPPs) still lags behind. Here the authors are concerned with iterative solvers and their changing computing environment. In particular, they are considering migration from traditional vector supercomputers to DMPPs. Application requirements force one to use flexible and portable libraries. They want to extend the portability of iterative solvers rather than reimplementing everything for each new machine, or even for each new architecture.
An Investigation of the Performance of the Colored Gauss-Seidel Solver on CPU and GPU
International Nuclear Information System (INIS)
Yoon, Jong Seon; Choi, Hyoung Gwon; Jeon, Byoung Jin
2017-01-01
The performance of the colored Gauss–Seidel solver on CPU and GPU was investigated for the two- and three-dimensional heat conduction problems by using different mesh sizes. The heat conduction equation was discretized by the finite difference method and finite element method. The CPU yielded good performance for small problems but deteriorated when the total memory required for computing was larger than the cache memory for large problems. In contrast, the GPU performed better as the mesh size increased because of the latency hiding technique. Further, GPU computation by the colored Gauss–Siedel solver was approximately 7 times that by the single CPU. Furthermore, the colored Gauss–Seidel solver was found to be approximately twice that of the Jacobi solver when parallel computing was conducted on the GPU.
Teaching Problem Solving: Don't Forget the Problem Solver(s)
Ranade, Saidas M.; Corrales, Angela
2013-01-01
The importance of intrapersonal and interpersonal intelligences has long been known but educators have debated whether to and how to incorporate those topics in an already crowded engineering curriculum. In 2010, the authors used the classroom as a laboratory to observe the usefulness of including selected case studies and exercises from the…
Ekici, Didem Inel
2016-01-01
This study aimed to determine Turkish junior high-school students' perceptions of the general problem-solving process. The Turkish junior high-school students' perceptions of the general problem-solving process were examined in relation to their gender, grade level, age and their grade point with regards to the science course identified in the…
Directory of Open Access Journals (Sweden)
Phayap Katchang
2010-01-01
Full Text Available The purpose of this paper is to investigate the problem of finding a common element of the set of solutions for mixed equilibrium problems, the set of solutions of the variational inclusions with set-valued maximal monotone mappings and inverse-strongly monotone mappings, and the set of fixed points of a family of finitely nonexpansive mappings in the setting of Hilbert spaces. We propose a new iterative scheme for finding the common element of the above three sets. Our results improve and extend the corresponding results of the works by Zhang et al. (2008, Peng et al. (2008, Peng and Yao (2009, as well as Plubtieng and Sriprad (2009 and some well-known results in the literature.
Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers
Tang, Yu-Hang; Kudo, Shuhei; Bian, Xin; Li, Zhen; Karniadakis, George Em
2015-09-01
Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM).
A generalization of szebehely's inverse problem of dynamics in dimension three
Sarlet, W.; Mestdag, T.; Prince, G.
2017-06-01
Extending a previous paper, we present a generalization in dimension 3 of the traditional Szebehely-type inverse problem. In that traditional setting, the data are curves determined as the intersection of two families of surfaces, and the problem is to find a potential V such that the Lagrangian L = T - V, where T is the standard Euclidean kinetic energy function, generates integral curves which include the given family of curves. Our more general way of posing the problem makes use of ideas of the inverse problem of the calculus of variations and essentially consists of allowing more general kinetic energy functions, with a metric which is still constant, but need not be the standard Euclidean one. In developing our generalization, we review and clarify different aspects of the existing literature on the problem and illustrate the relevance of the newly introduced additional freedom with many examples.
Zwaanswijk, Marieke; Verhaak, Peter F M; van der Ende, Jan; Bensing, Jozien M; Verhulst, Frank C
2005-10-01
Child and adolescent psychological problems are rarely brought to the attention of GPs. Children and adolescents with psychological problems who do visit their GP are seldom identified as such by GPs. To investigate in a general population sample of 2,449 Dutch children and adolescents (4-17 years) GP consultation and GP diagnoses of child psychological problems, and the influence of child and family characteristics upon these variables. The degree to which parent, teacher, and adolescent reports of the presence of child psychological problems are in concordance with GP diagnoses of these problems was determined. Logistic regression analyses were used to examine correlates of GP consultation and psychological diagnoses. Approximately 80% of children and adolescents with psychological problems had visited their GP within the preceding year. GP consultation was most strongly associated with child/adolescent chronic physical disorders. Concordance between GP psychological diagnoses and parent, teacher, and adolescent reports of psychological problems was limited. Children and adolescents with psychological problems according to parent or teacher report, children with school problems, young boys, adolescents with negative health perceptions, and adolescents from single parent families were more likely to be diagnosed with psychological problems by GPs. Improving GPs' interview techniques, introducing standardised screening measures in general practice, increasing GPs' awareness of the possible presence of psychological problems in children consulting for physical problems, and strengthening collaboration between GPs and mental health professionals may increase GP identification of child psychological problems and enhance access to care for those in need.
A hybrid adaptive large neighborhood search algorithm applied to a lot-sizing problem
DEFF Research Database (Denmark)
Muller, Laurent Flindt; Spoorendonk, Simon
This paper presents a hybrid of a general heuristic framework that has been successfully applied to vehicle routing problems and a general purpose MIP solver. The framework uses local search and an adaptive procedure which choses between a set of large neighborhoods to be searched. A mixed integer...... programming solver and its built-in feasibility heuristics is used to search a neighborhood for improving solutions. The general reoptimization approach used for repairing solutions is specifically suited for combinatorial problems where it may be hard to otherwise design operations to define a neighborhood...
The impact of improved sparse linear solvers on industrial engineering applications
Energy Technology Data Exchange (ETDEWEB)
Heroux, M. [Cray Research, Inc., Eagan, MN (United States); Baddourah, M.; Poole, E.L.; Yang, Chao Wu
1996-12-31
There are usually many factors that ultimately determine the quality of computer simulation for engineering applications. Some of the most important are the quality of the analytical model and approximation scheme, the accuracy of the input data and the capability of the computing resources. However, in many engineering applications the characteristics of the sparse linear solver are the key factors in determining how complex a problem a given application code can solve. Therefore, the advent of a dramatically improved solver often brings with it dramatic improvements in our ability to do accurate and cost effective computer simulations. In this presentation we discuss the current status of sparse iterative and direct solvers in several key industrial CFD and structures codes, and show the impact that recent advances in linear solvers have made on both our ability to perform challenging simulations and the cost of those simulations. We also present some of the current challenges we have and the constraints we face in trying to improve these solvers. Finally, we discuss future requirements for sparse linear solvers on high performance architectures and try to indicate the opportunities that exist if we can develop even more improvements in linear solver capabilities.
Generalized ladder operators for the Dirac-Coulomb problem via SUSY QM
International Nuclear Information System (INIS)
Rodrigues, R. de Lima; Universidade Federal de Campina Grande, PB
2003-12-01
The supersymmetry in quantum mechanics and shape invariance condition are applied as an algebraic method to solving the Dirac-Coulomb problem. The ground state and the excited states are investigated via new generalized ladder operators. (author)
Cohen-Schotanus, Janke; Muijtjens, Arno M. M.; Schonrock-Adema, Johanna; Geertsma, Jelle; van der Vleuten, Cees P. M.
OBJECTIVE: To test hypotheses regarding the longitudinal effects of problem-based learning (PBL) and conventional learning relating to students' appreciation of the curriculum, self-assessment of general competencies, summative assessment of clinical competence and indicators of career development.
Energy Technology Data Exchange (ETDEWEB)
GARDNER, P.R.
2006-04-01
Sudoku, also known as Number Place, is a logic-based placement puzzle. The aim of the puzzle is to enter a numerical digit from 1 through 9 in each cell of a 9 x 9 grid made up of 3 x 3 subgrids (called ''regions''), starting with various digits given in some cells (the ''givens''). Each row, column, and region must contain only one instance of each numeral. Completing the puzzle requires patience and logical ability. Although first published in a U.S. puzzle magazine in 1979, Sudoku initially caught on in Japan in 1986 and attained international popularity in 2005. Last fall, after noticing Sudoku puzzles in some newspapers and magazines, I attempted a few just to see how hard they were. Of course, the difficulties varied considerably. ''Obviously'' one could use Trial and Error but all the advice was to ''Use Logic''. Thinking to flex, and strengthen, those powers, I began to tackle the puzzles systematically. That is, when I discovered a new tactical rule, I would write it down, eventually generating a list of ten or so, with some having overlap. They served pretty well except for the more difficult puzzles, but even then I managed to develop an additional three rules that covered all of them until I hit the Oregonian puzzle shown. With all of my rules, I could not seem to solve that puzzle. Initially putting my failure down to rapid mental fatigue (being unable to hold a sufficient quantity of information in my mind at one time), I decided to write a program to implement my rules and see what I had failed to notice earlier. The solver, too, failed. That is, my rules were insufficient to solve that particular puzzle. I happened across a book written by a fellow who constructs such puzzles and who claimed that, sometimes, the only tactic left was trial and error. With a trial and error routine implemented, my solver successfully completed the Oregonian puzzle, and has successfully
Code Verification of the HIGRAD Computational Fluid Dynamics Solver
Energy Technology Data Exchange (ETDEWEB)
Van Buren, Kendra L. [Los Alamos National Laboratory; Canfield, Jesse M. [Los Alamos National Laboratory; Hemez, Francois M. [Los Alamos National Laboratory; Sauer, Jeremy A. [Los Alamos National Laboratory
2012-05-04
The purpose of this report is to outline code and solution verification activities applied to HIGRAD, a Computational Fluid Dynamics (CFD) solver of the compressible Navier-Stokes equations developed at the Los Alamos National Laboratory, and used to simulate various phenomena such as the propagation of wildfires and atmospheric hydrodynamics. Code verification efforts, as described in this report, are an important first step to establish the credibility of numerical simulations. They provide evidence that the mathematical formulation is properly implemented without significant mistakes that would adversely impact the application of interest. Highly accurate analytical solutions are derived for four code verification test problems that exercise different aspects of the code. These test problems are referred to as: (i) the quiet start, (ii) the passive advection, (iii) the passive diffusion, and (iv) the piston-like problem. These problems are simulated using HIGRAD with different levels of mesh discretization and the numerical solutions are compared to their analytical counterparts. In addition, the rates of convergence are estimated to verify the numerical performance of the solver. The first three test problems produce numerical approximations as expected. The fourth test problem (piston-like) indicates the extent to which the code is able to simulate a 'mild' discontinuity, which is a condition that would typically be better handled by a Lagrangian formulation. The current investigation concludes that the numerical implementation of the solver performs as expected. The quality of solutions is sufficient to provide credible simulations of fluid flows around wind turbines. The main caveat associated to these findings is the low coverage provided by these four problems, and somewhat limited verification activities. A more comprehensive evaluation of HIGRAD may be beneficial for future studies.
IGA-ADS: Isogeometric analysis FEM using ADS solver
Łoś, Marcin M.; Woźniak, Maciej; Paszyński, Maciej; Lenharth, Andrew; Hassaan, Muhamm Amber; Pingali, Keshav
2017-08-01
In this paper we present a fast explicit solver for solution of non-stationary problems using L2 projections with isogeometric finite element method. The solver has been implemented within GALOIS framework. It enables parallel multi-core simulations of different time-dependent problems, in 1D, 2D, or 3D. We have prepared the solver framework in a way that enables direct implementation of the selected PDE and corresponding boundary conditions. In this paper we describe the installation, implementation of exemplary three PDEs, and execution of the simulations on multi-core Linux cluster nodes. We consider three case studies, including heat transfer, linear elasticity, as well as non-linear flow in heterogeneous media. The presented package generates output suitable for interfacing with Gnuplot and ParaView visualization software. The exemplary simulations show near perfect scalability on Gilbert shared-memory node with four Intel® Xeon® CPU E7-4860 processors, each possessing 10 physical cores (for a total of 40 cores).
Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics
Pavarino, L.F.
2015-07-18
The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.
Scalable parallel prefix solvers for discrete ordinates transport
International Nuclear Information System (INIS)
Pautz, S.; Pandya, T.; Adams, M.
2009-01-01
The well-known 'sweep' algorithm for inverting the streaming-plus-collision term in first-order deterministic radiation transport calculations has some desirable numerical properties. However, it suffers from parallel scaling issues caused by a lack of concurrency. The maximum degree of concurrency, and thus the maximum parallelism, grows more slowly than the problem size for sweeps-based solvers. We investigate a new class of parallel algorithms that involves recasting the streaming-plus-collision problem in prefix form and solving via cyclic reduction. This method, although computationally more expensive at low levels of parallelism than the sweep algorithm, offers better theoretical scalability properties. Previous work has demonstrated this approach for one-dimensional calculations; we show how to extend it to multidimensional calculations. Notably, for multiple dimensions it appears that this approach is limited to long-characteristics discretizations; other discretizations cannot be cast in prefix form. We implement two variants of the algorithm within the radlib/SCEPTRE transport code library at Sandia National Laboratories and show results on two different massively parallel systems. Both the 'forward' and 'symmetric' solvers behave similarly, scaling well to larger degrees of parallelism then sweeps-based solvers. We do observe some issues at the highest levels of parallelism (relative to the system size) and discuss possible causes. We conclude that this approach shows good potential for future parallel systems, but the parallel scalability will depend heavily on the architecture of the communication networks of these systems. (authors)
A spectral Poisson solver for kinetic plasma simulation
Szeremley, Daniel; Obberath, Jens; Brinkmann, Ralf
2011-10-01
Plasma resonance spectroscopy is a well established plasma diagnostic method, realized in several designs. One of these designs is the multipole resonance probe (MRP). In its idealized - geometrically simplified - version it consists of two dielectrically shielded, hemispherical electrodes to which an RF signal is applied. A numerical tool is under development which is capable of simulating the dynamics of the plasma surrounding the MRP in electrostatic approximation. In this contribution we concentrate on the specialized Poisson solver for that tool. The plasma is represented by an ensemble of point charges. By expanding both the charge density and the potential into spherical harmonics, a largely analytical solution of the Poisson problem can be employed. For a practical implementation, the expansion must be appropriately truncated. With this spectral solver we are able to efficiently solve the Poisson equation in a kinetic plasma simulation without the need of introducing a spatial discretization.
Zwaanswijk, M.; Verhaak, P.F.M.; Ende, J. van der; Bensing, J.M.; Verhulst, F.C.
2005-01-01
BACKGROUND: Child and adolescent psychological problems are rarely brought to the attention of GPs. Children and adolescents with psychological problems who do visit their GP are seldom identified as such by GPs. OBJECTIVE: To investigate in a general population sample of 2,449 Dutch children and
Zantinge, E.M.; Verhaak, P.F.M.; Kerssens, J.J.; Bensing, J.M.
2006-01-01
Background: Many mental problems are not recognized by the general practitioner (GP). Recognition of these problems is important because it is one of the critical stages in finding appropriate care for the patient. GPs are sometimes reluctant to get involved in mental health care because it requires
Czech Academy of Sciences Publication Activity Database
Dilna, N.; Rontó, András
2008-01-01
Roč. 133, č. 4 (2008), s. 435-445 ISSN 0862-7959 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : functional differential equation * Cauchy problem * initial value problem * differential inequality Subject RIV: BA - General Mathematics
DEFF Research Database (Denmark)
Helsgaun, Keld
2015-01-01
The equality generalized traveling salesman problem (E-GTSP) is an extension of the traveling salesman problem (TSP) where the set of cities is partitioned into clusters, and the salesman has to visit every cluster exactly once. It is well known that any instance of E-GTSP can be transformed...
The course of mental health problems in children presenting with abdominal pain in general practice
Gieteling, Marieke J.; Lisman-Van Leeuwen, Yvone; Passchier, Jan; Koes, Bart W.; Berger, Marjolein Y.; Leuwen, Y.L.V.
Objective. To investigate the course of mental health problems in children presenting to general practice with abdominal pain and to evaluate the extent to which abdominal pain characteristics during follow-up predict the presence of mental health problems at 12 months' follow-up. Design. A
The course of mental health problems in children presenting with abdominal pain in general practice
Passchier, J.; Gieteling, M.J.; Lisman-Van Leeuwen, Y.; Koes, B.W.; Berger, M.Y.
2012-01-01
Objective. To investigate the course of mental health problems in children presenting to general practice with abdominal pain and to evaluate the extent to which abdominal pain characteristics during follow-up predict the presence of mental health problems at 12 months' follow-up. Design. A
The development of an intelligent interface to a computational fluid dynamics flow-solver code
Williams, Anthony D.
1988-01-01
Researchers at NASA Lewis are currently developing an 'intelligent' interface to aid in the development and use of large, computational fluid dynamics flow-solver codes for studying the internal fluid behavior of aerospace propulsion systems. This paper discusses the requirements, design, and implementation of an intelligent interface to Proteus, a general purpose, three-dimensional, Navier-Stokes flow solver. The interface is called PROTAIS to denote its introduction of artificial intelligence (AI) concepts to the Proteus code.
A parallel direct solver for the self-adaptive hp Finite Element Method
Paszyński, Maciej R.
2010-03-01
In this paper we present a new parallel multi-frontal direct solver, dedicated for the hp Finite Element Method (hp-FEM). The self-adaptive hp-FEM generates in a fully automatic mode, a sequence of hp-meshes delivering exponential convergence of the error with respect to the number of degrees of freedom (d.o.f.) as well as the CPU time, by performing a sequence of hp refinements starting from an arbitrary initial mesh. The solver constructs an initial elimination tree for an arbitrary initial mesh, and expands the elimination tree each time the mesh is refined. This allows us to keep track of the order of elimination for the solver. The solver also minimizes the memory usage, by de-allocating partial LU factorizations computed during the elimination stage of the solver, and recomputes them for the backward substitution stage, by utilizing only about 10% of the computational time necessary for the original computations. The solver has been tested on 3D Direct Current (DC) borehole resistivity measurement simulations problems. We measure the execution time and memory usage of the solver over a large regular mesh with 1.5 million degrees of freedom as well as on the highly non-regular mesh, generated by the self-adaptive h p-FEM, with finite elements of various sizes and polynomial orders of approximation varying from p = 1 to p = 9. From the presented experiments it follows that the parallel solver scales well up to the maximum number of utilized processors. The limit for the solver scalability is the maximum sequential part of the algorithm: the computations of the partial LU factorizations over the longest path, coming from the root of the elimination tree down to the deepest leaf. © 2009 Elsevier Inc. All rights reserved.
The wetted solid - a generalization of Plateau's problem and its implications for sintered materials
International Nuclear Information System (INIS)
Salomon, P.; Berry, R.S.; Carrera-Patino, M.E.; Chicago Univ., IL; Andresen, B.
1988-01-01
We introduce a new generalization of the Plateau problem which includes the constraint of enclosing a given region. Physically the problem is important insofar as it bears on sintering processes and on the structure of wetted porous media. Some primal and dual characterizations of the solutions are offered, and aspects of the problem are illustrated in one and two dimensions in order to clarify the combinatorial elements and to demonstrate the importance of numerous local minima. (orig.)
Consultations for mental problems in general practices with and without mental health nurses.
Magnée, T.; Beurs, D. de; Verhaak, P.
2016-01-01
Background & Aim: It seems cost-effective to provide mental health care to patient with mild mental problems in general practices instead of in specialized care, but general practitioners (GPs) often lack time or expertise. Since 2008, Dutch GPs have been collaborating with nurses with mental health
Statistical problem of ideal gas in general two-dimensional regions
Song, Ci; Li, Wen-Du; Mwansa, Pardon; Zhang, Ping
2015-09-01
In this paper, based on the conformal mapping method and the perturbation theory, we develop a method to solve the statistical problem within general two-dimensional regions. We consider some examples and the numerical results and fitting results are given. We also give the thermodynamic quantities of the general two-dimensional regions, and compare the thermodynamic quantities of the different regions.
Generalizing the classical fixed-centres problem in a non-Hamiltonian way
International Nuclear Information System (INIS)
Albouy, A; Stuchi, T J
2004-01-01
The problem of two gravitational (or Coulombian) fixed centres is a classical integrable problem, stated and integrated by Euler in 1760. The integrability is due to the unexpected first integral G. We introduce some straightforward generalizations of the problem that still have the generalization of G as a first integral, but do not possess the energy integral. We present some numerical integrations showing the main features of their dynamics. In the domain of bounded orbits the behaviour of these a priori non-Hamiltonian systems is very similar to the behaviour of usual near-integrable systems
Gambling problems among patients in primary care: a cross-sectional study of general practices.
Cowlishaw, Sean; Gale, Lone; Gregory, Alison; McCambridge, Jim; Kessler, David
2017-04-01
Primary care is an important context for addressing health-related behaviours, and may provide a setting for identification of gambling problems. To indicate the extent of gambling problems among patients attending general practices, and explore settings or patient groups that experience heightened vulnerability. Cross-sectional study of patients attending 11 general practices in Bristol, South West England. Adult patients ( n = 1058) were recruited from waiting rooms of practices that were sampled on the basis of population characteristics. Patients completed anonymous questionnaires comprising measures of mental health problems (for example, depression) and addictive behaviours (for example, risky alcohol use). The Problem Gambling Severity Index (PGSI) measured gambling problems, along with a single-item measure of gambling problems among family members. Estimates of extent and variability according to practice and patient characteristics were produced. There were 0.9% of all patients exhibiting problem gambling (PGSI ≥5), and 4.3% reporting problems that were low to moderate in severity (PGSI 1-4). Around 7% of patients reported gambling problems among family members. Further analyses indicated that rates of any gambling problems (PGSI ≥1) were higher among males and young adults, and more tentatively, within a student healthcare setting. They were also elevated among patients exhibiting drug use, risky alcohol use, and depression. There is need for improved understanding of the burden of, and responses to, patients with gambling problems in general practices, and new strategies to increase identification to facilitate improved care and early intervention. © British Journal of General Practice 2017.
Modified Poisson solver for the simulation of the silicon-oxide interface in semiconductor detectors
Energy Technology Data Exchange (ETDEWEB)
Castoldi, A. E-mail: andrea.castoldi@polimi.it; Rehak, P.; Gatti, E.; Guazzoni, C.; De Geronimo, G
2000-01-11
We present a modified Poisson solver for depleted semiconductor detectors that takes into account the effects of possible accumulation of mobile charge at the silicon-oxide interfaces. The solver is based on a physical model that closely approximates the correct boundary condition at the silicon-oxide interface. The model assumes that the silicon-oxide interface is divided into an equipotential region, where the electron layer is located, and a fully depleted region. The actual extension and potential of the electron layer region are approximated with the desired accuracy by an iterative procedure. This model has been implemented in 2- and 3-D Poisson solvers. The comparison with a 2-D drift-diffusion simulator has shown the accuracy of the proposed method. The modified Poisson solver has shown to be useful in giving accurate solutions to 3-D design problems at high CPU speed.
Modified Poisson solver for the simulation of the silicon-oxide interface in semiconductor detectors
Castoldi, A; Gatti, E; Guazzoni, C; De Geronimo, G
2000-01-01
We present a modified Poisson solver for depleted semiconductor detectors that takes into account the effects of possible accumulation of mobile charge at the silicon-oxide interfaces. The solver is based on a physical model that closely approximates the correct boundary condition at the silicon-oxide interface. The model assumes that the silicon-oxide interface is divided into an equipotential region, where the electron layer is located, and a fully depleted region. The actual extension and potential of the electron layer region are approximated with the desired accuracy by an iterative procedure. This model has been implemented in 2- and 3-D Poisson solvers. The comparison with a 2-D drift-diffusion simulator has shown the accuracy of the proposed method. The modified Poisson solver has shown to be useful in giving accurate solutions to 3-D design problems at high CPU speed.
A Survey of Solver-Related Geometry and Meshing Issues
Masters, James; Daniel, Derick; Gudenkauf, Jared; Hine, David; Sideroff, Chris
2016-01-01
There is a concern in the computational fluid dynamics community that mesh generation is a significant bottleneck in the CFD workflow. This is one of several papers that will help set the stage for a moderated panel discussion addressing this issue. Although certain general "rules of thumb" and a priori mesh metrics can be used to ensure that some base level of mesh quality is achieved, inadequate consideration is often given to the type of solver or particular flow regime on which the mesh will be utilized. This paper explores how an analyst may want to think differently about a mesh based on considerations such as if a flow is compressible vs. incompressible or hypersonic vs. subsonic or if the solver is node-centered vs. cell-centered. This paper is a high-level investigation intended to provide general insight into how considering the nature of the solver or flow when performing mesh generation has the potential to increase the accuracy and/or robustness of the solution and drive the mesh generation process to a state where it is no longer a hindrance to the analysis process.
Algebraic structures in generalized Clifford analysis and applications to boundary value problems
Directory of Open Access Journals (Sweden)
José Játem
2015-12-01
Full Text Available The present article has a threefold purpose: First it is a survey of the algebraic structures of generalized Clifford-type algebras and shows the main results of the corresponding Clifford-type analysis and its application to boundary value problems known so far. Second it is aimed to implement algorithms to provide the fast and accurate computation of boundary value problems for inhomogeneous equations in the framework of the generalized Clifford analysis. Finally it is also aimed to encourage the development of a generalized discrete Clifford analysis.
Exact Post-Selection Inference for Changepoint Detection and Other Generalized Lasso Problems
Hyun, Sangwon; G'Sell, Max; Tibshirani, Ryan J.
2016-01-01
We study tools for inference conditioned on model selection events that are defined by the generalized lasso regularization path. The generalized lasso estimate is given by the solution of a penalized least squares regression problem, where the penalty is the l1 norm of a matrix D times the coefficient vector. The generalized lasso path collects these estimates for a range of penalty parameter ({\\lambda}) values. Leveraging a sequential characterization of this path from Tibshirani & Taylor (...
Control of error and convergence in ODE solvers
International Nuclear Information System (INIS)
Gustafsson, K.
1992-03-01
Feedback is a general principle that can be used in many different contexts. In this thesis it is applied to numerical integration of ordinary differential equations. An advanced integration method includes parameters and variables that should be adjusted during the execution. In addition, the integration method should be able to automatically handle situations such as: initialization, restart after failures, etc. In this thesis we regard the algorithms for parameter adjustment and supervision as a controller. The controlled measures different variable that tell the current status of the integration, and based on this information it decides how to continue. The design of the controller is vital in order to accurately and efficiently solve a large class of ordinary differential equations. The application of feedback control may appear farfetched, but numerical integration methods are in fact dynamical systems. This is often overlooked in traditional numerical analysis. We derive dynamic models that describe the behavior of the integration method as well as the standard control algorithms in use today. Using these models it is possible to analyze properties of current algorithms, and also explain some generally observed misbehaviors. Further, we use the acquired insight to derive new and improved control algorithms, both for explicit and implicit Runge-Kutta methods. In the explicit case, the new controller gives good overall performance. In particular it overcomes the problem with oscillating stepsize sequence that is often experienced when the stepsize is restricted by numerical stability. The controller for implicit methods is designed so that it tracks changes in the differential equation better than current algorithms. In addition, it includes a new strategy for the equation solver, which allows the stepsize to vary more freely. This leads to smoother error control without excessive operations on the iteration matrix. (87 refs.) (au)
Zhao, Yingfeng; Liu, Sanyang
2016-01-01
We present a practical branch and bound algorithm for globally solving generalized linear multiplicative programming problem with multiplicative constraints. To solve the problem, a relaxation programming problem which is equivalent to a linear programming is proposed by utilizing a new two-phase relaxation technique. In the algorithm, lower and upper bounds are simultaneously obtained by solving some linear relaxation programming problems. Global convergence has been proved and results of some sample examples and a small random experiment show that the proposed algorithm is feasible and efficient.
Gambling problems among patients in primary care: a cross-sectional study of general practices
Cowlishaw, Sean; Gale, Lone; Gregory, Alison; McCambridge, Jim; Kessler, David
2017-01-01
Background Primary care is an important context for addressing health-related behaviours, and may provide a setting for identification of gambling problems. Aim To indicate the extent of gambling problems among patients attending general practices, and explore settings or patient groups that experience heightened vulnerability. Design and setting Cross-sectional study of patients attending 11 general practices in Bristol, South West England. Method Adult patients (n = 1058) were recruited from waiting rooms of practices that were sampled on the basis of population characteristics. Patients completed anonymous questionnaires comprising measures of mental health problems (for example, depression) and addictive behaviours (for example, risky alcohol use). The Problem Gambling Severity Index (PGSI) measured gambling problems, along with a single-item measure of gambling problems among family members. Estimates of extent and variability according to practice and patient characteristics were produced. Results There were 0.9% of all patients exhibiting problem gambling (PGSI ≥5), and 4.3% reporting problems that were low to moderate in severity (PGSI 1–4). Around 7% of patients reported gambling problems among family members. Further analyses indicated that rates of any gambling problems (PGSI ≥1) were higher among males and young adults, and more tentatively, within a student healthcare setting. They were also elevated among patients exhibiting drug use, risky alcohol use, and depression. Conclusion There is need for improved understanding of the burden of, and responses to, patients with gambling problems in general practices, and new strategies to increase identification to facilitate improved care and early intervention. PMID:28289016
NITSOL: A Newton iterative solver for nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States)
1996-12-31
Newton iterative methods, also known as truncated Newton methods, are implementations of Newton`s method in which the linear systems that characterize Newton steps are solved approximately using iterative linear algebra methods. Here, we outline a well-developed Newton iterative algorithm together with a Fortran implementation called NITSOL. The basic algorithm is an inexact Newton method globalized by backtracking, in which each initial trial step is determined by applying an iterative linear solver until an inexact Newton criterion is satisfied. In the implementation, the user can specify inexact Newton criteria in several ways and select an iterative linear solver from among several popular {open_quotes}transpose-free{close_quotes} Krylov subspace methods. Jacobian-vector products used by the Krylov solver can be either evaluated analytically with a user-supplied routine or approximated using finite differences of function values. A flexible interface permits a wide variety of preconditioning strategies and allows the user to define a preconditioner and optionally update it periodically. We give details of these and other features and demonstrate the performance of the implementation on a representative set of test problems.
Fast linear solvers for variable density turbulent flows
Pouransari, Hadi; Mani, Ali; Darve, Eric
2015-11-01
Variable density flows are ubiquitous in variety of natural and industrial systems. Two-phase and multi-phase flows in natural and industrial processes, astrophysical flows, and flows involved in combustion processes are such examples. For an ideal gas subject to low-Mach approximation, variations in temperature can lead to a non-uniform density field. In this work, we consider radiatively heated particle-laden turbulent flows as an example application in which density variability is resulted from inhomogeneities in the heat absorption by an inhomogeneous particle field. Under such conditions, the divergence constraint of the fluid is enforced through a variable coefficient Poisson equation. Inversion of the discretized variable coefficient Poisson operator is difficult using the conventional linear solvers as the size of the problem grows. We apply a novel hierarchical linear solve algorithm based on low-rank approximations. The proposed linear solver could be applied to variety of linear systems arising from discretized partial differential equations. It can be used as a standalone direct-solver with tunable accuracy and linear complexity, or as a high-accuracy pre-conditioner in conjunction with other iterative methods.
Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems
Directory of Open Access Journals (Sweden)
D. Baleanu
2013-01-01
Full Text Available We present a direct solution technique for approximating linear multiterm fractional differential equations (FDEs on semi-infinite interval, using generalized Laguerre polynomials. We derive the operational matrix of Caputo fractional derivative of the generalized Laguerre polynomials which is applied together with generalized Laguerre tau approximation for implementing a spectral solution of linear multiterm FDEs on semi-infinite interval subject to initial conditions. The generalized Laguerre pseudo-spectral approximation based on the generalized Laguerre operational matrix is investigated to reduce the nonlinear multiterm FDEs and its initial conditions to nonlinear algebraic system, thus greatly simplifying the problem. Through several numerical examples, we confirm the accuracy and performance of the proposed spectral algorithms. Indeed, the methods yield accurate results, and the exact solutions are achieved for some tested problems.
Cederlöf, Martin; Pettersson, Erik; Sariaslan, Amir; Larsson, Henrik; Östberg, Per; Kelleher, Ian; Långström, Niklas; Gumpert, Clara Hellner; Lundström, Sebastian; Lichtenstein, Paul
2016-03-01
Studies suggest associations between childhood autistic traits and adolescent psychotic experiences. However, recent research suggests that a general neuropsychiatric problems factor predicts adverse outcomes better than specific diagnostic entities. To examine if the alleged association between autistic traits and psychotic experiences could rather be explained by a general neuropsychiatric problems factor comprising symptoms of ADHD, tic disorder, developmental coordination disorder, and learning disorder, we conducted a prospective cohort study based on the Child and Adolescent Twin Study in Sweden. In addition, we examined the genetic and environmental influences on the associations. A total of 9,282 twins with data on childhood autistic traits and other neuropsychiatric problems, and follow-up data on psychotic experiences at ages 15 and/or 18 years were included. First, psychotic experiences were regressed on autistic traits and second, the general neuropsychiatric problems factor was added to the model. Auditory hallucinations were analyzed separately from the other psychotic experiences. Finally, twin analyses were employed to disentangle genetic from environmental influences in the observed associations. Replicating prior research, significant associations were found between autistic traits in childhood and auditory hallucinations at ages 15 and 18. However, after controlling for the general neuropsychiatric problems factor, the associations between autistic traits and auditory hallucinations disappeared, whereas the association between the general neuropsychiatric problems factor and auditory hallucinations persisted after controlling for autistic traits. Twin analyses revealed that the association between the general neuropsychiatric problems factor and auditory hallucinations was driven by shared genetic influences. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.
Gainullin, I. K.; Sonkin, M. A.
2015-03-01
A parallelized three-dimensional (3D) time-dependent Schrodinger equation (TDSE) solver for one-electron systems is presented in this paper. The TDSE Solver is based on the finite-difference method (FDM) in Cartesian coordinates and uses a simple and explicit leap-frog numerical scheme. The simplicity of the numerical method provides very efficient parallelization and high performance of calculations using Graphics Processing Units (GPUs). For example, calculation of 106 time-steps on the 1000ṡ1000ṡ1000 numerical grid (109 points) takes only 16 hours on 16 Tesla M2090 GPUs. The TDSE Solver demonstrates scalability (parallel efficiency) close to 100% with some limitations on the problem size. The TDSE Solver is validated by calculation of energy eigenstates of the hydrogen atom (13.55 eV) and affinity level of H- ion (0.75 eV). The comparison with other TDSE solvers shows that a GPU-based TDSE Solver is 3 times faster for the problems of the same size and with the same cost of computational resources. The usage of a non-regular Cartesian grid or problem-specific non-Cartesian coordinates increases this benefit up to 10 times. The TDSE Solver was applied to the calculation of the resonant charge transfer (RCT) in nanosystems, including several related physical problems, such as electron capture during H+-H0 collision and electron tunneling between H- ion and thin metallic island film.
Matlab Geochemistry: An open source geochemistry solver based on MRST
McNeece, C. J.; Raynaud, X.; Nilsen, H.; Hesse, M. A.
2017-12-01
The study of geological systems often requires the solution of complex geochemical relations. To address this need we present an open source geochemical solver based on the Matlab Reservoir Simulation Toolbox (MRST) developed by SINTEF. The implementation supports non-isothermal multicomponent aqueous complexation, surface complexation, ion exchange, and dissolution/precipitation reactions. The suite of tools available in MRST allows for rapid model development, in particular the incorporation of geochemical calculations into transport simulations of multiple phases, complex domain geometry and geomechanics. Different numerical schemes and additional physics can be easily incorporated into the existing tools through the object-oriented framework employed by MRST. The solver leverages the automatic differentiation tools available in MRST to solve arbitrarily complex geochemical systems with any choice of species or element concentration as input. Four mathematical approaches enable the solver to be quite robust: 1) the choice of chemical elements as the basis components makes all entries in the composition matrix positive thus preserving convexity, 2) a log variable transformation is used which transfers the nonlinearity to the convex composition matrix, 3) a priori bounds on variables are calculated from the structure of the problem, constraining Netwon's path and 4) an initial guess is calculated implicitly by sequentially adding model complexity. As a benchmark we compare the model to experimental and semi-analytic solutions of the coupled salinity-acidity transport system. Together with the reservoir simulation capabilities of MRST the solver offers a promising tool for geochemical simulations in reservoir domains for applications in a diversity of fields from enhanced oil recovery to radionuclide storage.
A Rule-Based Local Search Algorithm for General Shift Design Problems in Airport Ground Handling
DEFF Research Database (Denmark)
Clausen, Tommy
We consider a generalized version of the shift design problem where shifts are created to cover a multiskilled demand and fit the parameters of the workforce. We present a collection of constraints and objectives for the generalized shift design problem. A local search solution framework with mul...... with multiple neighborhoods and a loosely coupled rule engine based on simulated annealing is presented. Computational experiments on real-life data from various airport ground handling organization show the performance and flexibility of the proposed algorithm....
Directory of Open Access Journals (Sweden)
Valeriy Yu. Bykov
2010-08-01
Full Text Available In the article the problems, which appear under the creation of monitoring systems concerning the condition of informatization of general educational institutions, such as definition of monitoring object and list of parameters that will be traced during the monitoring, technologies of obtaining and actualization of data parameters, that are to be monitored, formats of data submission and ways of its processing, monitoring time period etc. are considered. In the article some decision of these problems are offered. Here is also mentioned the data of some characteristics and possibilities of the creation of monitoring systems concerning the condition of informatization of general educational institutions in Ukraine.
Learning generalization in problem solving by a blue-fronted parrot (Amazona aestiva).
de Mendonça-Furtado, Olívia; Ottoni, Eduardo B
2008-10-01
Pepperberg (The Alex studies: cognitive and communicative abilities of gray parrots. Harvard University Press, Cambridge;1999) showed that some of the complex cognitive capabilities found in primates are also present in psittacine birds. Through the replication of an experiment performed with cotton-top tamarins (Saguinus oedipus oedipus) by Hauser et al. (Anim Behav 57:565-582; 1999), we examined a blue-fronted parrot's (Amazona aestiva) ability to generalize the solution of a particular problem in new but similar cases. Our results show that, at least when it comes to solving this particular problem, our parrot subject exhibited learning generalization capabilities resembling the tamarins'.
Accelerated Cyclic Reduction: A Distributed-Memory Fast Solver for Structured Linear Systems
Chávez, Gustavo
2017-12-15
We present Accelerated Cyclic Reduction (ACR), a distributed-memory fast solver for rank-compressible block tridiagonal linear systems arising from the discretization of elliptic operators, developed here for three dimensions. Algorithmic synergies between Cyclic Reduction and hierarchical matrix arithmetic operations result in a solver that has O(kNlogN(logN+k2)) arithmetic complexity and O(k Nlog N) memory footprint, where N is the number of degrees of freedom and k is the rank of a block in the hierarchical approximation, and which exhibits substantial concurrency. We provide a baseline for performance and applicability by comparing with the multifrontal method with and without hierarchical semi-separable matrices, with algebraic multigrid and with the classic cyclic reduction method. Over a set of large-scale elliptic systems with features of nonsymmetry and indefiniteness, the robustness of the direct solvers extends beyond that of the multigrid solver, and relative to the multifrontal approach ACR has lower or comparable execution time and size of the factors, with substantially lower numerical ranks. ACR exhibits good strong and weak scaling in a distributed context and, as with any direct solver, is advantageous for problems that require the solution of multiple right-hand sides. Numerical experiments show that the rank k patterns are of O(1) for the Poisson equation and of O(n) for the indefinite Helmholtz equation. The solver is ideal in situations where low-accuracy solutions are sufficient, or otherwise as a preconditioner within an iterative method.
Parallelization of the preconditioned IDR solver for modern multicore computer systems
Bessonov, O. A.; Fedoseyev, A. I.
2012-10-01
This paper present the analysis, parallelization and optimization approach for the large sparse matrix solver CNSPACK for modern multicore microprocessors. CNSPACK is an advanced solver successfully used for coupled solution of stiff problems arising in multiphysics applications such as CFD, semiconductor transport, kinetic and quantum problems. It employs iterative IDR algorithm with ILU preconditioning (user chosen ILU preconditioning order). CNSPACK has been successfully used during last decade for solving problems in several application areas, including fluid dynamics and semiconductor device simulation. However, there was a dramatic change in processor architectures and computer system organization in recent years. Due to this, performance criteria and methods have been revisited, together with involving the parallelization of the solver and preconditioner using Open MP environment. Results of the successful implementation for efficient parallelization are presented for the most advances computer system (Intel Core i7-9xx or two-processor Xeon 55xx/56xx).
Yagain, Deepa; Vijaya Krishna, A.
2014-01-01
Retiming is a transformation which can be applied to digital filter blocks that can increase the clock frequency. This transformation requires computation of critical path and shortest path at various stages. In literature, this problem is addressed at multiple points. However, very little attention is given to path solver blocks in retiming transformation algorithm which takes up most of the computation time. In this paper, we address the problem of optimizing the speed of path solvers in re...
International Nuclear Information System (INIS)
Kastanya, Doddy Yozef Febrian; Turinsky, Paul J.
2005-01-01
A Newton-Krylov iterative solver has been developed to reduce the CPU execution time of boiling water reactor (BWR) core simulators implemented in the core simulator part of the Fuel Optimization for Reloads Multiple Objectives by Simulated Annealing for BWR (FORMOSA-B) code, which is an in-core fuel management optimization code for BWRs. This new solver utilizes Newton's method to explicitly treat strong nonlinearities in the problem, replacing the traditionally used nested iterative approach. Newton's method provides the solver with a higher-than-linear convergence rate, assuming that good initial estimates of the unknowns are provided. Within each Newton iteration, an appropriately preconditioned Krylov solver is utilized for solving the linearized system of equations. Taking advantage of the higher convergence rate provided by Newton's method and utilizing an efficient preconditioned Krylov solver, we have developed a Newton-Krylov solver to evaluate the three-dimensional, two-group neutron diffusion equations coupled with a two-phase flow model within a BWR core simulator. Numerical tests on the new solver have shown that speedups ranging from 1.6 to 2.1, with reference to the traditional approach of employing nested iterations to treat the nonlinear feedbacks, can be achieved. However, if a preconditioned Krylov solver is employed to complete the inner iterations of the traditional approach, negligible CPU time differences are noted between the Newton-Krylov and traditional (Krylov) approaches
State and problems of physical education in regional general education educational institutions
Мамешина, Маргарита Анатоліївна; Масляк, Ірина Павлівна
2015-01-01
Margarita Mameshina, Irina MaslyakPurpose: to study a state and problems of physical education in regional general education educational institutions. Material and Methods: 29 teachers of physical culture of Izyum and Izyum district of the Kharkov region took part in the research. The following methods were used: theoretical analysis and generalization of scientific literature, opinion poll, and mathematical statistics. Results: it is established that most of teachers aren't absolutely satisf...
State and problems of physical education in regional general education educational institutions
Mameshina, Margarita; Maslyak, Irina; Zhuk, Vjacheslav
2015-01-01
Purpose: to study a state and problems of physical education in regional general education educational institutions. Material and Methods: 29 teachers of physical culture of Izyum and Izyum district of the Kharkov region took part in the research. The following methods were used: theoretical analysis and generalization of scientific literature, opinion poll, and mathematical statistics. Results: it is established that most of teachers aren't absolutely satisfied with the relation of pupils to...
International Nuclear Information System (INIS)
Schulze-Halberg, Axel
2010-01-01
We study Green's functions of the generalized Sturm-Liouville problems that are related to each other by Darboux -equivalently, supersymmetrical - transformations. We establish an explicit relation between the corresponding Green's functions and derive a simple formula for their trace. The class of equations considered here includes the conventional Schroedinger equation and generalizations, such as for position-dependent mass and with linearly energy-dependent potential, as well as the stationary Fokker-Planck equation.
Domain decomposition solvers for nonlinear multiharmonic finite element equations
Copeland, D. M.
2010-01-01
In many practical applications, for instance, in computational electromagnetics, the excitation is time-harmonic. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series and approximating the Fourier coefficients by finite elements, we arrive at a large-scale coupled nonlinear system for determining the finite element approximation to the Fourier coefficients. The construction of fast solvers for such systems is very crucial for the efficiency of this multiharmonic approach. In this paper we look at nonlinear, time-harmonic potential problems as simple model problems. We construct and analyze almost optimal solvers for the Jacobi systems arising from the Newton linearization of the large-scale coupled nonlinear system that one has to solve instead of performing the expensive time-integration procedure. © 2010 de Gruyter.
Inductive ionospheric solver for magnetospheric MHD simulations
Directory of Open Access Journals (Sweden)
H. Vanhamäki
2011-01-01
Full Text Available We present a new scheme for solving the ionospheric boundary conditions required in magnetospheric MHD simulations. In contrast to the electrostatic ionospheric solvers currently in use, the new solver takes ionospheric induction into account by solving Faraday's law simultaneously with Ohm's law and current continuity. From the viewpoint of an MHD simulation, the new inductive solver is similar to the electrostatic solvers, as the same input data is used (field-aligned current [FAC] and ionospheric conductances and similar output is produced (ionospheric electric field. The inductive solver is tested using realistic, databased models of an omega-band and westward traveling surge. Although the tests were performed with local models and MHD simulations require a global ionospheric solution, we may nevertheless conclude that the new solution scheme is feasible also in practice. In the test cases the difference between static and electrodynamic solutions is up to ~10 V km−1 in certain locations, or up to 20-40% of the total electric field. This is in agreement with previous estimates. It should also be noted that if FAC is replaced by the ground magnetic field (or ionospheric equivalent current in the input data set, exactly the same formalism can be used to construct an inductive version of the KRM method originally developed by Kamide et al. (1981.
General versus executive cognitive ability in pupils with ADHD and with milder attention problems
Directory of Open Access Journals (Sweden)
Ek U
2013-01-01
Full Text Available Ulla Ek,1 Joakim Westerlund,2 Elisabeth Fernell31Department of Special Education, 2Department of Psychology, Stockholm University, Stockholm, 3Gillberg Neuropsychiatry Centre, Sahlgrenska Academy, University of Gothenburg and the Research and Development Centre, Skaraborg Hospital Skövde, SwedenBackground: The aim of this study was to analyze two main types of cognitive domains in school children with different types and severities of attention-related problems. The cognitive domains examined were general cognitive ability and executive abilities.Methods: Three different clinical samples of pupils with school problems were analyzed to assess their cognitive Wechsler Intelligence Scale for Children profiles. In particular, the general cognitive ability index and the executive markers (ie, verbal memory index and processing speed index were of interest. Of the total sample (n = 198, two main groups were contrasted; one met the full criteria for attention deficit hyperactivity disorder (ADHD/subthreshold ADHD, and one was comprised of those with milder attention problems, insufficient to meet the criteria for ADHD/subthreshold ADHD.Results: It could be demonstrated that both groups had a significantly higher score on the general cognitive ability index than on measures of working memory and processing speed. This difference was more pronounced for boys.Conclusion: These types of cognitive differences need to be considered in children with different kinds of learning, behavior, and attention problems; this is also true for children presenting with an average general intelligence quotient and with milder attention problems. Current educational expectations are demanding for children with mild difficulties, and such cognitive information will add to the understanding of the child's learning problems, hopefully leading to a better adapted education than that conventionally available.Keywords: working memory, processing speed, children, learning and
Directory of Open Access Journals (Sweden)
Hutton Catherine
2007-05-01
Full Text Available Abstract Background Psychological problems present a huge burden of illness in our community and GPs are the main providers of care. There is evidence that longer consultations in general practice are associated with improved quality of care; but this needs to be balanced against the fact that doctor time is a limited resource and longer consultations may lead to reduced access to health care. The aim of this research was to conduct a systematic literature review to determine whether management of psychological problems in general practice is associated with an increased consultation length and to explore whether longer consultations are associated with better health outcomes for patients with psychological problems. Methods A search was conducted on Medline (Ovid databases up to7 June 2006. The following search terms, were used: general practice or primary health care (free text or family practice (MeSH AND consultation length or duration (free text or time factors (MeSH AND depression or psychological problems or depressed (free text. A similar search was done in Web of Science, Pubmed, Google Scholar, and Cochrane Library and no other papers were found. Studies were included if they contained data comparing consultation length and management or detection of psychological problems in a general practice or primary health care setting. The studies were read and categories developed to enable systematic data extraction and synthesis. Results 29 papers met the inclusion criteria. Consultations with a recorded diagnosis of a psychological problem were reported to be longer than those with no recorded psychological diagnosis. It is not clear if this is related to the extra time or the consultation style. GPs reported that time pressure is a major barrier to treating depression. There was some evidence that increased consultation length is associated with more accurate diagnosis of psychological problems. Conclusion Further research is needed to
Domain decomposed preconditioners with Krylov subspace methods as subdomain solvers
Energy Technology Data Exchange (ETDEWEB)
Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States)
1994-12-31
Domain decomposed preconditioners for nonsymmetric partial differential equations typically require the solution of problems on the subdomains. Most implementations employ exact solvers to obtain these solutions. Consequently work and storage requirements for the subdomain problems grow rapidly with the size of the subdomain problems. Subdomain solves constitute the single largest computational cost of a domain decomposed preconditioner, and improving the efficiency of this phase of the computation will have a significant impact on the performance of the overall method. The small local memory available on the nodes of most message-passing multicomputers motivates consideration of the use of an iterative method for solving subdomain problems. For large-scale systems of equations that are derived from three-dimensional problems, memory considerations alone may dictate the need for using iterative methods for the subdomain problems. In addition to reduced storage requirements, use of an iterative solver on the subdomains allows flexibility in specifying the accuracy of the subdomain solutions. Substantial savings in solution time is possible if the quality of the domain decomposed preconditioner is not degraded too much by relaxing the accuracy of the subdomain solutions. While some work in this direction has been conducted for symmetric problems, similar studies for nonsymmetric problems appear not to have been pursued. This work represents a first step in this direction, and explores the effectiveness of performing subdomain solves using several transpose-free Krylov subspace methods, GMRES, transpose-free QMR, CGS, and a smoothed version of CGS. Depending on the difficulty of the subdomain problem and the convergence tolerance used, a reduction in solution time is possible in addition to the reduced memory requirements. The domain decomposed preconditioner is a Schur complement method in which the interface operators are approximated using interface probing.
Variational P1 approximations of general-geometry multigroup transport problems
International Nuclear Information System (INIS)
Rulko, R.P.; Tomasevic, D.; Larsen, E.W.
1995-01-01
A variational approximation is developed for general-geometry multigroup transport problems with arbitrary anisotropic scattering. The variational principle is based on a functional that approximates a reaction rate in a subdomain of the system. In principle, approximations that result from this functional ''optimally'' determine such reaction rates. The functional contains an arbitrary parameter α and requires the approximate solutions of a forward and an adjoint transport problem. If the basis functions for the forward and adjoint solutions are chosen to be linear functions of the angular variable Ω, the functional yields the familiar multigroup P 1 equations for all values of α. However, the boundary conditions that result from the functional depend on α. In particular, for problems with vacuum boundaries, one obtains the conventional mixed boundary condition, but with an extrapolation distance that depends continuously on α. The choice α = 0 yields a generalization of boundary conditions derived earlier by Federighi and Pomraning for a more limited class of problems. The choice α = 1 yields a generalization of boundary conditions derived previously by Davis for monoenergetic problems. Other boundary conditions are obtained by choosing different values of α. The authors discuss this indeterminancy of α in conjunction with numerical experiments
Barbagallo, Annamaria; Di Meglio, Guglielmo; Mauro, Paolo
2017-07-01
The aim of the paper is to study, in a Hilbert space setting, a general random oligopolistic market equilibrium problem in presence of both production and demand excesses and to characterize the random Cournot-Nash equilibrium principle by means of a stochastic variational inequality. Some existence results are presented.
M. Nool (Margreet); A. van der Ploeg (Auke)
1997-01-01
textabstractWe study the solution of generalized eigenproblems generated by a model which is used for stability investigation of tokamak plasmas. The eigenvalue problems are of the form $A x = lambda B x$, in which the complex matrices $A$ and $B$ are block tridiagonal, and $B$ is Hermitian positive
Parametric general variational-like inequality problem in uniformly smooth Banach space
Directory of Open Access Journals (Sweden)
Kazmi KR
2006-01-01
Full Text Available Using the concept of - -proximal mapping, we study the existence and sensitivity analysis of solution of a parametric general variational-like inequality problem in uniformly smooth Banach space. The approach used may be treated as an extension and unification of approaches for studying sensitivity analysis for various important classes of variational inequalities given by many authors in this direction.
R.R.K. Hartmann (Ed.). Solving Language Problems: From General to
African Journals Online (AJOL)
Solving Language Problems: From General to. Applied Linguistics, 1st edition 1996, vi + 298 pp. ISBN 0-85989-484-3. Exeter: University of Exeter Press. Price £13,95. Questions about the nature of linguistics and its contribution to human intel- lectual pursuit often appear in academic discussions and in casual conversa-.
Modelo de selección de cartera con Solver
Directory of Open Access Journals (Sweden)
P. Fogués Zornoza
2012-04-01
Full Text Available In this paper, we present an example of linear optimization in the context of degrees in Economics or Business Administration and Management. We show techniques that enable students to go deep and investigate in real problems that have been modelled using the Excel platform. The model shown here has been developed by a student and it consists in minimizing the absolute deviations over the average expected return of a portfolio of securities, using the solver tool that it is included in this software.
A Parallel Algebraic Multigrid Solver on Graphics Processing Units
Haase, Gundolf
2010-01-01
The paper presents a multi-GPU implementation of the preconditioned conjugate gradient algorithm with an algebraic multigrid preconditioner (PCG-AMG) for an elliptic model problem on a 3D unstructured grid. An efficient parallel sparse matrix-vector multiplication scheme underlying the PCG-AMG algorithm is presented for the many-core GPU architecture. A performance comparison of the parallel solver shows that a singe Nvidia Tesla C1060 GPU board delivers the performance of a sixteen node Infiniband cluster and a multi-GPU configuration with eight GPUs is about 100 times faster than a typical server CPU core. © 2010 Springer-Verlag.
Collier, Nathan
2012-03-01
We study the performance of direct solvers on linear systems of equations resulting from isogeometric analysis. The problem of choice is the canonical Laplace equation in three dimensions. From this study we conclude that for a fixed number of unknowns and polynomial degree of approximation, a higher degree of continuity k drastically increases the CPU time and RAM needed to solve the problem when using a direct solver. This paper presents numerical results detailing the phenomenon as well as a theoretical analysis that explains the underlying cause. © 2011 Elsevier B.V.
A Family of High-Performance Solvers for Linear Model Predictive Control
DEFF Research Database (Denmark)
Frison, Gianluca; Sokoler, Leo Emil; Jørgensen, John Bagterp
2014-01-01
In Model Predictive Control (MPC), an optimization problem has to be solved at each sampling time, and this has traditionally limited the use of MPC to systems with slow dynamic. In this paper, we propose an e_cient solution strategy for the unconstrained sub-problems that give the search......, and techniques such as inexact search direction and mixed precision computation. Finally, we test our HPMPC toolbox, a family of high-performance solvers tailored for MPC and implemented using these techniques, that is shown to be several times faster than current state-of-the-art solvers for linear MPC....
Using SPARK as a Solver for Modelica
Energy Technology Data Exchange (ETDEWEB)
Wetter, Michael; Wetter, Michael; Haves, Philip; Moshier, Michael A.; Sowell, Edward F.
2008-06-30
Modelica is an object-oriented acausal modeling language that is well positioned to become a de-facto standard for expressing models of complex physical systems. To simulate a model expressed in Modelica, it needs to be translated into executable code. For generating run-time efficient code, such a translation needs to employ algebraic formula manipulations. As the SPARK solver has been shown to be competitive for generating such code but currently cannot be used with the Modelica language, we report in this paper how SPARK's symbolic and numerical algorithms can be implemented in OpenModelica, an open-source implementation of a Modelica modeling and simulation environment. We also report benchmark results that show that for our air flow network simulation benchmark, the SPARK solver is competitive with Dymola, which is believed to provide the best solver for Modelica.
New iterative solvers for the NAG Libraries
Energy Technology Data Exchange (ETDEWEB)
Salvini, S.; Shaw, G. [Numerical Algorithms Group Ltd., Oxford (United Kingdom)
1996-12-31
The purpose of this paper is to introduce the work which has been carried out at NAG Ltd to update the iterative solvers for sparse systems of linear equations, both symmetric and unsymmetric, in the NAG Fortran 77 Library. Our current plans to extend this work and include it in our other numerical libraries in our range are also briefly mentioned. We have added to the Library the new Chapter F11, entirely dedicated to sparse linear algebra. At Mark 17, the F11 Chapter includes sparse iterative solvers, preconditioners, utilities and black-box routines for sparse symmetric (both positive-definite and indefinite) linear systems. Mark 18 will add solvers, preconditioners, utilities and black-boxes for sparse unsymmetric systems: the development of these has already been completed.
Nakai, Minori; Hotta, Hiroshi; Ootsuru, Taku; Hiejima, Shigeto; Murakami, Masaru; Yuzuriha, Takefumi; Kondo, Tsuyoshi
2013-04-01
In Japan, many problems related to alcohol are pointed out from before. We believe that there is a unique drinking culture in Okinawa, such as a large amount of alcohol. Therefore, we estimate many people in Okinawa have a drinking problem. We conducted a survey of patients who visited general hospital (medical or surgical or orthopedic) in 2007. The purpose of this study is to collect basic data for introducing alcoholics to specialized treatment as early as possible, detecting the person who drink large amounts of alcohol, performing early intervention for people who drink large amount of alcohol, and advancing cooperation with specialized medical agencies of alcohol. As a result, Among the patients who visited general hospital in Okinawa, many problem drinkers are concentrated in the young age. and they have strong fears of health. The possibility of early intervention with intervention techniques, such as brief intervention, has been suggested.
s-Step Krylov Subspace Methods as Bottom Solvers for Geometric Multigrid
Energy Technology Data Exchange (ETDEWEB)
Williams, Samuel [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Lijewski, Mike [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Almgren, Ann [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Straalen, Brian Van [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Carson, Erin [Univ. of California, Berkeley, CA (United States); Knight, Nicholas [Univ. of California, Berkeley, CA (United States); Demmel, James [Univ. of California, Berkeley, CA (United States)
2014-08-14
Geometric multigrid solvers within adaptive mesh refinement (AMR) applications often reach a point where further coarsening of the grid becomes impractical as individual sub domain sizes approach unity. At this point the most common solution is to use a bottom solver, such as BiCGStab, to reduce the residual by a fixed factor at the coarsest level. Each iteration of BiCGStab requires multiple global reductions (MPI collectives). As the number of BiCGStab iterations required for convergence grows with problem size, and the time for each collective operation increases with machine scale, bottom solves in large-scale applications can constitute a significant fraction of the overall multigrid solve time. In this paper, we implement, evaluate, and optimize a communication-avoiding s-step formulation of BiCGStab (CABiCGStab for short) as a high-performance, distributed-memory bottom solver for geometric multigrid solvers. This is the first time s-step Krylov subspace methods have been leveraged to improve multigrid bottom solver performance. We use a synthetic benchmark for detailed analysis and integrate the best implementation into BoxLib in order to evaluate the benefit of a s-step Krylov subspace method on the multigrid solves found in the applications LMC and Nyx on up to 32,768 cores on the Cray XE6 at NERSC. Overall, we see bottom solver improvements of up to 4.2x on synthetic problems and up to 2.7x in real applications. This results in as much as a 1.5x improvement in solver performance in real applications.
Directory of Open Access Journals (Sweden)
Nurdan Cetin
2014-01-01
Full Text Available We consider a multiobjective linear fractional transportation problem (MLFTP with several fractional criteria, such as, the maximization of the transport profitability like profit/cost or profit/time, and its two properties are source and destination. Our aim is to introduce MLFTP which has not been studied in literature before and to provide a fuzzy approach which obtain a compromise Pareto-optimal solution for this problem. To do this, first, we present a theorem which shows that MLFTP is always solvable. And then, reducing MLFTP to the Zimmermann’s “min” operator model which is the max-min problem, we construct Generalized Dinkelbach’s Algorithm for solving the obtained problem. Furthermore, we provide an illustrative numerical example to explain this fuzzy approach.
A theory of general solutions of 3D problems in 1D hexagonal quasicrystals
International Nuclear Information System (INIS)
Gao Yang; Xu Sipeng; Zhao Baosheng
2008-01-01
A theory of general solutions of three-dimensional (3D) problems is developed for the coupled equilibrium equations in 1D hexagonal quasicrystals (QCs), and two new general solutions, which are called generalized Lekhnitskii-Hu-Nowacki (LHN) and Elliott-Lodge (E-L) solutions, respectively, are presented based on three theorems. As a special case, the generalized LHN solution is obtained from our previous general solution by introducing three high-order displacement functions. For further simplification, considering three cases in which three characteristic roots are distinct or possibly equal to each other, the generalized E-L solution shall take different forms, and be expressed in terms of four quasi-harmonic functions which are very simple and useful. It is proved that the general solution presented by Peng and Fan is consistent with one case of the generalized E-L solution, while does not include the other two cases. It is important to note that generalized LHN and E-L solutions are complete in z-convex domains, while incomplete in the usual non-z-convex domains
High-performance small-scale solvers for linear Model Predictive Control
DEFF Research Database (Denmark)
Frison, Gianluca; Sørensen, Hans Henrik Brandenborg; Dammann, Bernd
2014-01-01
, with the two main research areas of explicit MPC and tailored on-line MPC. State-of-the-art solvers in this second class can outperform optimized linear-algebra libraries (BLAS) only for very small problems, and do not explicitly exploit the hardware capabilities, relying on compilers for that. This approach......In Model Predictive Control (MPC), an optimization problem needs to be solved at each sampling time, and this has traditionally limited use of MPC to systems with slow dynamic. In recent years, there has been an increasing interest in the area of fast small-scale solvers for linear MPC...... can attain only a small fraction of the peak performance on modern processors. In our paper, we combine high-performance computing techniques with tailored solvers for MPC, and use the specific instruction sets of the target architectures. The resulting software (called HPMPC) can solve linear MPC...
Generalized Roe's numerical scheme for a two-fluid model
International Nuclear Information System (INIS)
Toumi, I.; Raymond, P.
1993-01-01
This paper is devoted to a mathematical and numerical study of a six equation two-fluid model. We will prove that the model is strictly hyperbolic due to the inclusion of the virtual mass force term in the phasic momentum equations. The two-fluid model is naturally written under a nonconservative form. To solve the nonlinear Riemann problem for this nonconservative hyperbolic system, a generalized Roe's approximate Riemann solver, is used, based on a linearization of the nonconservative terms. A Godunov type numerical scheme is built, using this approximate Riemann solver. 10 refs., 5 figs,
Frequent attenders in general practice: problem solving treatment provided by nurses [ISRCTN51021015
Directory of Open Access Journals (Sweden)
van Oppen P
2005-10-01
Full Text Available Abstract Background There is a need for assistance from primary care mental health workers in general practice in the Netherlands. General practitioners (GPs experience an overload of frequent attenders suffering from psychological problems. Problem Solving Treatment (PST is a brief psychological treatment tailored for use in a primary care setting. PST is provided by nurses, and earlier research has shown that it is a treatment at least as effective as usual care. However, research outcomes are not totally satisfying. This protocol describes a randomized clinical trial on the effectiveness of PST provided by nurses for patients in general practice. The results of this study, which currently being carried out, will be presented as soon as they are available. Methods/design This study protocol describes the design of a randomized controlled trial to investigate the effectiveness and cost-effectiveness of PST and usual care compared to usual care only. Patients, 18 years and older, who present psychological problems and are frequent attenders in general practice are recruited by the research assistant. The participants receive questionnaires at baseline, after the intervention, and again after 3 months and 9 months. Primary outcome is the reduction of symptoms, and other outcomes measured are improvement in problem solving skills, psychological and physical well being, daily functioning, social support, coping styles, problem evaluation and health care utilization. Discussion Our results may either confirm that PST in primary care is an effective way of dealing with emotional disorders and a promising addition to the primary care in the UK and USA, or may question this assumption. This trial will allow an evaluation of the effects of PST in practical circumstances and in a rather heterogeneous group of primary care patients. This study delivers scientific support for this use and therefore indications for optimal treatment and referral.
Generalized multiscale finite element methods for problems in perforated heterogeneous domains
Chung, Eric T.
2015-06-08
Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales. Moreover, these problems are intrinsically multiscale and their discretizations can yield very large linear or nonlinear systems. In this paper, we investigate multiscale approaches that attempt to solve such problems on a coarse grid by constructing multiscale basis functions in each coarse grid, where the coarse grid can contain many perforations. In particular, we are interested in cases when there is no scale separation and the perforations can have different sizes. In this regard, we mention some earlier pioneering works, where the authors develop multiscale finite element methods. In our paper, we follow Generalized Multiscale Finite Element Method (GMsFEM) and develop a multiscale procedure where we identify multiscale basis functions in each coarse block using snapshot space and local spectral problems. We show that with a few basis functions in each coarse block, one can approximate the solution, where each coarse block can contain many small inclusions. We apply our general concept to (1) Laplace equation in perforated domains; (2) elasticity equation in perforated domains; and (3) Stokes equations in perforated domains. Numerical results are presented for these problems using two types of heterogeneous perforated domains. The analysis of the proposed methods will be presented elsewhere. © 2015 Taylor & Francis
Magrabi, Farah; Liaw, Siaw Teng; Arachi, Diana; Runciman, William; Coiera, Enrico; Kidd, Michael R
2016-11-01
To identify the categories of problems with information technology (IT), which affect patient safety in general practice. General practitioners (GPs) reported incidents online or by telephone between May 2012 and November 2013. Incidents were reviewed against an existing classification for problems associated with IT and the clinical process impacted. 87 GPs across Australia. Types of problems, consequences and clinical processes. GPs reported 90 incidents involving IT which had an observable impact on the delivery of care, including actual patient harm as well as near miss events. Practice systems and medications were the most affected clinical processes. Problems with IT disrupted clinical workflow, wasted time and caused frustration. Issues with user interfaces, routine updates to software packages and drug databases, and the migration of records from one package to another generated clinical errors that were unique to IT; some could affect many patients at once. Human factors issues gave rise to some errors that have always existed with paper records but are more likely to occur and cause harm with IT. Such errors were linked to slips in concentration, multitasking, distractions and interruptions. Problems with patient identification and hybrid records generated errors that were in principle no different to paper records. Problems associated with IT include perennial risks with paper records, but additional disruptions in workflow and hazards for patients unique to IT, occasionally affecting multiple patients. Surveillance for such hazards may have general utility, but particularly in the context of migrating historical records to new systems and software updates to existing systems. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/.
Variational methods for problems from plasticity theory and for generalized Newtonian fluids
Fuchs, Martin
2000-01-01
Variational methods are applied to prove the existence of weak solutions for boundary value problems from the deformation theory of plasticity as well as for the slow, steady state flow of generalized Newtonian fluids including the Bingham and Prandtl-Eyring model. For perfect plasticity the role of the stress tensor is emphasized by studying the dual variational problem in appropriate function spaces. The main results describe the analytic properties of weak solutions, e.g. differentiability of velocity fields and continuity of stresses. The monograph addresses researchers and graduate students interested in applications of variational and PDE methods in the mechanics of solids and fluids.
Directory of Open Access Journals (Sweden)
Qinghai He
2013-01-01
Full Text Available In general Banach spaces, we consider a vector optimization problem (SVOP in which the objective is a set-valued mapping whose graph is the union of finitely many polyhedra or the union of finitely many generalized polyhedra. Dropping the compactness assumption, we establish some results on structure of the weak Pareto solution set, Pareto solution set, weak Pareto optimal value set, and Pareto optimal value set of (SVOP and on connectedness of Pareto solution set and Pareto optimal value set of (SVOP. In particular, we improved and generalize, Arrow, Barankin, and Blackwell’s classical results in Euclidean spaces and Zheng and Yang’s results in general Banach spaces.
The stochastic mechanics of fields in a general relativistic context: Problems and perspectives
International Nuclear Information System (INIS)
De Falco, D.
1987-01-01
The problem of a formulation of Nelson's stochastic mechanics of scalar fields in the context of general relativity is considered. The simple example of the scalar field in the Wightman vacuum state on the Rindler wedge is examined, the stochastic counterpart of the Fulling ambiguity of canonical quantization is formulated, and the role of the stochastic quantization is formulated, and the role of the stochastic mechanics of thermal mixtures, as formulated by Guerra and Loffredo, is analyzed in the solution, in the spirit of Davies and Unruh, of the above ambiguity. An overall picture emerges which, both in the explicit example considered here and in its straightforward generalizations to static submanifolds of more general space-times, confirms Smolin's point of view that stochastic quantization is a very natural conceptual frame in which to study the general non covariance of the distinction between quantum and thermal fluctuations. (orig.)
Tree-based solvers for adaptive mesh refinement code FLASH - I: gravity and optical depths
Wünsch, R.; Walch, S.; Dinnbier, F.; Whitworth, A.
2018-04-01
We describe an OctTree algorithm for the MPI parallel, adaptive mesh refinement code FLASH, which can be used to calculate the gas self-gravity, and also the angle-averaged local optical depth, for treating ambient diffuse radiation. The algorithm communicates to the different processors only those parts of the tree that are needed to perform the tree-walk locally. The advantage of this approach is a relatively low memory requirement, important in particular for the optical depth calculation, which needs to process information from many different directions. This feature also enables a general tree-based radiation transport algorithm that will be described in a subsequent paper, and delivers excellent scaling up to at least 1500 cores. Boundary conditions for gravity can be either isolated or periodic, and they can be specified in each direction independently, using a newly developed generalization of the Ewald method. The gravity calculation can be accelerated with the adaptive block update technique by partially re-using the solution from the previous time-step. Comparison with the FLASH internal multigrid gravity solver shows that tree-based methods provide a competitive alternative, particularly for problems with isolated or mixed boundary conditions. We evaluate several multipole acceptance criteria (MACs) and identify a relatively simple approximate partial error MAC which provides high accuracy at low computational cost. The optical depth estimates are found to agree very well with those of the RADMC-3D radiation transport code, with the tree-solver being much faster. Our algorithm is available in the standard release of the FLASH code in version 4.0 and later.
General practice-based clinical trials in Germany - a problem analysis
Directory of Open Access Journals (Sweden)
Hummers-Pradier Eva
2012-11-01
Full Text Available Abstract Background In Germany, clinical trials and comparative effectiveness studies in primary care are still very rare, while their usefulness has been recognised in many other countries. A network of researchers from German academic general practice has explored the reasons for this discrepancy. Methods Based on a comprehensive literature review and expert group discussions, problem analyses as well as structural and procedural prerequisites for a better implementation of clinical trials in German primary care are presented. Results In Germany, basic biomedical science and technology is more reputed than clinical or health services research. Clinical trials are funded by industry or a single national programme, which is highly competitive, specialist-dominated, exclusive of pilot studies, and usually favours innovation rather than comparative effectiveness studies. Academic general practice is still not fully implemented, and existing departments are small. Most general practitioners (GPs work in a market-based, competitive setting of small private practices, with a high case load. They have no protected time or funding for research, and mostly no research training or experience. Good Clinical Practice (GCP training is compulsory for participation in clinical trials. The group defined three work packages to be addressed regarding clinical trials in German general practice: (1 problem analysis, and definition of (2 structural prerequisites and (3 procedural prerequisites. Structural prerequisites comprise specific support facilities for general practice-based research networks that could provide practices with a point of contact. Procedural prerequisites consist, for example, of a summary of specific relevant key measures, for example on a web platform. The platform should contain standard operating procedures (SOPs, templates, checklists and other supporting materials for researchers. Conclusion All in all, our problem analyses revealed that
New generalized variable stepsizes of the CQ algorithm for solving the split feasibility problem
Directory of Open Access Journals (Sweden)
Peiyuan Wang
2017-06-01
Full Text Available Abstract Variable stepsize methods are effective for various modified CQ algorithms to solve the split feasibility problem (SFP. The purpose of this paper is first to introduce two new simpler variable stepsizes of the CQ algorithm. Then two new generalized variable stepsizes which can cover the former ones are also proposed in real Hilbert spaces. And then, two more general KM (Krasnosel’skii-Mann-CQ algorithms are also presented. Several weak and strong convergence properties are established. Moreover, some numerical experiments have been taken to illustrate the performance of the proposed stepsizes and algorithms.
Energy Technology Data Exchange (ETDEWEB)
Bordner, J.; Saied, F. [Univ. of Illinois, Urbana, IL (United States)
1996-12-31
GLab3D is an enhancement of an interactive environment (MGLab) for experimenting with iterative solvers and multigrid algorithms. It is implemented in MATLAB. The new version has built-in 3D elliptic pde`s and several iterative methods and preconditioners that were not available in the original version. A sparse direct solver option has also been included. The multigrid solvers have also been extended to 3D. The discretization and pde domains are restricted to standard finite differences on the unit square/cube. The power of this software studies in the fact that no programming is needed to solve, for example, the convection-diffusion equation in 3D with TFQMR and a customized V-cycle preconditioner, for a variety of problem sizes and mesh Reynolds, numbers. In addition to the graphical user interface, some sample drivers are included to show how experiments can be composed using the underlying suite of problems and solvers.
Association of Problem Gambling with Type of Gambling Among Italian General Population.
Scalese, Marco; Bastiani, Luca; Salvadori, Stefano; Gori, Mercedes; Lewis, Isabella; Jarre, Paolo; Molinaro, Sabrina
2016-09-01
The origin of gambling disorders is uncertain; however, research has shown a tendency to focus on specific types of games as a potential important risk factor. The principal aim of this study is to examine the relationships between types of gambling practices and gambling disorder. The data were extracted from IPSAD-Italia(®) 2010-2011 (Italian Population Survey on Alcohol and other Drugs), a survey among the Italian general population which collects socio-cultural information, information about the use of drugs, legal substances and gambling habits. In order to identify the "problem gambler" we used the Problem Gambling Severity Index. Three groups are considered in this analysis: no-risk gamblers, low-risk gamblers, moderate-risk/problem gamblers. Type of gambling practice was considered among two types of gambler: one-game players and multi-games players. 1.9 % of multi-game players were considered problem gamblers, only 0.6 % of one-game players were problem gamblers (p gambling severity was associated with multi-game players (OR = 2.23, p gambling severity among both one-game players and multi-game players, with scores of OR equal to 4.3 and 4.5 respectively. These findings suggest a popular perception of risk associated with this type of gambling for the development of gambling problems.
An Extensive Evaluation of Portfolio Approaches for Constraint Satisfaction Problems
Directory of Open Access Journals (Sweden)
Roberto Amadini
2016-06-01
Full Text Available In the context of Constraint Programming, a portfolio approach exploits the complementary strengths of a portfolio of different constraint solvers. The goal is to predict and run the best solver(s of the portfolio for solving a new, unseen problem. In this work we reproduce, simulate, and evaluate the performance of different portfolio approaches on extensive benchmarks of Constraint Satisfaction Problems. Empirical results clearly show the benefits of portfolio solvers in terms of both solved instances and solving time.
Application of alternating decision trees in selecting sparse linear solvers
Bhowmick, Sanjukta
2010-01-01
The solution of sparse linear systems, a fundamental and resource-intensive task in scientific computing, can be approached through multiple algorithms. Using an algorithm well adapted to characteristics of the task can significantly enhance the performance, such as reducing the time required for the operation, without compromising the quality of the result. However, the best solution method can vary even across linear systems generated in course of the same PDE-based simulation, thereby making solver selection a very challenging problem. In this paper, we use a machine learning technique, Alternating Decision Trees (ADT), to select efficient solvers based on the properties of sparse linear systems and runtime-dependent features, such as the stages of simulation. We demonstrate the effectiveness of this method through empirical results over linear systems drawn from computational fluid dynamics and magnetohydrodynamics applications. The results also demonstrate that using ADT can resolve the problem of over-fitting, which occurs when limited amount of data is available. © 2010 Springer Science+Business Media LLC.
Algorithm for Solving a Generalized Mixed Equilibrium Problem with Perturbation in a Banach Space
Kum Sangho; Yao Jen-Chih; Ceng Lu-Chuan
2010-01-01
Let be a real Banach space with the dual space . Let be a proper functional and let be a bifunction. In this paper, a new concept of -proximal mapping of with respect to is introduced. The existence and Lipschitz continuity of the -proximal mapping of with respect to are proved. By using properties of the -proximal mapping of with respect to , a generalized mixed equilibrium problem with perturbation (for short, GMEPP) is introduced and studied in Banach space . An exis...
Inverse planning for x-ray rotation therapy: a general solution of the inverse problem
International Nuclear Information System (INIS)
Oelfke, U.; Bortfeld, T.
1999-01-01
Rotation therapy with photons is currently under investigation for the delivery of intensity modulated radiotherapy (IMRT). An analytical approach for inverse treatment planning of this radiotherapy technique is described. The inverse problem for the delivery of arbitrary 2D dose profiles is first formulated and then solved analytically. In contrast to previously applied strategies for solving the inverse problem, it is shown that the most general solution for the fluence profiles consists of two independent solutions of different parity. A first analytical expression for both fluence profiles is derived. The mathematical derivation includes two different strategies, an elementary expansion of fluence and dose into polynomials and a more practical approach in terms of Fourier transforms. The obtained results are discussed in the context of previous work on this problem. (author)
Reply to C. M. Will on the axially symmetric two-body problem in general relativity
International Nuclear Information System (INIS)
Cooperstock, F.I.; Lim, P.H.
1985-01-01
The recent paper by Will (1983) is considered which purports to demonstrate that the gravitational radiation which the authors had computed from their model two-body free-fall system is consistent with the so-called quadrupole formula. It is shown that in fact the system presented by Will is different from the authors and that the illegitimate application of the quadrupole formula to the authors system leads to a smaller flux than that which is correctly deduced using general relativity and a proper consideration of nonlinearities. It is demonstrated that a judicious choice of stress release is propagated through the bodies as a superposition of plane and spherical waves leading to pressure fluctuations to the order in question. This underlines the essential distinction between the authors problem and the Will problem. Various aspects of the problem are also discussed. 25 references
An analogue of Morse theory for planar linear networks and the generalized Steiner problem
International Nuclear Information System (INIS)
Karpunin, G A
2000-01-01
A study is made of the generalized Steiner problem: the problem of finding all the locally minimal networks spanning a given boundary set (terminal set). It is proposed to solve this problem by using an analogue of Morse theory developed here for planar linear networks. The space K of all planar linear networks spanning a given boundary set is constructed. The concept of a critical point and its index is defined for the length function l of a planar linear network. It is shown that locally minimal networks are local minima of l on K and are critical points of index 1. The theorem is proved that the sum of the indices of all the critical points is equal to χ(K)=1. This theorem is used to find estimates for the number of locally minimal networks spanning a given boundary set
Energy Technology Data Exchange (ETDEWEB)
Stathopoulos, A.; Fischer, C.F. [Vanderbilt Univ., Nashville, TN (United States); Saad, Y.
1994-12-31
The solution of the large, sparse, symmetric eigenvalue problem, Ax = {lambda}x, is central to many scientific applications. Among many iterative methods that attempt to solve this problem, the Lanczos and the Generalized Davidson (GD) are the most widely used methods. The Lanczos method builds an orthogonal basis for the Krylov subspace, from which the required eigenvectors are approximated through a Rayleigh-Ritz procedure. Each Lanczos iteration is economical to compute but the number of iterations may grow significantly for difficult problems. The GD method can be considered a preconditioned version of Lanczos. In each step the Rayleigh-Ritz procedure is solved and explicit orthogonalization of the preconditioned residual ((M {minus} {lambda}I){sup {minus}1}(A {minus} {lambda}I)x) is performed. Therefore, the GD method attempts to improve convergence and robustness at the expense of a more complicated step.
Kim, Hyoun S; Salmon, Melissa; Wohl, Michael J A; Young, Matthew
2016-04-01
The current research examined whether alcohol consumption exacerbates suicidal ideations among gamblers in the general population. While prior research suggests problem gambling severity and excessive alcohol consumption are unique predictors of suicidal behaviors, the extant literature as almost exclusively focused on gamblers in treatment. This represents a significant gap in the literature as less than 10% of gamblers seek treatment. Furthermore, gamblers in treatment are not representative of gamblers in the general population, precluding a simple generalization of research findings. We address this gap using data obtained from the Canadian Community Health Survey (Cycle 4.1)--a cross-sectional national survey that assesses health-related information among the Canadian population. To this end, we conducted a moderation analysis with problem gambling severity as the independent variable, weekly alcohol consumption as the moderator variable and suicidal ideations (in the past 12 months) as the dependent variable. The results found that alcohol consumption alone did not reliably predict suicidal ideation among gamblers who did not gamble problematically. However, as predicted, the odds of suicidal ideation were greatest among problem gamblers who frequently consumed alcohol. Thus, it may behoove policy makers to re-visit the availability of alcohol in gambling venues. Moreover, responsible gambling-oriented education initiatives may be advanced by informing gamblers about the increased risk of suicidal ideations when problematic gambling is combined with frequent alcohol consumption.
Feng, Wenqiang; Guo, Zhenlin; Lowengrub, John S.; Wise, Steven M.
2018-01-01
We present a mass-conservative full approximation storage (FAS) multigrid solver for cell-centered finite difference methods on block-structured, locally cartesian grids. The algorithm is essentially a standard adaptive FAS (AFAS) scheme, but with a simple modification that comes in the form of a mass-conservative correction to the coarse-level force. This correction is facilitated by the creation of a zombie variable, analogous to a ghost variable, but defined on the coarse grid and lying under the fine grid refinement patch. We show that a number of different types of fine-level ghost cell interpolation strategies could be used in our framework, including low-order linear interpolation. In our approach, the smoother, prolongation, and restriction operations need never be aware of the mass conservation conditions at the coarse-fine interface. To maintain global mass conservation, we need only modify the usual FAS algorithm by correcting the coarse-level force function at points adjacent to the coarse-fine interface. We demonstrate through simulations that the solver converges geometrically, at a rate that is h-independent, and we show the generality of the solver, applying it to several nonlinear, time-dependent, and multi-dimensional problems. In several tests, we show that second-order asymptotic (h → 0) convergence is observed for the discretizations, provided that (1) at least linear interpolation of the ghost variables is employed, and (2) the mass conservation corrections are applied to the coarse-level force term.
PROBLEMS OF EFFICIENCY OF BUDGET SPENDING ON GENERAL EDUCATION DURING ITS REFORMING
Directory of Open Access Journals (Sweden)
E. B. Krylova
2016-01-01
Full Text Available This article presents an analysis of the main problems of the Russian general education during the ongoing reform of the general education system, as well as identified the main reasons for reducing the efficiency of budget spending in this area.Analysis is based on data provided by the State Statistics Service of the changes in the number of state and municipal educational institutions for the period of the general reform of the education sector from 1981 to 2016. The authors highlighted that reduced the total number of educational institutions of higher education, compared with 2014. by 5.7% and significantly reduced the number of students and school pupils in particular on specific professional areas, and there was a decrease in the overall number of educational institutions.The authors identified factors that influenced this process, including the demographic collapse in the birth rate in the last decade of the 20th century and marks them active reform activities of the Government of the Russian Federation in the field of general education. The dynamics in the financing of general education. The problems of financing of general education, which is not so much the amount of funds allocated, how much as using them in the educational process.The main problems of inefficient budget spending on general education authors attributed such as: the lack of a unified approach to the optimization of budgets (by type of education spending; inadequate budget planning and control system, lack of a direct link between allocated resources and indicators of the effectiveness of the educational institutions; procedural complications monitoring the effectiveness of budget spending. The necessity to optimize the proportion of the federal budget for education spending and improve the utilization of allocated budget, which will undoubtedly impact on improving the quality of educational services.The authors noted the key role of the budget funding for support of
Novel Spreadsheet Direct Method for Optimal Control Problems
Directory of Open Access Journals (Sweden)
Chahid Kamel Ghaddar
2018-01-01
Full Text Available We devise a simple yet highly effective technique for solving general optimal control problems in Excel spreadsheets. The technique exploits Excel’s native nonlinear programming (NLP Solver Command, in conjunction with two calculus worksheet functions, namely, an initial value problem solver and a discrete data integrator, in a direct solution paradigm adapted to the spreadsheet. The technique is tested on several highly nonlinear constrained multivariable control problems with remarkable results in terms of reliability, consistency with pseudo-spectral reported answers, and computing times in the order of seconds. The technique requires no more than defining a few analogous formulas to the problem mathematical equations using basic spreadsheet operations, and no programming skills are needed. It introduces an alternative, simpler tool for solving optimal control problems in social and natural science disciplines.
Approximation in generalized Hardy classes and resolution of inverse problems for tokamaks
International Nuclear Information System (INIS)
Fisher, Y.
2011-11-01
This thesis concerns both the theoretical and constructive resolution of inverse problems for isotropic diffusion equation in planar domains, simply and doubly connected. From partial Cauchy boundary data (potential, flux), we look for those quantities on the remaining part of the boundary, where no information is available, as well as inside the domain. The proposed approach proceeds by considering solutions to the diffusion equation as real parts of complex valued solutions to some conjugated Beltrami equation. These particular generalized analytic functions allow to introduce Hardy classes, where the inverse problem is stated as a best constrained approximation issue (bounded extrema problem), and thereby is regularized. Hence, existence and smoothness properties, together with density results of traces on the boundary, ensure well-posedness. An application is studied, to a free boundary problem for a magnetically confined plasma in the tokamak Tore Supra (CEA Cadarache France). The resolution of the approximation problem on a suitable basis of functions (toroidal harmonics) leads to a qualification criterion for the estimated plasma boundary. A descent algorithm makes it decrease, and refines the estimations. The method does not require any integration of the solution in the overall domain. It furnishes very accurate numerical results, and could be extended to other devices, like JET or ITER. (author)
Still a difficult business? Negotiating alcohol-related problems in general practice consultations.
Rapley, Tim; May, Carl; Frances Kaner, Eileen
2006-11-01
This paper describes general practitioners' (GPs) experiences of detecting and managing alcohol and alcohol-related problems in consultations. We undertook qualitative research in two phases in the North-East of England. Initially, qualitative interviews with 29 GPs explored their everyday work with patients with alcohol-related issues. We then undertook group interviews--two with GPs and one with a primary care team--where they discussed and challenged findings of the interviews. The GPs reported routinely discussing alcohol with patients with a range of alcohol-related problems. GPs believed that this work is important, but felt that until patients were willing to accept that their alcohol consumption was problematic they could achieve very little. They tentatively introduced alcohol as a potential problem, re-introduced the topic periodically, and then waited until the patient decided to change their behaviour. They were aware that they could identify and manage more patients. A lack of time and having to work with the multiple problems that patients brought to consultations were the main factors that stopped GPs managing more risky drinkers. Centrally, we compared the results of our study with [Thom, B., & Tellez, C. (1986). A difficult business-Detecting and managing alcohol-problems in general-practice. British Journal of Addiction, 81, 405-418] seminal study that was undertaken 20 years ago. We show how the intellectual, moral, emotional and practical difficulties that GPs currently face are quite similar to those faced by GPs from 20 years ago. As the definition of what could constitute abnormal alcohol consumption has expanded, so the range of consultations that they may have to negotiate these difficulties in has also expanded.
A Direct Elliptic Solver Based on Hierarchically Low-Rank Schur Complements
Chávez, Gustavo
2017-03-17
A parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic operations result in a solver with O(Nlog2N) arithmetic complexity and O(NlogN) memory footprint. We provide a baseline for performance and applicability by comparing with well-known implementations of the $$\\\\mathcal{H}$$ -LU factorization and algebraic multigrid within a shared-memory parallel environment that leverages the concurrency features of the method. Numerical experiments reveal that this method is comparable with other fast direct solvers based on Hierarchical Matrices such as $$\\\\mathcal{H}$$ -LU and that it can tackle problems where algebraic multigrid fails to converge.
Algorithms for parallel flow solvers on message passing architectures
Vanderwijngaart, Rob F.
1995-01-01
The purpose of this project has been to identify and test suitable technologies for implementation of fluid flow solvers -- possibly coupled with structures and heat equation solvers -- on MIMD parallel computers. In the course of this investigation much attention has been paid to efficient domain decomposition strategies for ADI-type algorithms. Multi-partitioning derives its efficiency from the assignment of several blocks of grid points to each processor in the parallel computer. A coarse-grain parallelism is obtained, and a near-perfect load balance results. In uni-partitioning every processor receives responsibility for exactly one block of grid points instead of several. This necessitates fine-grain pipelined program execution in order to obtain a reasonable load balance. Although fine-grain parallelism is less desirable on many systems, especially high-latency networks of workstations, uni-partition methods are still in wide use in production codes for flow problems. Consequently, it remains important to achieve good efficiency with this technique that has essentially been superseded by multi-partitioning for parallel ADI-type algorithms. Another reason for the concentration on improving the performance of pipeline methods is their applicability in other types of flow solver kernels with stronger implied data dependence. Analytical expressions can be derived for the size of the dynamic load imbalance incurred in traditional pipelines. From these it can be determined what is the optimal first-processor retardation that leads to the shortest total completion time for the pipeline process. Theoretical predictions of pipeline performance with and without optimization match experimental observations on the iPSC/860 very well. Analysis of pipeline performance also highlights the effect of uncareful grid partitioning in flow solvers that employ pipeline algorithms. If grid blocks at boundaries are not at least as large in the wall-normal direction as those
Nonlinear Multigrid solver exploiting AMGe Coarse Spaces with Approximation Properties
DEFF Research Database (Denmark)
Christensen, Max la Cour; Villa, Umberto; Engsig-Karup, Allan Peter
spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method), were less successful due to lack of such good approximation...... properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on unstructured meshes has the ability to be as powerful/successful as FAS on geometrically refined meshes. For comparison, Newton’s method and Picard iterations with an inner state-of-the-art linear solver...... are compared to FAS on a nonlinear saddle point problem with applications to porous media flow. It is demonstrated that FAS is faster than Newton’s method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate...
A Nitsche cut finite element method for the Oseen problem with general Navier boundary conditions
Winter, M.; Schott, B.; Massing, A.; Wall, W. A.
2018-03-01
In this work a Nitsche-based imposition of generalized Navier conditions on cut meshes for the Oseen problem is presented. Other methods from literature dealing with the generalized Navier condition impose this condition by means of substituting the tangential Robin condition in a classical Galerkin way. These methods work fine for a large slip length coefficient but lead to conditioning and stability issues when it approaches zero. We introduce a novel method for the weak imposition of the generalized Navier condition which remains well-posed and stable for arbitrary choice of slip length, including zero. The method proposed here builds on the formulation done by [1]. They impose a Robin condition for the Poisson problem by means of Nitsche's method for an arbitrary combination of the Dirichlet and Neumann parts of the condition. The analysis conducted for the proposed method is done in a similar fashion as in [2], but is done here for a more general type of boundary condition. The analysis proves stability for all flow regimes and all choices of slip lengths. Also an L2-optimal estimate for the velocity error is shown, which was not conducted in the previously mentioned work. A numerical example is carried out for varying slip lengths to verify the robustness and stability of the method with respect to the choice of slip length. Even though proofs and formulations are presented for the more general case of an unfitted grid method, they can easily be reduced to the simpler case of a boundary-fitted grid with the removal of the ghost-penalty stabilization terms.
M2Di: MATLAB 2D Stokes solvers using the Finite Difference method
Räss, Ludovic; Duretz, Thibault; Schmalholz, Stefan; Podladchikov, Yury
2017-04-01
The study of coupled processes in Earth Sciences leads to the development of multiphysics modelling tools. Mechanical solvers represent the essential ingredient of any of these tools such that their performance and robustness is generally dictated by that of the mechanical solver. Here, we present M2Di, a collection of MATLAB routines designed for studying 2D linear and power law incompressible viscous flow using Finite Difference discretisation. The scripts are written in a concise vectorised MATLAB fashion and rely on fast and robust linear and non-linear solvers (Picard and Newton iterations). As a result, time to solution of 22 seconds for linear viscous flow with 104 viscosity jump on 10002 grid points can be achieved on a standard personal computer. We will present a numerous example of applications that span from high resolution crystal-melt dynamics, deformation of heterogeneous power law viscous fluids, instantaneous mantle flow patterns in cylindrical coordinates, and calculation of pressure gradients around inclusions using variable grid spacing. We use analytical solution for linear viscous flow with highly variable viscosity to validate the linear flow solver. Validation of the non-linear solver is achieved by comparing numerical solution to analytic and benchmark solutions of power law viscous folding and necking. The M2Di codes are open source and can hence be used for research or educational purposes.
International Nuclear Information System (INIS)
Garba, Abdou; Haldenwang, Pierre
2003-01-01
The aim of the paper is concerned with the iterative resolution of the generalized Stokes problem in the framework of collocation Chebyshev approximation. More precisely, we analyze the performance of several preconditioners improving the classical Uzawa method. We first recall that the general Stokes problem (GSP) is an elementary substep of general interest for computing not only incompressible flows but also low Mach number flows. We then remark that performances of the classical Uzawa algorithm for solving the GSP are in fact closely related to the Reynolds number. In order to overcome this dependence, preconditioners are needed. The preconditioners we analyze here are recommended by Fourier analysis of the pressure operator. We additionally give interpretation of the preconditioners in terms of influence (or capacitance) techniques. We give a detailed analysis of the conditioning of the discrete collocation Chebyshev versions of the operators. Numerical comparison is conducted in 2D as well as in 3D rectangular geometry. Our comparative study shows that the fictitious wall permeability (FWP) method is the most efficient preconditioner. If complemented with a suitable pressure filtering, its efficiency still increases
The initial boundary value problem for free-evolution formulations of general relativity
Hilditch, David; Ruiz, Milton
2018-01-01
We consider the initial boundary value problem for free-evolution formulations of general relativity coupled to a parametrized family of coordinate conditions that includes both the moving puncture and harmonic gauges. We concentrate primarily on boundaries that are geometrically determined by the outermost normal observer to spacelike slices of the foliation. We present high-order-derivative boundary conditions for the gauge, constraint violating and gravitational wave degrees of freedom of the formulation. Second order derivative boundary conditions are presented in terms of the conformal variables used in numerical relativity simulations. Using Kreiss–Agranovich–Métivier theory we demonstrate, in the frozen coefficient approximation, that with sufficiently high order derivative boundary conditions the initial boundary value problem can be rendered boundary stable. The precise number of derivatives required depends on the gauge. For a choice of the gauge condition that renders the system strongly hyperbolic of constant multiplicity, well-posedness of the initial boundary value problem follows in this approximation. Taking into account the theory of pseudo-differential operators, it is expected that the nonlinear problem is also well-posed locally in time.
Guo, Peng; Cheng, Wenming; Wang, Yi
2014-10-01
The quay crane scheduling problem (QCSP) determines the handling sequence of tasks at ship bays by a set of cranes assigned to a container vessel such that the vessel's service time is minimized. A number of heuristics or meta-heuristics have been proposed to obtain the near-optimal solutions to overcome the NP-hardness of the problem. In this article, the idea of generalized extremal optimization (GEO) is adapted to solve the QCSP with respect to various interference constraints. The resulting GEO is termed the modified GEO. A randomized searching method for neighbouring task-to-QC assignments to an incumbent task-to-QC assignment is developed in executing the modified GEO. In addition, a unidirectional search decoding scheme is employed to transform a task-to-QC assignment to an active quay crane schedule. The effectiveness of the developed GEO is tested on a suite of benchmark problems introduced by K.H. Kim and Y.M. Park in 2004 (European Journal of Operational Research, Vol. 156, No. 3). Compared with other well-known existing approaches, the experiment results show that the proposed modified GEO is capable of obtaining the optimal or near-optimal solution in a reasonable time, especially for large-sized problems.
Efficient generalized Golub-Kahan based methods for dynamic inverse problems
Chung, Julianne; Saibaba, Arvind K.; Brown, Matthew; Westman, Erik
2018-02-01
We consider efficient methods for computing solutions to and estimating uncertainties in dynamic inverse problems, where the parameters of interest may change during the measurement procedure. Compared to static inverse problems, incorporating prior information in both space and time in a Bayesian framework can become computationally intensive, in part, due to the large number of unknown parameters. In these problems, explicit computation of the square root and/or inverse of the prior covariance matrix is not possible, so we consider efficient, iterative, matrix-free methods based on the generalized Golub-Kahan bidiagonalization that allow automatic regularization parameter and variance estimation. We demonstrate that these methods for dynamic inversion can be more flexible than standard methods and develop efficient implementations that can exploit structure in the prior, as well as possible structure in the forward model. Numerical examples from photoacoustic tomography, space-time deblurring, and passive seismic tomography demonstrate the range of applicability and effectiveness of the described approaches. Specifically, in passive seismic tomography, we demonstrate our approach on both synthetic and real data. To demonstrate the scalability of our algorithm, we solve a dynamic inverse problem with approximately 43 000 measurements and 7.8 million unknowns in under 40 s on a standard desktop.
A general approach to regularizing inverse problems with regional data using Slepian wavelets
Michel, Volker; Simons, Frederik J.
2017-12-01
Slepian functions are orthogonal function systems that live on subdomains (for example, geographical regions on the Earth’s surface, or bandlimited portions of the entire spectrum). They have been firmly established as a useful tool for the synthesis and analysis of localized (concentrated or confined) signals, and for the modeling and inversion of noise-contaminated data that are only regionally available or only of regional interest. In this paper, we consider a general abstract setup for inverse problems represented by a linear and compact operator between Hilbert spaces with a known singular-value decomposition (svd). In practice, such an svd is often only given for the case of a global expansion of the data (e.g. on the whole sphere) but not for regional data distributions. We show that, in either case, Slepian functions (associated to an arbitrarily prescribed region and the given compact operator) can be determined and applied to construct a regularization for the ill-posed regional inverse problem. Moreover, we describe an algorithm for constructing the Slepian basis via an algebraic eigenvalue problem. The obtained Slepian functions can be used to derive an svd for the combination of the regionalizing projection and the compact operator. As a result, standard regularization techniques relying on a known svd become applicable also to those inverse problems where the data are regionally given only. In particular, wavelet-based multiscale techniques can be used. An example for the latter case is elaborated theoretically and tested on two synthetic numerical examples.
Lin, John J. H.; Lin, Sunny S. J.
2018-01-01
To deepen our understanding of those aspects of problems that cause the most difficulty for solvers, this study integrated eye-tracking with handwriting devices to investigate problem solvers' online processes while solving geometry problems. We are interested in whether the difference between successful and unsuccessful solvers can be identified…
Assessment of achievement in problem-solving skills in a General Chemistry course
Directory of Open Access Journals (Sweden)
Patricia Morales Bueno
2014-12-01
Full Text Available This article reports the development and validation study of tests to assess achievements at three levels of knowledge structure, following the model proposed by Sugrue to measure problem-solving skills. This model is particularly consistent with the theoretical constructs underlying problem-based learning (PBL methodology. The tests were constructed for a General Chemistry course in a curriculum of engineering, which implements PBL methodology at a Peruvian university. The content validation of the tests was performed, as well as a pilot implementation with Peruvian students of first year enginnering. The results obtained in omissions percentage, difficulty degree, items response pattern and the point biserial coefficient (rpb, let us to conclude that these are appropiate tools for assessing these skills, so constitute a significant contribution to future research in this line.
Multigrid method applied to the solution of an elliptic, generalized eigenvalue problem
Energy Technology Data Exchange (ETDEWEB)
Alchalabi, R.M. [BOC Group, Murray Hill, NJ (United States); Turinsky, P.J. [North Carolina State Univ., Raleigh, NC (United States)
1996-12-31
The work presented in this paper is concerned with the development of an efficient MG algorithm for the solution of an elliptic, generalized eigenvalue problem. The application is specifically applied to the multigroup neutron diffusion equation which is discretized by utilizing the Nodal Expansion Method (NEM). The underlying relaxation method is the Power Method, also known as the (Outer-Inner Method). The inner iterations are completed using Multi-color Line SOR, and the outer iterations are accelerated using Chebyshev Semi-iterative Method. Furthermore, the MG algorithm utilizes the consistent homogenization concept to construct the restriction operator, and a form function as a prolongation operator. The MG algorithm was integrated into the reactor neutronic analysis code NESTLE, and numerical results were obtained from solving production type benchmark problems.
Asynchronous Parallelization of a CFD Solver
Abdi, Daniel S.; Bitsuamlak, Girma T.
2015-01-01
The article of record as published may be found at http://dx.doi.org/10.1155/2015/295393 A Navier-Stokes equations solver is parallelized to run on a cluster of computers using the domain decomposition method. Two approaches of communication and computation are investigated, namely, synchronous and asynchronous methods. Asynchronous communication between subdomains is not commonly used inCFDcodes; however, it has a potential to alleviate scaling bottlenecks incurred due to process...
Chemical Mechanism Solvers in Air Quality Models
Directory of Open Access Journals (Sweden)
John C. Linford
2011-09-01
Full Text Available The solution of chemical kinetics is one of the most computationally intensivetasks in atmospheric chemical transport simulations. Due to the stiff nature of the system,implicit time stepping algorithms which repeatedly solve linear systems of equations arenecessary. This paper reviews the issues and challenges associated with the construction ofefficient chemical solvers, discusses several families of algorithms, presents strategies forincreasing computational efficiency, and gives insight into implementing chemical solverson accelerated computer architectures.
[Validation of the general help-seeking questionnaire for mental health problems in adolescents].
Olivari, Cecilia; Guzmán-González, Mónica
2017-06-01
Help-seeking behavior is a protective factor in young people, essential for their mental health, well-being and development. However, some adolescents do not seek professional help when they need to. In this context, it is relevant to study the help-seeking behavior for mental health problems in adolescent population. To adapt and validate the general help-seeking questionnaire for mental health problems in Chilean adolescents. Cross-sectional and correlational study of a non-random sample of 793 adolescent students, between 14 and 19 years old, from the city of Talca (Chile). The general help-seeking questionnaire, vignette version, (GHSQ-V) was administered after a transcultural adaptation and criterion validation. Descriptive statistics, exploratory factor analysis and non-parametric Mann-Whitney U test were used for analysis. An exploratory analysis identified two factors regarding available sources of help: 1) informal sources; 2) formal sources. Reliability was calculated separately for each of the health problems, resulting alpha values ranging from 0.87 to 0.75. In addition, the scale showed significant association with the variables self-efficacy and depression in the hypothesized directions. Finally, significant differences were identified in the willingness to seek help by adolescents level of mental health literacy, for all mental health issues presented, except suicide. The adaptation of the GHSQ-V for Chilean adolescent and youth population is a valid and reliable instrument to measure willingness to seek help for mental health problems in our socio-cultural environment.
Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers
Woźniak, Maciej
2014-06-01
In this paper we present computational cost estimates for parallel shared memory isogeometric multi-frontal solvers. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as O( p2log(N/p)) for one dimensional problems, O(Np2) for two dimensional problems, and O(N4/3p2) for three dimensional problems, where N is the number of degrees of freedom, and p is the polynomial order of approximation. The computational costs of the shared memory parallel isogeometric direct solver are compared with those corresponding to the sequential isogeometric direct solver, being the latest equal to O(N p2) for the one dimensional case, O(N1.5p3) for the two dimensional case, and O(N2p3) for the three dimensional case. The shared memory version significantly reduces both the scalability in terms of N and p. Theoretical estimates are compared with numerical experiments performed with linear, quadratic, cubic, quartic, and quintic B-splines, in one and two spatial dimensions. © 2014 Elsevier Ltd. All rights reserved.
Iterative Solvers within Sequences of Large Linear Systems in Non-linear Structural Mechanics
Czech Academy of Sciences Publication Activity Database
Hartmann, S.; Duintjer Tebbens, Jurjen; Quint, K.J.; Meister, A.
2009-01-01
Roč. 89, č. 9 (2009), s. 711-728 ISSN 0044-2267 R&D Projects: GA AV ČR KJB100300703 Institutional research plan: CEZ:AV0Z10300504 Keywords : iterative solver * non-symmetric matrices * sequences of linear systems * finite strains * finite elements Subject RIV: BA - General Mathematics Impact factor: 0.866, year: 2009
George, D.L.
2011-01-01
The simulation of advancing flood waves over rugged topography, by solving the shallow-water equations with well-balanced high-resolution finite volume methods and block-structured dynamic adaptive mesh refinement (AMR), is described and validated in this paper. The efficiency of block-structured AMR makes large-scale problems tractable, and allows the use of accurate and stable methods developed for solving general hyperbolic problems on quadrilateral grids. Features indicative of flooding in rugged terrain, such as advancing wet-dry fronts and non-stationary steady states due to balanced source terms from variable topography, present unique challenges and require modifications such as special Riemann solvers. A well-balanced Riemann solver for inundation and general (non-stationary) flow over topography is tested in this context. The difficulties of modeling floods in rugged terrain, and the rationale for and efficacy of using AMR and well-balanced methods, are presented. The algorithms are validated by simulating the Malpasset dam-break flood (France, 1959), which has served as a benchmark problem previously. Historical field data, laboratory model data and other numerical simulation results (computed on static fitted meshes) are shown for comparison. The methods are implemented in GEOCLAW, a subset of the open-source CLAWPACK software. All the software is freely available at. Published in 2010 by John Wiley & Sons, Ltd.
Formulations and Branch-and-Cut Algorithms for the Generalized Vehicle Routing Problem
DEFF Research Database (Denmark)
Bektas, Tolga; Erdogan, Günes; Røpke, Stefan
2011-01-01
The Generalized Vehicle Routing Problem (GVRP) consists of nding a set of routes for a number of vehicles with limited capacities on a graph with the vertices partitioned into clusters with given demands such that the total cost of travel is minimized and all demands are met. This paper offers fo...... new integer linear programming formulations for the GVRP, two based on multicommodity flow and the other two based on exponential sets of inequalities. Branch-and-cut algorithms are proposed for the latter two. Computational results on a large set of instances are presented....
Georgevic, R. M.; Anderson, J. D.
1973-01-01
The relationships between the osculating orbital elements for a family of solutions of the general relativistic Schwarzschild problems are developed. These relationships provide a method for evaluating orbital elements in different Schwarzschild coordinate systems without the necessity of fitting to real data every time the system of coordinates is changed. The objectivity of different coordinate systems is discussed. Considerations of orbital motions favor the standard Schwarzschild metric, but the propagation of light signals is more objective in the metric of Painleve. Because the orbital motions usually dominate the representation of data, the standard Schwarzschild coordinates are the best objective choice for most applications.
ALAM/CLAM and some applications of computer algebra systems to problems in general relativity
International Nuclear Information System (INIS)
Russell-Clark, R.A.
1973-01-01
This paper is divided into three parts. Part A presents a historical survey of the development of the system, a brief description of its features and, finally, a critical assessment. ALAM and CLAM have been used in many problems in General Relativity; the vast majority of these belong to a set of standard calculations termed ''metric applications''. However, four large non-standard applications have been attempted successfully and these are described in Part B. CAMAL is the only other system which has been used extensively for work in relativity. CAMAL has played an important role in two research projects and details of these are given in Part C
International Nuclear Information System (INIS)
Dattoli, G.; Torre, A.; Mancho, A.M.
2000-01-01
The theory of generalized Bessel functions has found significant applications in the analysis of radiation phenomena, associated with charges moving in magnetic devices. In this paper we exploit the monomiality principle to discuss the theory of two-variable Laguerre polynomials and introduce the associated Laguerre-Bessel functions. We study their properties (addition and multiplication theorems, generating function, recurrence relations and so on) and discuss the link with the ordinary case. The usefulness of the obtained results to treat problems relevant to the paraxial propagation of electromagnetic waves is also discussed.
Comparison of three-dimensional ocean general circulation models on a benchmark problem
International Nuclear Information System (INIS)
Chartier, M.
1990-12-01
A french and an american Ocean General Circulation Models for deep-sea disposal of radioactive wastes are compared on a benchmark test problem. Both models are three-dimensional. They solve the hydrostatic primitive equations of the ocean with two different finite difference techniques. Results show that the dynamics simulated by both models are consistent. Several methods for the running of a model from a known state are tested in the French model: the diagnostic method, the prognostic method, the acceleration of convergence and the robust-diagnostic method
Multi-choice stochastic transportation problem involving general form of distributions.
Quddoos, Abdul; Ull Hasan, Md Gulzar; Khalid, Mohammad Masood
2014-01-01
Many authors have presented studies of multi-choice stochastic transportation problem (MCSTP) where availability and demand parameters follow a particular probability distribution (such as exponential, weibull, cauchy or extreme value). In this paper an MCSTP is considered where availability and demand parameters follow general form of distribution and a generalized equivalent deterministic model (GMCSTP) of MCSTP is obtained. It is also shown that all previous models obtained by different authors can be deduced with the help of GMCSTP. MCSTP with pareto, power function or burr-XII distributions are also considered and equivalent deterministic models are obtained. To illustrate the proposed model two numerical examples are presented and solved using LINGO 13.0 software package.
Conformal changes of metrics and the initial-value problem of general relativity
International Nuclear Information System (INIS)
Mielke, E.W.
1977-01-01
Conformal techniques are reviewed with respect to applications to the initial-value problem of general relativity. Invariant transverse traceless decompositions of tensors, one of its main tools, are related to representations of the group of 'conformeomorphisms' acting on the space of all Riemannian metrics on M. Conformal vector fields, a kernel in the decomposition, are analyzed on compact manifolds with constant scalar curvature. The realization of arbitrary functions as scalar curvature of conformally equivalent metrics, a generalization of Yamabe's (Osaka Math. J.; 12:12 (1960)) conjecture, is applied to the Hamiltonian constraint and to the issue of positive energy of gravitational fields. Various approaches to the solution of the initial-value equations produced by altering the scaling behaviour of the second fundamental form are compared. (author)
Some aspects of the inverse problem for general first order systems
International Nuclear Information System (INIS)
Sarlet, W.; Cantrijn, F.
1978-01-01
In this paper we investigate the most general systems of first-order ordinary differential equations which satisfy the integrability conditions of the inverse problem for canonical formulations, i.e., are derivable from a variational principle. It is shown that they have a structure which is invariant under arbitrary coordinate-transformations. A special class of transformations, called identity-isotopic transformations, is described. It is illustrated how these transformations share all properties with classical canonical transformations except one: the solutions of the system, viewed as transformations from the set of initial values, generally are not identity-isotopic. This failure is shown to be due to the explicit time-dependence of the functions which characterise the system, and the special role of this time-dependence is further clarified using the possibility of a reduction to conventional Hamiltonian systems. All properties are derived here within the framework of an analytic treatment of a system of differential equations
Rijswijk, E. van; Borghuis, M.; Lisdonk, E.H. van de; Zitman, F.G.; Weel, C. van
2007-01-01
OBJECTIVE: Real-life data on the treatment of patients with mental health problems are important as a reference to evaluate care and benchmarking. This study describes the treatment of mental health problems in general practice as diagnosed by general practitioners (GP). MATERIAL AND METHODS: Data
A generalized electro-magneto-thermo-elastic problem for an infinitely long solid cylinder
International Nuclear Information System (INIS)
Tianhu, H.; Xiaogeng, T.; Yapeng, S.; Tianhu, H.
2005-01-01
The theory of generalized thermoelasticity, based on the theory of Lord and Shulman with one relaxation time, is used to study the electro-magneto-thermo-elastic interactions in an infinitely long perfectly conducting solid cylinder subjected to a thermal shock on its surface when the cylinder and its adjoining vacuum is subjected to a uniform axial magnetic field. The cylinder deforms because of thermal shock, and due to the application of the magnetic field, there result an induced magnetic and an induced electric field in the cylinder. The Maxwell's equations are formulated and the generalized electro-magneto-thermo-elastic coupled governing equations are established. By means of the Laplace transform and numerical Laplace inversion the problem is solved. The distributions of the considered temperature, stress, displacement, induced magnetic and electric field are represented graphically. From the distributions, it can be found the electromagnetic-thermoelastic coupled effects and the wave type heat propagation in the medium. This indicates that the generalized heat conduction mechanism is completely different from the classic Fourier's in essence. In generalized thermoelasticity theory heat propagates as a wave with finite velocity instead of infinite velocity in medium. (authors)
Mataka, Lloyd M.; Cobern, William W.; Grunert, Megan L.; Mutambuki, Jacinta; Akom, George
2014-01-01
This study investigate the effectiveness of adding an "explicit general problem solving teaching strategy" (EGPS) to guided inquiry (GI) on pre-service elementary school teachers' ability to solve heat transfer problems. The pre-service elementary teachers in this study were enrolled in two sections of a chemistry course for pre-service…
Trust-region based solver for nonlinear transport in heterogeneous porous media
Wang, Xiaochen; Tchelepi, Hamdi A.
2013-11-01
We describe a new nonlinear solver for immiscible two-phase transport in porous media, where viscous, buoyancy, and capillary forces are significant. The flux (fractional flow) function, F, is a nonlinear function of saturation and typically has inflection points and can be non-monotonic. The non-convexity and non-monotonicity of F are major sources of difficulty for nonlinear solvers of coupled multiphase flow and transport in natural porous media. We describe a modified Newton algorithm that employs trust regions of the flux function to guide the Newton iterations. The flux function is divided into saturation trust regions delineated by the inflection, unit-flux, and end points. The updates are performed such that two successive iterations cannot cross any trust-region boundary. If a crossing is detected, the saturation value is chopped back to the appropriate trust-region boundary. The proposed trust-region Newton solver, which is demonstrated across the parameter space of viscous, buoyancy and capillary effects, is a significant extension of the inflection-point strategy of Jenny et al. (JCP, 2009) [5] for viscous dominated flows. We analyze the discrete nonlinear transport equation obtained using finite-volume discretization with phase-based upstream weighting. Then, we prove convergence of the trust-region Newton method irrespective of the timestep size for single-cell problems. Numerical results across the full range of the parameter space of viscous, gravity and capillary forces indicate that our trust-region scheme is unconditionally convergent for 1D transport. That is, for a given choice of timestep size, the unique discrete solution is found independently of the initial guess. For problems dominated by buoyancy and capillarity, the trust-region Newton solver overcomes the often severe limits on timestep size associated with existing methods. To validate the effectiveness of the new nonlinear solver for large reservoir models with strong heterogeneity
An analysis of the Rayleigh–Stokes problem for a generalized second-grade fluid
Bazhlekova, Emilia
2014-11-26
© 2014, The Author(s). We study the Rayleigh–Stokes problem for a generalized second-grade fluid which involves a Riemann–Liouville fractional derivative in time, and present an analysis of the problem in the continuous, space semidiscrete and fully discrete formulations. We establish the Sobolev regularity of the homogeneous problem for both smooth and nonsmooth initial data v, including v∈^{L2}(Ω). A space semidiscrete Galerkin scheme using continuous piecewise linear finite elements is developed, and optimal with respect to initial data regularity error estimates for the finite element approximations are derived. Further, two fully discrete schemes based on the backward Euler method and second-order backward difference method and the related convolution quadrature are developed, and optimal error estimates are derived for the fully discrete approximations for both smooth and nonsmooth initial data. Numerical results for one- and two-dimensional examples with smooth and nonsmooth initial data are presented to illustrate the efficiency of the method, and to verify the convergence theory.
Equihash: Asymmetric Proof-of-Work Based on the Generalized Birthday Problem
Directory of Open Access Journals (Sweden)
Alex Biryukov
2017-04-01
Full Text Available Proof-of-work is a central concept in modern cryptocurrencies and denial-ofservice protection tools, but the requirement for fast verification so far has made it an easy prey for GPU-, ASIC-, and botnet-equipped users. The attempts to rely on memory-intensive computations in order to remedy the disparity between architectures have resulted in slow or broken schemes. In this paper we solve this open problem and show how to construct an asymmetric proof-of-work (PoW based on a computationally-hard problem, which requires a great deal of memory to generate a proof (called a ”memory-hardness” feature but is instant to verify. Our primary proposal, Equihash, is a PoW based on the generalized birthday problem and enhanced Wagner’s algorithm for it. We introduce the new technique of algorithm binding to prevent cost amortization and demonstrate that possible parallel implementations are constrained by memory bandwidth. Our scheme has tunable and steep time-space tradeoffs, which impose large computational penalties if less memory is used. Our solution is practical and ready to deploy: a reference implementation of a proof-of-work requiring 700 MB of RAM runs in 15 seconds on a 2.1 GHz CPU, increases the computations by a factor of 1000 if memory is halved, and presents a proof of just 120 bytes long.
International Nuclear Information System (INIS)
Nelson, E.M.
1993-12-01
Some two-dimensional finite element electromagnetic field solvers are described and tested. For TE and TM modes in homogeneous cylindrical waveguides and monopole modes in homogeneous axisymmetric structures, the solvers find approximate solutions to a weak formulation of the wave equation. Second-order isoparametric lagrangian triangular elements represent the field. For multipole modes in axisymmetric structures, the solver finds approximate solutions to a weak form of the curl-curl formulation of Maxwell's equations. Second-order triangular edge elements represent the radial (ρ) and axial (z) components of the field, while a second-order lagrangian basis represents the azimuthal (φ) component of the field weighted by the radius ρ. A reduced set of basis functions is employed for elements touching the axis. With this basis the spurious modes of the curl-curl formulation have zero frequency, so spurious modes are easily distinguished from non-static physical modes. Tests on an annular ring, a pillbox and a sphere indicate the solutions converge rapidly as the mesh is refined. Computed eigenvalues with relative errors of less than a few parts per million are obtained. Boundary conditions for symmetric, periodic and symmetric-periodic structures are discussed and included in the field solver. Boundary conditions for structures with inversion symmetry are also discussed. Special corner elements are described and employed to improve the accuracy of cylindrical waveguide and monopole modes with singular fields at sharp corners. The field solver is applied to three problems: (1) cross-field amplifier slow-wave circuits, (2) a detuned disk-loaded waveguide linear accelerator structure and (3) a 90 degrees overmoded waveguide bend. The detuned accelerator structure is a critical application of this high accuracy field solver. To maintain low long-range wakefields, tight design and manufacturing tolerances are required
Particle size-shape distributions: the general spheroid problem. I. Mathematical model.
Orive, L M
1976-08-01
The development of stereological methods for the study of dilute phases of particles, voids or organelles embedded in a matrix, from measurements made on plane or linear intercepts through the aggregate, has deserved a great deal of effort. With almost no exception, the problem of describing the particulate phase is reduced to that of identifying the statistical distribution--histogram in practice--of a relevant size parameter, with the previous assumption that the particles are modelled by geometrical objects of a constant shape (e.g. spheres). Therefore, particles exhibiting a random variation about a given type of shape as well as a random variation in size, escape previous analyses. Such is the case of unequiaxed particles modelled by triaxial ellipsoids of variable size and eccentricity parameters. It has been conjectured (Moran, 1972) that this problem is indetermined in its generally (i.e. the elliptical sections do not furnish a sufficient information which permits a complete description of the ellipsoids). A proof of this conjecture is given in the Appendix. When the ellipsoids are biaxial (spheroids) and of the same type (prolate or oblate), the problem is identifiable. Previous attempts to solve it assume statistical independence between size and shape. A complete, theoretical solution of the spheroids problem--with the independence condition relaxed--is presented. A number of exact relationships--some of them of a striking simplicity--linking particle properties (e.g. mean-mean caliper length, mean axial ratio, correlation coefficient between principal diameters, etc.) on the one hand, with the major and minor dimensions of the ellipses of section on the other, emerge, and natural, consistent estimators of the mentioned properties are made easily accessible for practical computation. Finally, the scope and limitations of the mathematical model are discussed.
Seo, Jongmin; Schiavazzi, Daniele; Marsden, Alison
2017-11-01
Cardiovascular simulations are increasingly used in clinical decision making, surgical planning, and disease diagnostics. Patient-specific modeling and simulation typically proceeds through a pipeline from anatomic model construction using medical image data to blood flow simulation and analysis. To provide confidence intervals on simulation predictions, we use an uncertainty quantification (UQ) framework to analyze the effects of numerous uncertainties that stem from clinical data acquisition, modeling, material properties, and boundary condition selection. However, UQ poses a computational challenge requiring multiple evaluations of the Navier-Stokes equations in complex 3-D models. To achieve efficiency in UQ problems with many function evaluations, we implement and compare a range of iterative linear solver and preconditioning techniques in our flow solver. We then discuss applications to patient-specific cardiovascular simulation and how the problem/boundary condition formulation in the solver affects the selection of the most efficient linear solver. Finally, we discuss performance improvements in the context of uncertainty propagation. Support from National Institute of Health (R01 EB018302) is greatly appreciated.
A wavelet-based PWTD algorithm-accelerated time domain surface integral equation solver
Liu, Yang
2015-10-26
© 2015 IEEE. The multilevel plane-wave time-domain (PWTD) algorithm allows for fast and accurate analysis of transient scattering from, and radiation by, electrically large and complex structures. When used in tandem with marching-on-in-time (MOT)-based surface integral equation (SIE) solvers, it reduces the computational and memory costs of transient analysis from equation and equation to equation and equation, respectively, where Nt and Ns denote the number of temporal and spatial unknowns (Ergin et al., IEEE Trans. Antennas Mag., 41, 39-52, 1999). In the past, PWTD-accelerated MOT-SIE solvers have been applied to transient problems involving half million spatial unknowns (Shanker et al., IEEE Trans. Antennas Propag., 51, 628-641, 2003). Recently, a scalable parallel PWTD-accelerated MOT-SIE solver that leverages a hiearchical parallelization strategy has been developed and successfully applied to the transient problems involving ten million spatial unknowns (Liu et. al., in URSI Digest, 2013). We further enhanced the capabilities of this solver by implementing a compression scheme based on local cosine wavelet bases (LCBs) that exploits the sparsity in the temporal dimension (Liu et. al., in URSI Digest, 2014). Specifically, the LCB compression scheme was used to reduce the memory requirement of the PWTD ray data and computational cost of operations in the PWTD translation stage.
Handy, C R; Okbagabir, S; Yarahmad, T
2003-01-01
For one-dimensional Schroedinger quantum systems, the correlation expression S(x, tau, a) ident to PSI*(x - tau/2/a)PSI(x + tau/2) satisfies a fourth-order linear differential equation with regard to x. This generalizes the result previously derived by Handy (2001 J. Phys. A: Math. Gen. 34 L271), and Handy and Wang (2001 J. Phys. A: Math. Gen. 34 8297), with regard to S(x, 0, 1). We are then able to incorporate this within a generalized Wigner transform representation, through the use of scalets (Handy C R and Brooks H A 2001 J. Phys. A: Math. Gen. 34 3577). Energy quantization is achieved through a moment problem positivity analysis (focusing on the moments of the probability density, vertical bar PSI vertical bar sup 2) at a=1, tau=0. The wavefunction, PSI, is then generated through a multiscale analysis proceeding from the unity scale, extended into the zero scale limit. The power moments, mu sub p =integral dx x sup p PSI(x), can be generated through a similar procedure. We present the general formalism a...
Domain Decomposition Solvers for Frequency-Domain Finite Element Equations
Copeland, Dylan
2010-10-05
The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.
Periodic Density Functional Theory Solver using Multiresolution Analysis with MADNESS
Harrison, Robert; Thornton, William
2011-03-01
We describe the first implementation of the all-electron Kohn-Sham density functional periodic solver (DFT) using multi-wavelets and fast integral equations using MADNESS (multiresolution adaptive numerical environment for scientific simulation; http://code.google.com/p/m-a-d-n-e-s-s). The multiresolution nature of a multi-wavelet basis allows for fast computation with guaranteed precision. By reformulating the Kohn-Sham eigenvalue equation into the Lippmann-Schwinger equation, we can avoid using the derivative operator which allows better control of overall precision for the all-electron problem. Other highlights include the development of periodic integral operators with low-rank separation, an adaptable model potential for nuclear potential, and an implementation for Hartree Fock exchange. This work was supported by NSF project OCI-0904972 and made use of resources at the Center for Computational Sciences at Oak Ridge National Laboratory under contract DE-AC05-00OR22725.
Two-point boundary value and Cauchy formulations in an axisymmetrical MHD equilibrium problem
International Nuclear Information System (INIS)
Atanasiu, C.V.; Subbotin, A.A.
1999-01-01
In this paper we present two equilibrium solvers for axisymmetrical toroidal configurations, both based on the expansion in poloidal angle method. The first one has been conceived as a two-point boundary value solver in a system of coordinates with straight field lines, while the second one uses a well-conditioned Cauchy formulation of the problem in a general curvilinear coordinate system. In order to check the capability of our moment methods to describe equilibrium accurately, a comparison of the moment solutions with analytical solutions obtained for a Solov'ev equilibrium has been performed. (author)
General competencies of problem-based learning (PBL) and non-PBL graduates.
Prince, Katinka J A H; van Eijs, Patrick W L J; Boshuizen, Henny P A; van der Vleuten, Cees P M; Scherpbier, Albert J J A
2005-04-01
Junior doctors have reported shortcomings in their general competencies, such as organisational skills and teamwork. We explored graduates' perceptions of how well their training had prepared them for medical practice and in general competencies in particular. We compared the opinions of graduates from problem-based learning (PBL) and non-PBL schools, because PBL is supposed to enhance general competencies. We analysed the responses of 1159 graduates from 1 PBL and 4 non-PBL schools to a questionnaire survey administered 18 months after graduation. Compared with their non-PBL colleagues, the PBL graduates gave higher ratings for the connection between school and work, their medical training and preparation for practice. According to the graduates, the most frequently used competencies with sufficient coverage during medical training were expert knowledge, profession-specific skills and communication skills. The majority of the PBL graduates, but less than half of the non-PBL graduates, indicated that communication skills had been covered sufficiently. All the graduates called for more curriculum attention on working with computers, planning and organisation, and leadership skills. More PBL graduates than non-PBL graduates indicated that they had learned profession-specific methods, communication skills and teamwork in medical school. Overall, the graduates appeared to be satisfied with their knowledge and skills. The results suggest that the PBL school provided better preparation with respect to several of the competencies. However, both PBL and non-PBL graduates identified deficits in their general competencies, such as working with computers and planning and organising work. These competencies should feature more prominently in undergraduate medical education.
Nonlinear Chance Constrained Problems: Optimality Conditions, Regularization and Solvers
Czech Academy of Sciences Publication Activity Database
Adam, Lukáš; Branda, Martin
2016-01-01
Roč. 170, č. 2 (2016), s. 419-436 ISSN 0022-3239 R&D Projects: GA ČR GA15-00735S Institutional support: RVO:67985556 Keywords : Chance constrained programming * Optimality conditions * Regularization * Algorithms * Free MATLAB codes Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 1.289, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/adam-0460909.pdf
Ebola and beyond: How Canada backs African problem-solvers ...
International Development Research Centre (IDRC) Digital Library (Canada)
2014-10-10
Oct 10, 2014 ... Photo credit: AIMS. Martial Ndeffo is battling Ebola with mathematics. The epidemiologist from Cameroon is helping Liberia's Ministry of Health make decisions that will affect us all as it races to halt the spread of the fast-moving disease. Officials in the West African country hardest hit by the epidemic are ...
An implicit and explicit solver for contact problems
Schutte, J.H.; Dannenberg, J.F.; Wijnant, Ysbrand H.; de Boer, Andries; Sas, P; Bergen, B.
2010-01-01
The interaction of rolling tyres with road surfaces is one of the major contributions to road traffic noise. The generation mechanisms of tyre/road noise are usually separated in structure borne and airborne noise. In both mechanisms the contact zone is important. In order to reduce tyre/road noise
A Generalized Measure for the Optimal Portfolio Selection Problem and its Explicit Solution
Directory of Open Access Journals (Sweden)
Zinoviy Landsman
2018-03-01
Full Text Available In this paper, we offer a novel class of utility functions applied to optimal portfolio selection. This class incorporates as special cases important measures such as the mean-variance, Sharpe ratio, mean-standard deviation and others. We provide an explicit solution to the problem of optimal portfolio selection based on this class. Furthermore, we show that each measure in this class generally reduces to the efficient frontier that coincides or belongs to the classical mean-variance efficient frontier. In addition, a condition is provided for the existence of the a one-to-one correspondence between the parameter of this class of utility functions and the trade-off parameter λ in the mean-variance utility function. This correspondence essentially provides insight into the choice of this parameter. We illustrate our results by taking a portfolio of stocks from National Association of Securities Dealers Automated Quotation (NASDAQ.
Optimal Stochastic Control Problem for General Linear Dynamical Systems in Neuroscience
Directory of Open Access Journals (Sweden)
Yan Chen
2017-01-01
Full Text Available This paper considers a d-dimensional stochastic optimization problem in neuroscience. Suppose the arm’s movement trajectory is modeled by high-order linear stochastic differential dynamic system in d-dimensional space, the optimal trajectory, velocity, and variance are explicitly obtained by using stochastic control method, which allows us to analytically establish exact relationships between various quantities. Moreover, the optimal trajectory is almost a straight line for a reaching movement; the optimal velocity bell-shaped and the optimal variance are consistent with the experimental Fitts law; that is, the longer the time of a reaching movement, the higher the accuracy of arriving at the target position, and the results can be directly applied to designing a reaching movement performed by a robotic arm in a more general environment.
Mikami, Katsunaka; Jorge, Ricardo E; Moser, David J; Arndt, Stephan; Jang, Mijin; Solodkin, Ana; Small, Steven L; Fonzetti, Pasquale; Hegel, Mark T; Robinson, Robert G
2014-01-01
This study examined the efficacy of antidepressant treatment for preventing the onset of generalized anxiety disorder (GAD) among patients with recent stroke. Of 799 patients assessed, 176 were randomized, and 149 patients without evidence of GAD at the initial visit were included in this double-blind treatment with escitalopram (N=47) or placebo (N=49) or non-blinded problem-solving therapy (PST; 12 total sessions; N=53). Participants given placebo over 12 months were 4.95 times more likely to develop GAD than patients given escitalopram and 4.00 times more likely to develop GAD than patients given PST. Although these results should be considered preliminary, the authors found that both escitalopram and PST were effective in preventing new onset of post-stroke GAD.
Algorithm for Solving a Generalized Mixed Equilibrium Problem with Perturbation in a Banach Space
Directory of Open Access Journals (Sweden)
Kum Sangho
2010-01-01
Full Text Available Let be a real Banach space with the dual space . Let be a proper functional and let be a bifunction. In this paper, a new concept of -proximal mapping of with respect to is introduced. The existence and Lipschitz continuity of the -proximal mapping of with respect to are proved. By using properties of the -proximal mapping of with respect to , a generalized mixed equilibrium problem with perturbation (for short, GMEPP is introduced and studied in Banach space . An existence theorem of solutions of the GMEPP is established and a new iterative algorithm for computing approximate solutions of the GMEPP is suggested. The strong convergence criteria of the iterative sequence generated by the new algorithm are established in a uniformly smooth Banach space , and the weak convergence criteria of the iterative sequence generated by this new algorithm are also derived in a Hilbert space.
Normal Mode Analysis to a Poroelastic Half-Space Problem under Generalized Thermoelasticity
Directory of Open Access Journals (Sweden)
Chunbao Xiong
Full Text Available Abstract The thermo-hydro-mechanical problems associated with a poroelastic half-space soil medium with variable properties under generalized thermoelasticity theory were investigated in this study. By remaining faithful to Biot’s theory of dynamic poroelasticity, we idealized the foundation material as a uniform, fully saturated, poroelastic half-space medium. We first subjected this medium to time harmonic loads consisting of normal or thermal loads, then investigated the differences between the coupled thermohydro-mechanical dynamic models and the thermo-elastic dynamic models. We used normal mode analysis to solve the resulting non-dimensional coupled equations, then investigated the effects that non-dimensional vertical displacement, excess pore water pressure, vertical stress, and temperature distribution exerted on the poroelastic half-space medium and represented them graphically.
A generalized number theory problem applied to ideal liquids and to terminological lexis
Maslov, V. P.; Maslova, T. V.
2017-01-01
We consider the notion of number of degrees of freedom in number theory and thermodynamics. This notion is applied to notions of terminology such as terms, slogans, themes, rules, and regulations. Prohibitions are interpreted as restrictions on the number of degrees of freedom. We present a theorem on the small number of degrees of freedom as a consequence of the generalized partitio numerorum problem. We analyze the relationship between thermodynamically ideal liquids with the lexical background that a term acquires in the process of communication. Examples showing how this background may be enhanced are considered. We discuss the question of the coagulation of drops in connection with the forecast of analogs of the gas-ideal liquid phase transition in social-political processes.
The Openpipeflow Navier–Stokes solver
Directory of Open Access Journals (Sweden)
Ashley P. Willis
2017-01-01
Full Text Available Pipelines are used in a huge range of industrial processes involving fluids, and the ability to accurately predict properties of the flow through a pipe is of fundamental engineering importance. Armed with parallel MPI, Arnoldi and Newton–Krylov solvers, the Openpipeflow code can be used in a range of settings, from large-scale simulation of highly turbulent flow, to the detailed analysis of nonlinear invariant solutions (equilibria and periodic orbits and their influence on the dynamics of the flow.
New multigrid solver advances in TOPS
International Nuclear Information System (INIS)
Falgout, R D; Brannick, J; Brezina, M; Manteuffel, T; McCormick, S
2005-01-01
In this paper, we highlight new multigrid solver advances in the Terascale Optimal PDE Simulations (TOPS) project in the Scientific Discovery Through Advanced Computing (SciDAC) program. We discuss two new algebraic multigrid (AMG) developments in TOPS: the adaptive smoothed aggregation method (αSA) and a coarse-grid selection algorithm based on compatible relaxation (CR). The αSA method is showing promising results in initial studies for Quantum Chromodynamics (QCD) applications. The CR method has the potential to greatly improve the applicability of AMG
Donoghue, John R.
2015-01-01
At the heart of van der Linden's approach to automated test assembly (ATA) is a linear programming/integer programming (LP/IP) problem. A variety of IP solvers are available, ranging in cost from free to hundreds of thousands of dollars. In this paper, I compare several approaches to solving the underlying IP problem. These approaches range from…
A finite element field solver for dipole modes
International Nuclear Information System (INIS)
Nelson, E.M.
1992-01-01
A finite element field solver for dipole modes in axisymmetric structures has been written. The second-order elements used in this formulation yield accurate mode frequencies with no spurious modes. Quasi-periodic boundaries are included to allow travelling waves in periodic structures. The solver is useful in applications requiring precise frequency calculations such as detuned accelerator structures for linear colliders. Comparisons are made with measurements and with the popular but less accurate field solver URMEL. (author). 7 refs., 4 figs
Improving mathematical problem solving : A computerized approach
Harskamp, EG; Suhre, CJM
Mathematics teachers often experience difficulties in teaching students to become skilled problem solvers. This paper evaluates the effectiveness of two interactive computer programs for high school mathematics problem solving. Both programs present students with problems accompanied by instruction
A Generalized Mathematical Model for the Fracture Problem of the Suspended Highway
Directory of Open Access Journals (Sweden)
Zhao Ying
2017-01-01
Full Text Available In order to answer dangling fracture problems of highway, the suspended pavement equivalent for non - suspended pavement, through the special boundary conditions has been suspended highway stress field of expression, in accordance with the 3D fracture model of crack formation, and establish a vacant, a general mathematics model for fracture problems of highway and analysis in highway suspended segment weight and vehicle load limit of highway capacity of Pu For overturning road inPu is less than the force of carrying more than compared to the work and fruit Bridge Hydropower Station Road engineering examples to verify suspended highway should force field expressions for the correctness and applicability. The results show that: when the hanging ratio R 0. 243177 limits of Pu design axle load 100kN. When the vertical crack in the vacant in the direction of length greater than 0. 1, the ultimate bearing capacity is less than the design axle load 100kN; when the hanging ratio R is less than 0. 5, the road to local fracture, the ultimate bearing capacity of suspended stress field expressions in solution; when the hanging ratio is greater than or equal to 0. 5, the road does not reach the limit bearing capacity of the whole body; torque shear surface of the effect is far less than the bending moments on shear planes.
Sweller, John; Clark, Richard; Kirschner, Paul A.
2010-01-01
Sweller, J., Clark, R., & Kirschner, P. A. (2010). Teaching general problem-solving skills is not a substitute for, or a viable addition to, teaching mathematics. Notices of the American Mathematical Society, 57, 1303-1304.
S.E. Mous (Sabine)
2015-01-01
markdownabstractThis thesis focuses on the neurobiology and neuropsychology of attention-deficit/hyperactivity problems in the general population. The notion that child psychopathology might be better described within a dimensional framework, rather than with clearly defined diagnostic categories,
Directory of Open Access Journals (Sweden)
Sánchez Álvarez , I.
1998-01-01
Full Text Available La relevancia de los problemas de optimización en el mundo empresarial ha generado la introducción de herramientas de optimización cada vez más sofisticadas en las últimas versiones de las hojas de cálculo de utilización generalizada. Estas utilidades, conocidas habitualmente como «solvers», constituyen una alternativa a los programas especializados de optimización cuando no se trata de problemas de gran escala, presentado la ventaja de su facilidad de uso y de comunicación con el usuario final. Frontline Systems Inc es la empresa que desarrolla el «solver» de Excel, si bien existen asimismo versiones para Lotus y Quattro Pro con ligeras diferencias de uso. En su dirección de internet (www.frontsys.com se puede obtener información técnica sobre las diferentes versiones de dicha utilidad y diversos aspectos operativos del programa, algunos de los cuales se comentan en este trabajo.
A sparse-grid isogeometric solver
Beck, Joakim
2018-02-28
Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90’s in the context of the approximation of high-dimensional PDEs.The tests that we report show that, in accordance to the literature, a sparse-grid construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.
A sparse version of IGA solvers
Beck, Joakim
2017-07-30
Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90s in the context of the approximation of high-dimensional PDEs. The tests that we report show that, in accordance to the literature, a sparse grids construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.
Goldberg, Sarah E.; Whittamore, Kathy H.; Harwood, Rowan H.; Bradshaw, Lucy E.; Gladman, John R. F.; Jones, Rob G.
2011-01-01
Background: a high prevalence of co-morbid mental health problems is reported among older adults admitted to general hospitals. Setting: an 1,800 bed teaching hospital. Design: consecutive general medical and trauma orthopaedic admissions aged 70 or older were screened for mental health problems. Those screening positive were invited to undergo further assessment, and were interviewed to complete a battery of health status measurements. Results: of 1,004 patients screened, 36% had no mental h...
A fast mass spring model solver for high-resolution elastic objects
Zheng, Mianlun; Yuan, Zhiyong; Zhu, Weixu; Zhang, Guian
2017-03-01
Real-time simulation of elastic objects is of great importance for computer graphics and virtual reality applications. The fast mass spring model solver can achieve visually realistic simulation in an efficient way. Unfortunately, this method suffers from resolution limitations and lack of mechanical realism for a surface geometry model, which greatly restricts its application. To tackle these problems, in this paper we propose a fast mass spring model solver for high-resolution elastic objects. First, we project the complex surface geometry model into a set of uniform grid cells as cages through *cages mean value coordinate method to reflect its internal structure and mechanics properties. Then, we replace the original Cholesky decomposition method in the fast mass spring model solver with a conjugate gradient method, which can make the fast mass spring model solver more efficient for detailed surface geometry models. Finally, we propose a graphics processing unit accelerated parallel algorithm for the conjugate gradient method. Experimental results show that our method can realize efficient deformation simulation of 3D elastic objects with visual reality and physical fidelity, which has a great potential for applications in computer animation.
Scalable domain decomposition solvers for stochastic PDEs in high performance computing
International Nuclear Information System (INIS)
Desai, Ajit; Pettit, Chris; Poirel, Dominique; Sarkar, Abhijit
2017-01-01
Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolution in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.
Graph Grammar-Based Multi-Frontal Parallel Direct Solver for Two-Dimensional Isogeometric Analysis
Kuźnik, Krzysztof
2012-06-02
This paper introduces the graph grammar based model for developing multi-thread multi-frontal parallel direct solver for two dimensional isogeometric finite element method. Execution of the solver algorithm has been expressed as the sequence of graph grammar productions. At the beginning productions construct the elimination tree with leaves corresponding to finite elements. Following sequence of graph grammar productions generates element frontal matri-ces at leaf nodes, merges matrices at parent nodes and eliminates rows corresponding to fully assembled degrees of freedom. Finally, there are graph grammar productions responsible for root problem solution and recursive backward substitutions. Expressing the solver algorithm by graph grammar productions allows us to explore the concurrency of the algorithm. The graph grammar productions are grouped into sets of independent tasks that can be executed concurrently. The resulting concurrent multi-frontal solver algorithm is implemented and tested on NVIDIA GPU, providing O(NlogN) execution time complexity where N is the number of degrees of freedom. We have confirmed this complexity by solving up to 1 million of degrees of freedom with 448 cores GPU.
van der Hoorn, Anouk; Oldehinkel, A.J.; Ormel, J.; Bruggeman, R; Uiterwaal, C.S.P.M.; Burger, Huib
2010-01-01
To determine whether the association between non-right-handedness and mental problems among adolescents is specific for psychotic symptoms, we included a group of 2096 adolescents with a mean age of 14 years from the general population. Mental health problems were assessed using the parent,
Teunissen, E.; Bavel, E. Van; Driessen Mareeuw, F.A. van den; Macfarlane, A.; Weel-Baumgarten, E.M. van; Muijsenbergh, M.E.T.C. van den; Weel, C. van
2015-01-01
OBJECTIVE: To explore the views and experiences of general practitioners (GPs) in relation to recognition, recording, and treatment of mental health problems of undocumented migrants (UMs), and to gain insight in the reasons for under-registration of mental health problems in the electronic medical
Generalized Uncertainty Quantification for Linear Inverse Problems in X-ray Imaging
Energy Technology Data Exchange (ETDEWEB)
Fowler, Michael James [Clarkson Univ., Potsdam, NY (United States)
2014-04-25
In industrial and engineering applications, X-ray radiography has attained wide use as a data collection protocol for the assessment of material properties in cases where direct observation is not possible. The direct measurement of nuclear materials, particularly when they are under explosive or implosive loading, is not feasible, and radiography can serve as a useful tool for obtaining indirect measurements. In such experiments, high energy X-rays are pulsed through a scene containing material of interest, and a detector records a radiograph by measuring the radiation that is not attenuated in the scene. One approach to the analysis of these radiographs is to model the imaging system as an operator that acts upon the object being imaged to produce a radiograph. In this model, the goal is to solve an inverse problem to reconstruct the values of interest in the object, which are typically material properties such as density or areal density. The primary objective in this work is to provide quantitative solutions with uncertainty estimates for three separate applications in X-ray radiography: deconvolution, Abel inversion, and radiation spot shape reconstruction. For each problem, we introduce a new hierarchical Bayesian model for determining a posterior distribution on the unknowns and develop efficient Markov chain Monte Carlo (MCMC) methods for sampling from the posterior. A Poisson likelihood, based on a noise model for photon counts at the detector, is combined with a prior tailored to each application: an edge-localizing prior for deconvolution; a smoothing prior with non-negativity constraints for spot reconstruction; and a full covariance sampling prior based on a Wishart hyperprior for Abel inversion. After developing our methods in a general setting, we demonstrate each model on both synthetically generated datasets, including those from a well known radiation transport code, and real high energy radiographs taken at two U. S. Department of Energy
Johnson, David T.
Quantum mechanics is an extremely successful and accurate physical theory, yet since its inception, it has been afflicted with numerous conceptual difficulties. The primary subject of this thesis is the theory of entropic quantum dynamics (EQD), which seeks to avoid these conceptual problems by interpreting quantum theory from an informational perspective. We begin by reviewing Cox's work in describing probability theory as a means of rationally and consistently quantifying uncertainties. We then discuss how probabilities can be updated according to either Bayes' theorem or the extended method of maximum entropy (ME). After that discussion, we review the work of Caticha and Giffin that shows that Bayes' theorem is a special case of ME. This important result demonstrates that the ME method is the general method for updating probabilities. We then review some motivating difficulties in quantum mechanics before discussing Caticha's work in deriving quantum theory from the approach of entropic dynamics, which concludes our review. After entropic dynamics is introduced, we develop the concepts of symmetries and transformations from an informational perspective. The primary result is the formulation of a symmetry condition that any transformation must satisfy in order to qualify as a symmetry in EQD. We then proceed to apply this condition to the extended Galilean transformation. This transformation is of interest as it exhibits features of both special and general relativity. The transformation yields a gravitational potential that arises from an equivalence of information. We conclude the thesis with a discussion of the measurement problem in quantum mechanics. We discuss the difficulties that arise in the standard quantum mechanical approach to measurement before developing our theory of entropic measurement. In entropic dynamics, position is the only observable. We show how a theory built on this one observable can account for the multitude of measurements present in
Preston, L. A.
2017-12-01
Marine hydrokinetic (MHK) devices offer a clean, renewable alternative energy source for the future. Responsible utilization of MHK devices, however, requires that the effects of acoustic noise produced by these devices on marine life and marine-related human activities be well understood. Paracousti is a 3-D full waveform acoustic modeling suite that can accurately propagate MHK noise signals in the complex bathymetry found in the near-shore to open ocean environment and considers real properties of the seabed, water column, and air-surface interface. However, this is a deterministic simulation that assumes the environment and source are exactly known. In reality, environmental and source characteristics are often only known in a statistical sense. Thus, to fully characterize the expected noise levels within the marine environment, this uncertainty in environmental and source factors should be incorporated into the acoustic simulations. One method is to use Monte Carlo (MC) techniques where simulation results from a large number of deterministic solutions are aggregated to provide statistical properties of the output signal. However, MC methods can be computationally prohibitive since they can require tens of thousands or more simulations to build up an accurate representation of those statistical properties. An alternative method, using the technique of stochastic partial differential equations (SPDE), allows computation of the statistical properties of output signals at a small fraction of the computational cost of MC. We are developing a SPDE solver for the 3-D acoustic wave propagation problem called Paracousti-UQ to help regulators and operators assess the statistical properties of environmental noise produced by MHK devices. In this presentation, we present the SPDE method and compare statistical distributions of simulated acoustic signals in simple models to MC simulations to show the accuracy and efficiency of the SPDE method. Sandia National Laboratories
Overweight in adolescent, psychiatric inpatients: A problem of general or food-specific impulsivity?
Deux, Natalie; Schlarb, Angelika A; Martin, Franziska; Holtmann, Martin; Hebebrand, Johannes; Legenbauer, Tanja
2017-05-01
Adolescent psychiatric patients are vulnerable to weight problems and show an overrepresentation of overweight compared to the healthy population. One potential factor that can contribute to the etiology of overweight is higher impulsivity. As of yet, it is unclear whether it is a general impulse control deficit or weight-related aspects such as lower impulse control in response to food that have an impact on body weight. As this may have therapeutic implications, the current study investigated differences between overweight and non-overweight adolescent psychiatric inpatients (N = 98; aged 12-20) in relation to trait impulsivity and behavioral inhibition performance. The Barratt Impulsiveness Scale and two go/no-go paradigms with neutral and food-related stimulus materials were applied. Results indicated no significant differences concerning trait impulsivity, but revealed that overweight inpatients had significantly more difficulties in inhibition performance (i.e. they reacted more impulsively) in response to both food and neutral stimuli compared to non-overweight inpatients. Furthermore, no specific inhibition deficit for high-caloric vs. low-caloric food cues emerged in overweight inpatients, whereas non-overweight participants showed significantly lower inhibition skills in response to high-caloric than low-caloric food stimuli. The results highlight a rather general, non-food-specific reduced inhibition performance in an overweight adolescent psychiatric population. Further research is necessary to enhance the understanding of the role of impulsivity in terms of body weight status in this high-risk group of adolescent inpatients. Copyright © 2017 Elsevier Ltd. All rights reserved.
Parallel performance of a preconditioned CG solver for unstructured finite element applications
Energy Technology Data Exchange (ETDEWEB)
Shadid, J.N.; Hutchinson, S.A.; Moffat, H.K. [Sandia National Labs., Albuquerque, NM (United States)
1994-12-31
A parallel unstructured finite element (FE) implementation designed for message passing MIMD machines is described. This implementation employs automated problem partitioning algorithms for load balancing unstructured grids, a distributed sparse matrix representation of the global finite element equations and a parallel conjugate gradient (CG) solver. In this paper a number of issues related to the efficient implementation of parallel unstructured mesh applications are presented. These include the differences between structured and unstructured mesh parallel applications, major communication kernels for unstructured CG solvers, automatic mesh partitioning algorithms, and the influence of mesh partitioning metrics on parallel performance. Initial results are presented for example finite element (FE) heat transfer analysis applications on a 1024 processor nCUBE 2 hypercube. Results indicate over 95% scaled efficiencies are obtained for some large problems despite the required unstructured data communication.
Generalized Supersoft Supersymmetry Breaking and a Solution to the μ Problem.
Nelson, Ann E; Roy, Tuhin S
2015-05-22
We propose the framework generalized supersoft supersymmetry breaking. "Supersoft" models, with D-type supersymmetry breaking and heavy Dirac gauginos, are considerably less constrained by the LHC searches than the well studied MSSM. These models also ameliorate the supersymmetric flavor and CP problems. However, previously considered mechanisms for obtaining a natural size Higgsino mass parameter (namely, μ) in supersoft models have been relatively complicated and contrived. Obtaining a 125 GeV for the mass of the lightest Higgs boson has also been difficult. Additional issues with the supersoft scenario arise from the fact that these models contain new scalars in the adjoint representation of the standard model, which may obtain negative squared-masses, breaking color and generating too large a T parameter. In this Letter, we introduce new operators into supersoft models which can potentially solve all these issues. A novel feature of this framework is that the new μ term can give unequal masses to the up and down type Higgs fields, and the Higgsinos can be much heavier than the Higgs boson without fine-tuning. However, unequal Higgs and Higgsino masses also remove some attractive features of supersoft supersymmetry.
Stein, Dan J; Lopez, Ana Garcia
2011-11-01
Disturbed sleep is a key symptom in major depressive disorder (MDD) and generalized anxiety disorder (GAD). First-line antidepressants, including the selective serotonin reuptake inhibitors (SSRIs) and serotonin noradrenaline reuptake inhibitors (SNRIs), may have different effects on sleep. Data from 22 randomized, controlled trials comparing escitalopram with SSRIs, SNRIs, or placebo in the treatment of adult MDD or GAD were included. Both last observation carried forward (LOCF) and repeated measurements (MMRM) were used to analyze the sleep item of the Montgomery Åsberg Depression Rating Scale (MADRS) or Hamilton Anxiety Rating Scale (HAM-A) after 8 weeks of treatment. Sleep-related treatment-emergent adverse events were also compared across groups. For patients with MDD (n = 5133), the treatment difference on MADRS item 4 ("reduced sleep") was significantly in favor of escitalopram versus placebo (LOCF [P = 0.0017] and MMRM [P = 0.0002]), versus SSRIs (LOCF [P = 0.0020] and MMRM [P 0.0787]). For patients with GAD (n = 2052) the treatment difference in sleep symptoms measured by HAM-A item 4 ("insomnia") was significantly in favor of escitalopram versus placebo (LOCF [P = 0.0005] and MMRM [P insomnia as an adverse event after escitalopram was higher than placebo, similar to SSRIs, and lower than SNRIs. Additional research assessing the comparative effects of antidepressants with polysomnography is needed. In the interim, from a clinical perspective, escitalopram appears to be beneficial for the treatment of sleep problems in MDD and GAD.
Flouri, Eirini; Mavroveli, Stella; Panourgia, Constantina
2013-02-01
Previous studies have established the role of various measures of cognitive functioning in dampening the association between adverse life events ('life stress') and adolescents' emotional and behavioural problems. However, it is not yet clear if general cognitive ability ('intelligence') is a protective factor. In this study of 1,175 10- to 19-year-olds in five secondary schools in England, we explored this issue. We found that even after controlling for sex, age, family poverty, and special educational needs, the association of life stress with emotional, hyperactivity, and conduct problems was significant. General cognitive ability moderated the association between life stress and conduct problems; among adolescents with higher than average general cognitive ability, the association between life stress and conduct problems was non-significant. © 2012 The British Psychological Society.
Vozmishcheva, Tatiana
2016-09-01
The connection between the problems of celestial mechanics: the Kepler problem, the two-center problem and the two body problem in spaces of constant curvature with the generalized Kepler and Hooke potentials is investigated. The limit passage in the two-center and two body problems in the Lobachevsky space and on a sphere is carried out as λto0 (λ is the curvature of the corresponding space) for the two potentials. The potentials and metrics in spaces under study are written in the gnomonic coordinates. It is shown that as the curvature radius tends to infinity, the generalized gravitational and elastic potentials transform to the Kepler and Hooke forms in the Euclidean space.
Asynchronous Parallelization of a CFD Solver
Directory of Open Access Journals (Sweden)
Daniel S. Abdi
2015-01-01
Full Text Available A Navier-Stokes equations solver is parallelized to run on a cluster of computers using the domain decomposition method. Two approaches of communication and computation are investigated, namely, synchronous and asynchronous methods. Asynchronous communication between subdomains is not commonly used in CFD codes; however, it has a potential to alleviate scaling bottlenecks incurred due to processors having to wait for each other at designated synchronization points. A common way to avoid this idle time is to overlap asynchronous communication with computation. For this to work, however, there must be something useful and independent a processor can do while waiting for messages to arrive. We investigate an alternative approach of computation, namely, conducting asynchronous iterations to improve local subdomain solution while communication is in progress. An in-house CFD code is parallelized using message passing interface (MPI, and scalability tests are conducted that suggest asynchronous iterations are a viable way of parallelizing CFD code.
An efficient preconditioning technique using Krylov subspace methods for 3D characteristics solvers
International Nuclear Information System (INIS)
Dahmani, M.; Le Tellier, R.; Roy, R.; Hebert, A.
2005-01-01
The Generalized Minimal RESidual (GMRES) method, using a Krylov subspace projection, is adapted and implemented to accelerate a 3D iterative transport solver based on the characteristics method. Another acceleration technique called the self-collision rebalancing technique (SCR) can also be used to accelerate the solution or as a left preconditioner for GMRES. The GMRES method is usually used to solve a linear algebraic system (Ax=b). It uses K(r (o) ,A) as projection subspace and AK(r (o) ,A) for the orthogonalization of the residual. This paper compares the performance of these two combined methods on various problems. To implement the GMRES iterative method, the characteristics equations are derived in linear algebra formalism by using the equivalence between the method of characteristics and the method of collision probability to end up with a linear algebraic system involving fluxes and currents. Numerical results show good performance of the GMRES technique especially for the cases presenting large material heterogeneity with a scattering ratio close to 1. Similarly, the SCR preconditioning slightly increases the GMRES efficiency
The Quantum Mechanics Solver How to Apply Quantum Theory to Modern Physics
Basdevant, Jean-Louis
2006-01-01
The Quantum Mechanics Solver grew from topics which are part of the final examination in quantum theory at the Ecole Polytechnique at Palaiseau near Paris, France. The aim of the text is to guide the student towards applying quantum mechanics to research problems in fields such as atomic and molecular physics, condensed matter physics, and laser physics. Advanced undergraduates and graduate students will find a rich and challenging source for improving their skills in this field.
Mang, Andreas; Ruthotto, Lars
2017-01-01
We present an efficient solver for diffeomorphic image registration problems in the framework of Large Deformations Diffeomorphic Metric Mappings (LDDMM). We use an optimal control formulation, in which the velocity field of a hyperbolic PDE needs to be found such that the distance between the final state of the system (the transformed/transported template image) and the observation (the reference image) is minimized. Our solver supports both stationary and non-stationary (i.e., transient or time-dependent) velocity fields. As transformation models, we consider both the transport equation (assuming intensities are preserved during the deformation) and the continuity equation (assuming mass-preservation). We consider the reduced form of the optimal control problem and solve the resulting unconstrained optimization problem using a discretize-then-optimize approach. A key contribution is the elimination of the PDE constraint using a Lagrangian hyperbolic PDE solver. Lagrangian methods rely on the concept of characteristic curves. We approximate these curves using a fourth-order Runge-Kutta method. We also present an efficient algorithm for computing the derivatives of the final state of the system with respect to the velocity field. This allows us to use fast Gauss-Newton based methods. We present quickly converging iterative linear solvers using spectral preconditioners that render the overall optimization efficient and scalable. Our method is embedded into the image registration framework FAIR and, thus, supports the most commonly used similarity measures and regularization functionals. We demonstrate the potential of our new approach using several synthetic and real world test problems with up to 14.7 million degrees of freedom.
International Nuclear Information System (INIS)
Na, Y. W.; Park, C. E.; Lee, S. Y.
2009-01-01
As a part of the Ministry of Knowledge Economy (MKE) project, 'Development of safety analysis codes for nuclear power plants', KOPEC has been developing the hydraulic solver code package applicable to the safety analyses of nuclear power plants (NPP's). The matrices of the hydraulic solver are usually sparse and may be asymmetric. In the earlier stage of this project, typical direct matrix solver packages MA48 and MA28 had been tested as matrix solver for the hydraulic solver code, SPACE. The selection was based on the reasonably reliable performance experience from their former version MA18 in RELAP computer code. In the later stage of this project, the iterative methodologies have been being tested in the SPACE code. Among a few candidate iterative solution methodologies tested so far, the biconjugate gradient stabilization methodology (BICGSTAB) has shown the best performance in the applicability test and in the application to the SPACE code. Regardless of all the merits of using the direct solver packages, there are some other aspects of tackling the iterative solution methodologies. The algorithm is much simpler and easier to handle. The potential problems related to the robustness of the iterative solution methodologies have been resolved by applying pre-conditioning methods adjusted and modified as appropriate to the application in the SPACE code. The application strategy of conjugate gradient method was introduced in detail by Schewchuk, Golub and Saad in the middle of 1990's. The application of his methodology to nuclear engineering in Korea started about the same time and is still going on and there are quite a few examples of application to neutronics. Besides, Yang introduced a conjugate gradient method programmed in C++ language. The purpose of this study is to assess the performance and behavior of the iterative solution methodology compared to those of the direct solution methodology still being preferred due to its robustness and reliability. The
Lower, Stephen K.
A brief overview of CHEMEX--a problem-solving, tutorial style computer-assisted instructional course--is provided and sample problems are offered. In CHEMEX, students receive problems in advance and attempt to solve them before moving through the computer program, which assists them in overcoming difficulties and serves as a review mechanism.…
An accurate, fast, and scalable solver for high-frequency wave propagation
Zepeda-Núñez, L.; Taus, M.; Hewett, R.; Demanet, L.
2017-12-01
In many science and engineering applications, solving time-harmonic high-frequency wave propagation problems quickly and accurately is of paramount importance. For example, in geophysics, particularly in oil exploration, such problems can be the forward problem in an iterative process for solving the inverse problem of subsurface inversion. It is important to solve these wave propagation problems accurately in order to efficiently obtain meaningful solutions of the inverse problems: low order forward modeling can hinder convergence. Additionally, due to the volume of data and the iterative nature of most optimization algorithms, the forward problem must be solved many times. Therefore, a fast solver is necessary to make solving the inverse problem feasible. For time-harmonic high-frequency wave propagation, obtaining both speed and accuracy is historically challenging. Recently, there have been many advances in the development of fast solvers for such problems, including methods which have linear complexity with respect to the number of degrees of freedom. While most methods scale optimally only in the context of low-order discretizations and smooth wave speed distributions, the method of polarized traces has been shown to retain optimal scaling for high-order discretizations, such as hybridizable discontinuous Galerkin methods and for highly heterogeneous (and even discontinuous) wave speeds. The resulting fast and accurate solver is consequently highly attractive for geophysical applications. To date, this method relies on a layered domain decomposition together with a preconditioner applied in a sweeping fashion, which has limited straight-forward parallelization. In this work, we introduce a new version of the method of polarized traces which reveals more parallel structure than previous versions while preserving all of its other advantages. We achieve this by further decomposing each layer and applying the preconditioner to these new components separately and
Basten, Maartje; Tiemeier, Henning; Althoff, Robert R; van de Schoot, Rens; Jaddoe, Vincent W V; Hofman, Albert; Hudziak, James J; Verhulst, Frank C; van der Ende, Jan
2016-02-01
This study examined the stability of internalizing and externalizing problems from age 1.5 to 6 years, while taking into account developmental changes in the presentation of problems. The study comprised a population-based cohort of 7,206 children (50.4 % boys). At ages 1.5, 3, and 6 years, mothers reported on problem behavior using the Child Behavior Checklist/1.5-5 (CBCL/1.5-5). At each age we performed latent profile analysis on the CBCL/1.5-5 scales. Latent transition analysis (LTA) was applied to study the stability of problem behavior. Profiles of problem behavior varied across ages. At each age, 82-87 % of the children did not have problems whereas approximately 2 % showed a profile of co-occurring internalizing and externalizing problems. This profile was more severe (with higher scores) at 6 years than at earlier ages. A predominantly internalizing profile only emerged at 6 years, while a profile with externalizing problems and emotional reactivity was present at each age. LTA showed that, based on profiles at 1.5 and 3 years, it was difficult to predict the type of profile at 6 years. Children with a profile of co-occurring internalizing and externalizing problems early in life were most likely to show problem behavior at 6 years. This study shows that the presentation of problem behavior changes across the preschool period and that heterotypic continuity of problems is very common among preschoolers. Children with co-occurring internalizing and externalizing problems were most likely to show persisting problems. The use of evidence-based treatment for these young children may prevent psychiatric problems across the life course.
Parallelization of Unsteady Adaptive Mesh Refinement for Unstructured Navier-Stokes Solvers
Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.
2014-01-01
This paper explores the implementation of the MPI parallelization in a Navier-Stokes solver using adaptive mesh re nement. Viscous and inviscid test problems are considered for the purpose of benchmarking, as are implicit and explicit time advancement methods. The main test problem for comparison includes e ects from boundary layers and other viscous features and requires a large number of grid points for accurate computation. Ex- perimental validation against double cone experiments in hypersonic ow are shown. The adaptive mesh re nement shows promise for a staple test problem in the hypersonic com- munity. Extension to more advanced techniques for more complicated ows is described.
Towards Batched Linear Solvers on Accelerated Hardware Platforms
Energy Technology Data Exchange (ETDEWEB)
Haidar, Azzam [University of Tennessee (UT); Dong, Tingzing Tim [University of Tennessee (UT); Tomov, Stanimire [University of Tennessee (UT); Dongarra, Jack J [ORNL
2015-01-01
As hardware evolves, an increasingly effective approach to develop energy efficient, high-performance solvers, is to design them to work on many small and independent problems. Indeed, many applications already need this functionality, especially for GPUs, which are known to be currently about four to five times more energy efficient than multicore CPUs for every floating-point operation. In this paper, we describe the development of the main one-sided factorizations: LU, QR, and Cholesky; that are needed for a set of small dense matrices to work in parallel. We refer to such algorithms as batched factorizations. Our approach is based on representing the algorithms as a sequence of batched BLAS routines for GPU-contained execution. Note that this is similar in functionality to the LAPACK and the hybrid MAGMA algorithms for large-matrix factorizations. But it is different from a straightforward approach, whereby each of GPU's symmetric multiprocessors factorizes a single problem at a time. We illustrate how our performance analysis together with the profiling and tracing tools guided the development of batched factorizations to achieve up to 2-fold speedup and 3-fold better energy efficiency compared to our highly optimized batched CPU implementations based on the MKL library on a two-sockets, Intel Sandy Bridge server. Compared to a batched LU factorization featured in the NVIDIA's CUBLAS library for GPUs, we achieves up to 2.5-fold speedup on the K40 GPU.
A problem of finding an acceptable variant in generalized project networks
Directory of Open Access Journals (Sweden)
David Blokh
2005-01-01
Full Text Available A project network often has some activities or groups of activities which can be performed at different stages of the project. Then, the problem of finding an optimal/acceptable time or/and optimal/acceptable order of such an activity or a group of activities arises. Such a problem emerges, in particular, in house-building management when the beginnings of some activities may vary in time or/and order. We consider a mathematical formulation of the problem, show its computational complexity, and describe an algorithm for solving the problem.
Gomez Penedo, Juan Martin; Constantino, Michael J; Coyne, Alice E; Westra, Henny A; Antony, Martin M
2017-10-01
To follow-up a randomized clinical trial that compared the acute and long-term efficacy of 15 sessions of cognitive-behavioral therapy (CBT) versus CBT integrated with motivational interviewing (MI) for severe generalized anxiety disorder (GAD; Westra, Constantino, & Antony, 2016), we (a) characterized the sample's baseline interpersonal problems, and (b) analyzed the role of several theory-relevant problems as moderators of the comparative treatment effects on outcome. We first compared clients' (N = 85) baseline interpersonal problems profile to a general clinical sample. We next conducted piecewise, 2-level growth models to analyze the interactive effects of treatment condition and the hypothesized interpersonal problem indices of nonassertiveness (ranging from low to high), exploitability (ranging from low to high on this specific combination of nonassertiveness and friendliness), and overall agency (ranging from more problems of being too submissive to more problems of being too domineering, including friendly or hostile variants) on acute and follow-up worry reduction. Finally, we conducted hierarchical generalized linear models to examine these interactive effects on the likelihood of achieving clinically meaningful worry reduction across follow-up. As expected, the GAD clients evidenced more nonassertive and exploitable interpersonal problems than the general clinical sample. Also as predicted, clients with more problematic nonassertiveness and low overall agency in their relationships had greater follow-up worry reduction in MI-CBT versus CBT, including to a clinically significant degree for the agency by treatment interaction. GAD-specific interpersonal problems can serve as contextual markers for integrative treatment selection and planning. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
Kuźnik, Krzysztof
2013-06-01
This paper introduces a grammar-based model for developing a multi-thread multi-frontal parallel direct solver for one- dimensional isogeometric finite element method. The model includes the integration of B-splines for construction of the element local matrices and the multi-frontal solver algorithm. The integration and the solver algorithm are partitioned into basic indivisible tasks, namely the grammar productions, that can be executed squentially. The partial order of execution of the basic tasks is analyzed to provide the scheduling for the execution of the concurrent integration and multi-frontal solver algo- rithm. This graph grammar analysis allows for optimal concurrent execution of all tasks. The model has been implemented and tested on NVIDIA CUDA GPU, delivering logarithmic execution time for linear, quadratic, cubic and higher order B-splines. Thus, the CUDA implementation delivers the optimal performance predicted by our graph grammar analysis. We utilize the solver for multiple right hand sides related to the solution of non-stationary or inverse problems.
Leitner, Markus
In this article, we introduce the Generalized [Formula: see text]-Survivable Network Design Problem ([Formula: see text]-GSNDP) which has applications in the design of backbone networks. Different mixed integer linear programming formulations are derived by combining previous results obtained for the related [Formula: see text]-GSNDP and Generalized Network Design Problems. An extensive computational study comparing the correspondingly developed branch-and-cut approaches shows clear advantages for two particular variants. Additional insights into individual advantages and disadvantages of the developed algorithms for different instance characteristics are given.
van Weert, K.; Dhaene, J.; Goovaerts, M.
2011-01-01
In this paper we discuss multiperiod portfolio selection problems related to a specific provisioning problem. Our results are an extension of Dhaene et al. (2005) [14], where optimal constant mix investment strategies are obtained in a provisioning and savings context, using an analytical approach
Brink-Muinen, A. van den; Bakker, D.H. de; Bensing, J.M.
1994-01-01
AIM. This study set out to examine the degree to which women choose to visit a woman doctor for women's health problems and the determinants of this choice. The differences between women and men doctors with regard to treating women's health problems were also studied. METHOD. Data from the Dutch
A Generalization of the Aumann-Shapley Value for Risk Capital Allocation Problems
Boonen, T.J.; De Waegenaere, A.M.B.; Norde, H.W.
2012-01-01
Abstract: This paper analyzes risk capital allocation problems. For risk capital allocation problems, the aim is to allocate the risk capital of a firm to its divisions. Risk capital allocation is of central importance in risk-based performance measurement. We consider a case in which the aggregate
Health problems of victims before and after disaster: a longitudinal study in general practice.
Yzermans, C.J.; Donker, G.A.; Kerssens, J.J.; Dirkzwager, A.J.E.; Soeteman, R.J.H.; Veen, P.M.H. ten
2005-01-01
BACKGROUND: We aimed to quantify the health problems and to assess the possible risk factors for developing health problems in persons affected by the explosion of a firework depot at Enschede, The Netherlands, on May 13, 2000. The explosion considerably damaged buildings in the local neighbourhood
Directory of Open Access Journals (Sweden)
Vladimir V. Kozoderov
1998-01-01
Full Text Available The overall problem of global change is considered as the mathematical discrete dynamics discipline that deals with the sets, measures and metrics (SMM categories in information sub-spaces. The SMM conception enables to unify techniques of data interpretation and analysis and to explain how effectively the giant amounts of information from multispectral satellite radiometers and ground-based instruments are to be processed. It is shown that Prigogine's chaos/order theory and Kolmogorov's probability space are two milestones in understanding the predictability problems of global change. The essence of the problems is maintained to be in filtering out a “useful signal” that would spread from key regions of the globe as compared to their background. Global analysis, interpretation and modelling issues are outlined in the framework of incorrect mathematical problems and of the SMM categories, which contribute to solving the comparability problem for different sets of observations.
A non-conforming 3D spherical harmonic transport solver
International Nuclear Information System (INIS)
Van Criekingen, S.
2006-01-01
A new 3D transport solver for the time-independent Boltzmann transport equation has been developed. This solver is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux in spherical harmonics (PN method). The novelty of this solver is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations such as the ones based on Raviart-Thomas finite elements. Encouraging numerical results are presented. (authors)
Investigation on the Use of a Multiphase Eulerian CFD solver to simulate breaking waves
DEFF Research Database (Denmark)
Tomaselli, Pietro D.; Christensen, Erik Damgaard
2015-01-01
The main challenge in CFD multiphase simulations of breaking waves is the wide range of interfacial length scales occurring in the flow: from the free surface measurable in meters down to the entrapped air bubbles with size of a fraction of a millimeter. This paper presents a preliminary...... investigation on a CFD model capable of handling this problem. The model is based on a solver, available in the open-source CFD toolkit OpenFOAM, which combines the Eulerian multi-fluid approach for dispersed flows with a numerical interface sharpening method. The solver, enhanced with additional formulations...... for mass and momentum transfer among phases, was satisfactorily tested against an experimental bubble column flow. The model was then used to simulate the propagation of a laboratory solitary breaking wave. The motion of the free surface was successfully reproduced up to the breaking point. Further...
Solving non-linear Horn clauses using a linear Horn clause solver
DEFF Research Database (Denmark)
Kafle, Bishoksan; Gallagher, John Patrick; Ganty, Pierre
2016-01-01
In this paper we show that checking satisfiability of a set of non-linear Horn clauses (also called a non-linear Horn clause program) can be achieved using a solver for linear Horn clauses. We achieve this by interleaving a program transformation with a satisfiability checker for linear Horn...... clauses (also called a solver for linear Horn clauses). The program transformation is based on the notion of tree dimension, which we apply to a set of non-linear clauses, yielding a set whose derivation trees have bounded dimension. Such a set of clauses can be linearised. The main algorithm...... dimension. We constructed a prototype implementation of this approach and performed some experiments on a set of verification problems, which shows some promise....
A Massively Parallel Solver for the Mechanical Harmonic Analysis of Accelerator Cavities
Energy Technology Data Exchange (ETDEWEB)
Kononenko, O. [SLAC National Accelerator Lab., Menlo Park, CA (United States)
2015-02-17
ACE3P is a 3D massively parallel simulation suite that developed at SLAC National Accelerator Laboratory that can perform coupled electromagnetic, thermal and mechanical study. Effectively utilizing supercomputer resources, ACE3P has become a key simulation tool for particle accelerator R and D. A new frequency domain solver to perform mechanical harmonic response analysis of accelerator components is developed within the existing parallel framework. This solver is designed to determine the frequency response of the mechanical system to external harmonic excitations for time-efficient accurate analysis of the large-scale problems. Coupled with the ACE3P electromagnetic modules, this capability complements a set of multi-physics tools for a comprehensive study of microphonics in superconducting accelerating cavities in order to understand the RF response and feedback requirements for the operational reliability of a particle accelerator. (auth)
Cardall, Christian Y.; Budiardja, Reuben D.
2018-01-01
The large-scale computer simulation of a system of physical fields governed by partial differential equations requires some means of approximating the mathematical limit of continuity. For example, conservation laws are often treated with a 'finite-volume' approach in which space is partitioned into a large number of small 'cells,' with fluxes through cell faces providing an intuitive discretization modeled on the mathematical definition of the divergence operator. Here we describe and make available Fortran 2003 classes furnishing extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon, along with individual 'unit test' programs and larger example problems demonstrating their use. These classes inaugurate the Mathematics division of our developing astrophysics simulation code GENASIS (Gen eral A strophysical Si mulation S ystem), which will be expanded over time to include additional meshing options, mathematical operations, solver types, and solver variations appropriate for many multiphysics applications.
Millstein, Daniel J; Orsillo, Susan M; Hayes-Skelton, Sarah A; Roemer, Lizabeth
2015-01-01
To better understand the role interpersonal problems play in response to two treatments for generalized anxiety disorder (GAD); an acceptance-based behavior therapy (ABBT) and applied relaxation (AR), and to examine how the development of mindfulness may be related to change in interpersonal problems over treatment and at follow-up. Eighty-one individuals diagnosed with GAD (65.4% female, 80.2% identified as white, average age 32.92) were randomized to receive 16 sessions of either ABBT or AR. GAD severity, interpersonal problems, and mindfulness were measured at pre-treatment, post-treatment, 6-month follow-up, and 12-month follow-up. Mixed effect regression models did not reveal any significant effects of pre-treatment interpersonal problems on GAD severity over treatment. After controlling for post-treatment GAD severity, remaining post-treatment interpersonal problems predicted 6- but not 12-month GAD severity. Participants in both conditions experienced a large decrease in interpersonal problems over treatment. Increases in mindfulness over treatment and through follow-up were associated with decreases in interpersonal problems, even when accounting for reductions in overall GAD severity. Interpersonal problems may be an important target of treatment in GAD, even if pre-treatment interpersonal problems are not predictive of outcome. Developing mindfulness in individuals with GAD may help ameliorate interpersonal difficulties among this population.
Brain dynamics of mathematical problem solving.
Lin, Chun-Ling; Jung, Melody; Wu, Ying Choon; Lin, Chin-Teng; She, Hsiao-Ching
2012-01-01
The purpose of this study is to examine brain activities of participants solving mental math problems. The research investigated how problem difficulty affected the subjects' responses and electroencephalogram (EEG) in different brain regions. In general, it was found that solution latencies (SL) to the math problems increased with difficulty. The EEG results showed that across subjects, the right-central beta, left-parietal theta, left-occipital theta and alpha, right-parietal alpha and beta, medial-frontal beta and medial central theta power decreased as task difficulty increased. This study further explored the effects of problem-solving performance on the EEG. Slow solvers exhibited greater frontal theta activities in the right hemisphere, whereas an inverse pattern of hemispheric asymmetry was found in fast solvers. Furthermore, analyses of spatio-temporal brain dynamics during problem solving show progressively stronger alpha- and beta-power suppression and theta-power augmentation as subjects were reaching a solution. These findings provide a better understanding of cortical activities mediating math-based problem solving and knowledge acquisition that can ultimately benefit math learning and education.
Teunissen, Erik; Van Bavel, Eric; Van Den Driessen Mareeuw, Francine; Macfarlane, Anne; Van Weel-Baumgarten, Evelyn; Van Den Muijsenbergh, Maria; Van Weel, Chris
2015-06-01
To explore the views and experiences of general practitioners (GPs) in relation to recognition, recording, and treatment of mental health problems of undocumented migrants (UMs), and to gain insight in the reasons for under-registration of mental health problems in the electronic medical records. Qualitative study design with semi-structured interviews using a topic guide. Sixteen GPs in the Netherlands with clinical expertise in the care of UMs. GPs recognized many mental health problems in UMs. Barriers that prevented them from recording these problems and from delivering appropriate care were their low consultation rates, physical presentation of mental health problems, high number of other problems, the UM's lack of trust towards health care professionals, and cultural differences in health beliefs and language barriers. Referrals to mental health care organizations were often seen as problematic by GPs. To overcome these barriers, GPs provided personalized care as far as possible, referred to other primary care professionals such as social workers or mental health care nurses in their practice, and were a little less restrictive in prescribing psychotropics than guidelines recommended. GPs experienced a variety of barriers in engaging with UMs when identifying or suspecting mental health problems. This explains why there is a gap between the high recognition of mental health problems and the low recording of these problems in general practice files. It is recommended that GPs address mental health problems more actively, strive for continuity of care in order to gain trust of the UMs, and look for opportunities to provide mental care that is accessible and acceptable for UMs.
Directory of Open Access Journals (Sweden)
Marleen H.M. De Moor
2011-11-01
Full Text Available This study examined the heritability of problem drinking and investigated the phenotypic and genetic relationships between problem drinking and personality. It was conducted in a sample of 5,870 twins and siblings and 4,420 additional family members from the Netherlands Twin Register. Data on problem drinking (assessed with the AUDIT and CAGE; 12 items and personality (NEO-FFI; 60 items were collected in 2009/2010 through surveys. Factor analysis on the AUDIT and CAGE items showed that the items clustered on two separate but highly correlated (r=0.74 underlying factors. A higher order factor was extracted that reflected those aspects of problem drinking that are common to the AUDIT and CAGE , which showed a heritability of 40%. The correlations between problem drinking and the five dimensions of personality were small but significant, ranging from 0.06 for Extraversion to -0.12 for Conscientiousness. All personality dimensions (with broad-sense heritabilities between 32% and 55%, and some evidence for non-additive genetic influences were genetically correlated with problem drinking. The genetic correlations were small to modest (between |0.12-0.41|. Future studies with longitudinal data and DNA polymorphisms are needed to determine the biological mechanisms that underlie the genetic link between problem drinking and personality.
Miller-Graff, Laura E; Cater, Åsa Källström; Howell, Kathryn H; Graham-Bermann, Sandra A
2015-10-01
The goal of the current study was to examine the direct relationship between diverse types of childhood victimization and physical health problems in early adulthood, controlling for other common factors that contribute to physical health problems, including psychopathology and health risk behaviors. The associations between types of victimization (e.g., physical assault) and specific health problems (e.g., pain) were also examined. 2500 Swedish young adults reported on their exposure to victimization in childhood and their current mental and physical health as adults. Using multiple regression, results indicated that the amount of childhood victimization was a significant predictor of health problems in adulthood, controlling for the significant negative effects of health risk behaviors and mental health problems on physical health. Logistic regressions indicated that physical assaults and sexual abuse were associated with all types of health problems assessed. Sleep problems were associated with almost all types of victimization history. The long-term effects of childhood victimization on physical health in adulthood are serious and warrant significant attention. Primary care providers should include assessments of past victimization as one way of screening for health risk. Health providers should also consider multiple points of intervention that may help to reduce physical illness. For example, providing a mental health intervention or social service support related to victimization experiences may not only address these difficulties, but also more broadly impact physical health as well. Copyright © 2015 Elsevier Inc. All rights reserved.
libmpdata++ 0.1: a library of parallel MPDATA solvers for systems of generalised transport equations
Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.
2014-11-01
This paper accompanies first release of libmpdata++, a C++ library implementing the Multidimensional Positive-Definite Advection Transport Algorithm (MPDATA). The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include: homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.
libmpdata++ 1.0: a library of parallel MPDATA solvers for systems of generalised transport equations
Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.
2015-04-01
This paper accompanies the first release of libmpdata++, a C++ library implementing the multi-dimensional positive-definite advection transport algorithm (MPDATA) on regular structured grid. The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; a shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.
libmpdata++ 1.0: a library of parallel MPDATA solvers for systems of generalised transport equations
Directory of Open Access Journals (Sweden)
A. Jaruga
2015-04-01
Full Text Available This paper accompanies the first release of libmpdata++, a C++ library implementing the multi-dimensional positive-definite advection transport algorithm (MPDATA on regular structured grid. The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; a shallow-water system compared with analytical solution (originally derived for a 2-D case; and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.
Directory of Open Access Journals (Sweden)
Guo Chun Wen
2009-05-01
Full Text Available This article concerns the oblique derivative problems for second-order quasilinear degenerate equations of mixed type with several characteristic boundaries, which include the Tricomi problem as a special case. First we formulate the problem and obtain estimates of its solutions, then we show the existence of solutions by the successive iterations and the Leray-Schauder theorem. We use a complex analytic method: elliptic complex functions are used in the elliptic domain, and hyperbolic complex functions in the hyperbolic domain, such that second-order equations of mixed type with degenerate curve are reduced to the first order mixed complex equations with singular coefficients. An application of the complex analytic method, solves (1.1 below with $m=n=1$, $a=b=0$, which was posed as an open problem by Rassias.
A Simulated Annealing method to solve a generalized maximal covering location problem
Directory of Open Access Journals (Sweden)
M. Saeed Jabalameli
2011-04-01
Full Text Available The maximal covering location problem (MCLP seeks to locate a predefined number of facilities in order to maximize the number of covered demand points. In a classical sense, MCLP has three main implicit assumptions: all or nothing coverage, individual coverage, and fixed coverage radius. By relaxing these assumptions, three classes of modelling formulations are extended: the gradual cover models, the cooperative cover models, and the variable radius models. In this paper, we develop a special form of MCLP which combines the characteristics of gradual cover models, cooperative cover models, and variable radius models. The proposed problem has many applications such as locating cell phone towers. The model is formulated as a mixed integer non-linear programming (MINLP. In addition, a simulated annealing algorithm is used to solve the resulted problem and the performance of the proposed method is evaluated with a set of randomly generated problems.
Koyanagi, Ai; Stickley, Andrew
2015-12-01
To assess the prevalence of sleep problems and their association with psychotic symptoms using a global database. Community-based cross-sectional study. Data were analyzed from the World Health Organization's World Health Survey (WHS), a population-based survey conducted in 70 countries between 2002 and 2004. 261,547 individuals aged ≥ 18 years from 56 countries. N/A. The presence of psychotic symptoms in the past 12 months was established using 4 questions pertaining to positive symptoms from the psychosis screening module of the Composite International Diagnostic Interview. Sleep problems referred to severe or extreme sleep problems in the past 30 days. Multivariable logistic regression was used to estimate the associations. The overall prevalence of sleep problems was 7.6% and ranged from 1.6% (China) to 18.6% (Morocco). Sleep problems were associated with significantly higher odds for at least one psychotic symptom in the vast majority of countries. In the pooled sample, after adjusting for demographic factors, alcohol consumption, smoking, and chronic medical conditions, having sleep problems resulted in an odds ratio (OR) for at least one psychotic symptom of 2.41 (95% confidence interval [CI] 2.18-2.65). This OR was 1.59 (1.40-1.81) when further adjusted for anxiety and depression. A strong association between sleep problems and psychotic symptoms was observed globally. These results have clinical implications and serve as a basis for future studies to elucidate the causal association between psychotic symptoms and sleep problems. © 2015 Associated Professional Sleep Societies, LLC.
A Mixed Enthalpy-Temperature Finite Element Method For Generalized Phase-Change Problems
DEFF Research Database (Denmark)
krabbenhøft, Kristian; Damkilde, Lars
2003-01-01
In a large number of problems of engineering interest the transition of the material from one phase to another is of vital importance in describing the overall physical behaviour. Common applications include metal casting, freezing and thawing of foodstuffs and other biological materials, ground...... freezing and solar energy storage. The phase-change problem is characterized by an abrupt change in enthalpy per unit temperature in a narrow temperature range around the freezing point....
International Nuclear Information System (INIS)
Mechitoua, N.; Boucker, M.; Lavieville, J.; Pigny, S.; Serre, G.
2003-01-01
Based on experience gained at EDF and Cea, a more general and robust 3-dimensional (3D) multiphase flow solver has been being currently developed for over three years. This solver, based on an elliptic oriented fractional step approach, is able to simulate multicomponent/multiphase flows. Discretization follows a 3D full unstructured finite volume approach, with a collocated arrangement of all variables. The non linear behaviour between pressure and volume fractions and a symmetric treatment of all fields are taken into account in the iterative procedure, within the time step. It greatly enforces the realizability of volume fractions (i.e 0 < α < 1), without artificial numerical needs. Applications to widespread test cases as static sedimentation, water hammer and phase separation are shown to assess the accuracy and the robustness of the flow solver in different flow conditions, encountered in nuclear reactors pipes. (authors)
Hinz, Andreas; Zenger, Markus; Brähler, Elmar; Spitzer, Silvia; Scheuch, Klaus; Seibt, Reingard
2016-08-01
High degrees of premature retirement among teachers warrant investigating the occupational burden and the mental health status of this profession. A sample of 1074 German teachers participated in this study. Two samples of the general population (N = 824 and N = 792) were used as comparison groups. Work distress was assessed with the Effort-Reward-Imbalance questionnaire, and mental health problems were measured with the General Health Questionnaire (GHQ-12). Teachers reported more effort-reward imbalance (M = 0.64) compared with the general population (M = 0.57), and they perceived more mental health problems (GHQ: M = 12.1) than the comparison group (M = 9.5). School type was not associated with work stress and mental health. Teachers with leading functions perceived high degrees of effort and reward, resulting in a moderate effort-reward ratio and no heightened mental health problems. Teachers working full time reported more effort than teachers working part time, but the reward mean values of both groups were similar. This results in a somewhat unfavourable effort-reward ratio of teachers working full time. Moreover, teachers working full time reported more mental health problems. The results support the appropriateness of the effort-reward conception, applied to the profession of teachers. The higher degree of effort-reward imbalance and the level of mental health problems warrant preventive measures. Copyright © 2014 John Wiley & Sons, Ltd. Copyright © 2014 John Wiley & Sons, Ltd.
Directory of Open Access Journals (Sweden)
Milena Netka
2009-01-01
Full Text Available The paper is concerned with weak solutions of a generalized Cauchy problem for a nonlinear system of first order differential functional equations. A theorem on the uniqueness of a solution is proved. Nonlinear estimates of the Perron type are assumed. A method of integral functional inequalities is used.
Bogan, Yu A.
2017-10-01
By means of a new approach, the general boundary value problem for a higher order elliptic equation with two independent variables, and a normal set of boundary conditions and simple complex characteristics is reduced to the Fredholm system of integral equations in a bounded region with a smooth boundary.
Directory of Open Access Journals (Sweden)
V. Rukavishnikov
2014-01-01
Full Text Available The existence and uniqueness of the Rv-generalized solution for the first boundary value problem and a second order elliptic equation with coordinated and uncoordinated degeneracy of input data and with strong singularity solution on all boundary of a two-dimensional domain are established.
Nygaard, Egil; Jensen, Tine K.; Dyb, Grete
2012-01-01
The aim of this study was to evaluate the structure of posttraumatic stress reaction factors and their relation to general mental health problems in Norwegian children exposed to the tsunami on December 26, 2004. A total of 133 children and adolescents (ages 6-17) were interviewed 10 months posttsunami using the UCLA PTSD Reaction Index, and 104…
The Role of General Physical Education in Solution of Health Problem of Russia’s Population
Directory of Open Access Journals (Sweden)
V.P. Lykyanenko
2012-06-01
Full Text Available The educational concept, worked out by the author rests on the ideas of fundamentalization of school physical educational process, basing on the unique general educational potential of this subject, acquiring the character of fundamental, backbone principle of general secondary education, reflecting its essence, goal and objectives in modern society with its core.
Extension problem for generalized multi-monogenic functions in Clifford analysis
International Nuclear Information System (INIS)
Tran Quyet Thang.
1992-10-01
The main purpose of this paper is to extend some properties of multi-monogenic functions, which is a generalization of monogenic functions in higher dimensions, for a class of functions satisfying Vekua-type generalized Cauchy-Riemann equations in Clifford Analysis. It is proved that the Hartogs theorem is valid for these functions. (author). 7 refs
Twenty Years of General Education in China: Progress, Problems, and Solutions
Wang, Hongcai; Xie, Debo
2018-01-01
General education is a subject with rich contents and that is highly contested in the field of higher education studies. It has been highly praised for its core concepts such as broad educational targets, liberating educational objectives, and balanced educational content. Looking back at the course of general education in China over the past 20…
Uncertainty Quantification for Production Navier-Stokes Solvers, Phase II
National Aeronautics and Space Administration — The uncertainty quantification methods developed under this program are designed for use with current state-of-the-art flow solvers developed by and in use at NASA....
Vatankhah, Saeed; Renaut, Rosemary A.; Ardestani, Vahid E.
2018-04-01
We present a fast algorithm for the total variation regularization of the 3-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved better than when using a conventional minimum-structure inversion. The associated problem formulation for the regularization is nonlinear but can be solved using an iteratively reweighted least-squares algorithm. For small-scale problems the regularized least-squares problem at each iteration can be solved using the generalized singular value decomposition. This is not feasible for large-scale, or even moderate-scale, problems. Instead we introduce the use of a randomized generalized singular value decomposition in order to reduce the dimensions of the problem and provide an effective and efficient solution technique. For further efficiency an alternating direction algorithm is used to implement the total variation weighting operator within the iteratively reweighted least-squares algorithm. Presented results for synthetic examples demonstrate that the novel randomized decomposition provides good accuracy for reduced computational and memory demands as compared to use of classical approaches.
Parallelizable approximate solvers for recursions arising in preconditioning
Energy Technology Data Exchange (ETDEWEB)
Shapira, Y. [Israel Inst. of Technology, Haifa (Israel)
1996-12-31
For the recursions used in the Modified Incomplete LU (MILU) preconditioner, namely, the incomplete decomposition, forward elimination and back substitution processes, a parallelizable approximate solver is presented. The present analysis shows that the solutions of the recursions depend only weakly on their initial conditions and may be interpreted to indicate that the inexact solution is close, in some sense, to the exact one. The method is based on a domain decomposition approach, suitable for parallel implementations with message passing architectures. It requires a fixed number of communication steps per preconditioned iteration, independently of the number of subdomains or the size of the problem. The overlapping subdomains are either cubes (suitable for mesh-connected arrays of processors) or constructed by the data-flow rule of the recursions (suitable for line-connected arrays with possibly SIMD or vector processors). Numerical examples show that, in both cases, the overhead in the number of iterations required for convergence of the preconditioned iteration is small relatively to the speed-up gained.
Development and acceleration of unstructured mesh-based cfd solver
Emelyanov, V.; Karpenko, A.; Volkov, K.
2017-06-01
The study was undertaken as part of a larger effort to establish a common computational fluid dynamics (CFD) code for simulation of internal and external flows and involves some basic validation studies. The governing equations are solved with ¦nite volume code on unstructured meshes. The computational procedure involves reconstruction of the solution in each control volume and extrapolation of the unknowns to find the flow variables on the faces of control volume, solution of Riemann problem for each face of the control volume, and evolution of the time step. The nonlinear CFD solver works in an explicit time-marching fashion, based on a three-step Runge-Kutta stepping procedure. Convergence to a steady state is accelerated by the use of geometric technique and by the application of Jacobi preconditioning for high-speed flows, with a separate low Mach number preconditioning method for use with low-speed flows. The CFD code is implemented on graphics processing units (GPUs). Speedup of solution on GPUs with respect to solution on central processing units (CPU) is compared with the use of different meshes and different methods of distribution of input data into blocks. The results obtained provide promising perspective for designing a GPU-based software framework for applications in CFD.
Modifications of steam condensation model implemented in commercial solver
Sova, Libor; Jun, Gukchol; ŠÅ¥astný, Miroslav
2017-09-01
Nucleation theory and droplet grow theory and methods how they are incorporated into numerical solvers are crucial factors for proper wet steam modelling. Unfortunately, they are still covered by cloud of uncertainty and therefore some calibration of these models according to reliable experimental results is important for practical analyses of steam turbines. This article demonstrates how is possible to calibrate wet steam model incorporated into commercial solver ANSYS CFX.
A generalization of Schauder's theorem and its application to Cauchy-Kovalevskaya problem
Directory of Open Access Journals (Sweden)
Oleg Zubelevich
2003-05-01
Full Text Available We extend the classical majorant functions method to a PDE system which right hand side is a mapping of one functional space to another. This extension is based on some generalization of the Schauder fixed point theorem.
SUSY shape-invariant Hamiltonians for the generalized dirac-coulomb problem
International Nuclear Information System (INIS)
Rodrigues, R. de Lima; Vaidya, Arvind Narayan
2007-02-01
A spin 1/2 relativistic particle described by a general potential in terms of the sum of the Coulomb potential with a Lorentz scalar potential is investigated via supersymmetry in quantum mechanics. (author)
2012-03-01
uncertainties. Pioneers in the study of optimal filtering were Norbert Wiener (1894-1964) in the 1940’s [84] and Ruldolf Kalman and Richard Bucy in the 1950...in this research and will be presented more thoroughly in the next subsection. 67 2.4.2 Generalized Polynomial Chaos. In 1938 Norbert Wiener introduced...Generalized Poly- nomial Chaos for Arbitrary Probability Measures”. SIAM Journal on Scientific Computing, 28(3):901–928, 2006. 83. Wiener , Norbert . “The
General linear methods and friends: Toward efficient solutions of multiphysics problems
Sandu, Adrian
2017-07-01
Time dependent multiphysics partial differential equations are of great practical importance as they model diverse phenomena that appear in mechanical and chemical engineering, aeronautics, astrophysics, meteorology and oceanography, financial modeling, environmental sciences, etc. There is no single best time discretization for the complex multiphysics systems of practical interest. We discuss "multimethod" approaches that combine different time steps and discretizations using the rigourous frameworks provided by Partitioned General Linear Methods and Generalize-structure Additive Runge Kutta Methods..
Estimates for a general fractional relaxation equation and application to an inverse source problem
Bazhlekova, Emilia
2018-01-01
A general fractional relaxation equation is considered with a convolutional derivative in time introduced by A. Kochubei (Integr. Equ. Oper. Theory 71 (2011), 583-600). This equation generalizes the single-term, multi-term and distributed-order fractional relaxation equations. The fundamental and the impulse-response solutions are studied in detail. Properties such as analyticity and subordination identities are established and employed in the proof of an upper and a lower bound. The obtained...
International Nuclear Information System (INIS)
Balsara, Dinshaw S.; Amano, Takanobu; Garain, Sudip; Kim, Jinho
2016-01-01
always divergence-free. This collocation also ensures that electromagnetic radiation that is propagating in a vacuum has both electric and magnetic fields that are exactly divergence-free. Coupled relativistic fluid dynamic equations are solved for the positively and negatively charged fluids. The fluids' numerical fluxes also provide a self-consistent current density for the update of the electric field. Our reconstruction strategy ensures that fluid velocities always remain sub-luminal. Our third innovation consists of an efficient design for several popular IMEX schemes so that they provide strong coupling between the finite-volume-based fluid solver and the electromagnetic fields at high order. This innovation makes it possible to efficiently utilize high order IMEX time update methods for stiff source terms in the update of high order finite-volume methods for hyperbolic conservation laws. We also show that this very general innovation should extend seamlessly to Runge–Kutta discontinuous Galerkin methods. The IMEX schemes enable us to use large CFL numbers even in the presence of stiff source terms. Several accuracy analyses are presented showing that our method meets its design accuracy in the MHD limit as well as in the limit of electromagnetic wave propagation. Several stringent test problems are also presented. We also present a relativistic version of the GEM problem, which shows that our algorithm can successfully adapt to challenging problems in high energy astrophysics.
Energy Technology Data Exchange (ETDEWEB)
Balsara, Dinshaw S., E-mail: dbalsara@nd.edu [Physics Department, University of Notre Dame (United States); Amano, Takanobu, E-mail: amano@eps.s.u-tokyo.ac.jp [Department of Earth and Planetary Science, University of Tokyo, Tokyo 113-0033 (Japan); Garain, Sudip, E-mail: sgarain@nd.edu [Physics Department, University of Notre Dame (United States); Kim, Jinho, E-mail: jkim46@nd.edu [Physics Department, University of Notre Dame (United States)
2016-08-01
always divergence-free. This collocation also ensures that electromagnetic radiation that is propagating in a vacuum has both electric and magnetic fields that are exactly divergence-free. Coupled relativistic fluid dynamic equations are solved for the positively and negatively charged fluids. The fluids' numerical fluxes also provide a self-consistent current density for the update of the electric field. Our reconstruction strategy ensures that fluid velocities always remain sub-luminal. Our third innovation consists of an efficient design for several popular IMEX schemes so that they provide strong coupling between the finite-volume-based fluid solver and the electromagnetic fields at high order. This innovation makes it possible to efficiently utilize high order IMEX time update methods for stiff source terms in the update of high order finite-volume methods for hyperbolic conservation laws. We also show that this very general innovation should extend seamlessly to Runge–Kutta discontinuous Galerkin methods. The IMEX schemes enable us to use large CFL numbers even in the presence of stiff source terms. Several accuracy analyses are presented showing that our method meets its design accuracy in the MHD limit as well as in the limit of electromagnetic wave propagation. Several stringent test problems are also presented. We also present a relativistic version of the GEM problem, which shows that our algorithm can successfully adapt to challenging problems in high energy astrophysics.
Tarber, Christel; Frostholm, Lisbeth
2014-01-01
Common mental disorders often go undetected in primary care. Sharpening general practitioners' (GPs') attention to potential signs thereof is therefore crucial. This conversation-analytic study arises from the observation that the consideration of psychological problems in new-concern visits can be achieved by way of 'gradual topic emergence'. This entails that the problem is not presented directly, but adjunct to somatic symptoms, and is hinted at by way of generic, ambiguous complaints, and furthermore by expressions of frustration and uncertainty and talk about lifeworld problems. It is argued that these materials are 'trouble-premonitory, alerting the GP to the presence of an underlying problem that can then be addressed throughfurther inquiry. The patient logic behind this approach is to assure the GP's recipiency and thus ratification of the problem's medical legitimacy. It allows the patient to introduce a potentially delicate problem 'off the record, thus guarding the patient against the loss of face that could resultfrom no uptake by the GP. The results of the study point to the importance of GPs being receptive to such interactional clues to psychological problems provided by patients.
Directory of Open Access Journals (Sweden)
Dieter Egerer Michael
2015-03-01
Full Text Available AIMS - Problem gambling is normally identified by fixed criteria of harm adapted from those of substance abuse and by focusing on the individual gambler. However, rigid definitions neglect institutional variations of gambling practices within different legislative configurations. This study proposes analysing the line between recreational and problem gambling by focusing on gambling behaviour and looking at the corruption of the defining factors of play (Cail-lois, 1958 in three different institutional contexts. DESIGN - A stimulated focus-group method (Reception Analytical Group Interview was applied to seven groups of Finnish and French general practitioners each and three groups of German ones to study the variations of conceptualising the defining factors of play as introduced by Caillois. RESULTS - Corruption of play was distinguished by participants from all three countries as the dividing line between recreational and problem gambling, but cultural variations were found: the French and German GPs emphasised the loss of the exceptionality of gambling, whereas the Finnish GPs highlighted the invasion of the home by online gambling. Furthermore, the Finnish and German participants were more concerned about the use of gambling as an emotional regulator, while French GPs echoed the French medical model in discussing the adrenaline rush of problem gamblers. CONCLUSIONS - Caillois' defining factors of play can be used to distinguish recreational from problem gambling and to offer a more encompassing definition of problem gambling. The perception of the line between recreational and problem gambling also seems to depend on the institutional and cultural context.
Balder, E.J.
1984-01-01
This note presents a new, quick approach to existence results without convexity conditions for optimal control problems with singular components in the sense of [11.], 438–485). Starting from the resolvent kernel representation of the solutions of a linear integral equation, a version of Fatou's
A Mixed Enthalpy-Temperature Finite Element Method For Generalized Phase-Change Problems
DEFF Research Database (Denmark)
krabbenhøft, Kristian; Damkilde, Lars
2003-01-01
In a large number of problems of engineering interest the transition of the material from one phase to another is of vital importance in describing the overall physical behaviour. Common applications include metal casting, freezing and thawing of foodstuffs and other biological materials, ground ...
A note on hierarchical hubbing for a generalization of the VPN problem
Olver, N.K.
2014-01-01
Robust network design refers to a class of optimization problems that occur when designing networks to efficiently handle variable demands. The notion of "hierarchical hubbing" was introduced (in the narrow context of a specific robust network design question), by Olver and Shepherd [2010].
A note on hierarchical hubbing for a generalization of the VPN problem
Olver, Neil
2016-01-01
Robust network design refers to a class of optimization problems that occur when designing networks to efficiently handle variable demands. In this context, Fréchette et al. (2013) recently explored hierarchical hubbing: a routing strategy involving a multiplicity of "hubs" connected to terminals
A note on hierarchical hubbing for a generalization of the VPN problem
N.K. Olver (Neil)
2016-01-01
textabstractRobust network design refers to a class of optimization problems that occur when designing networks to efficiently handle variable demands. In this context, Fréchette et al. (2013) recently explored hierarchical hubbing: a routing strategy involving a multiplicity of "hubs" connected to
A note on hierarchical hubbing for a generalization of the VPN problem
N.K. Olver (Neil)
2014-01-01
htmlabstractRobust network design refers to a class of optimization problems that occur when designing networks to efficiently handle variable demands. The notion of "hierarchical hubbing" was introduced (in the narrow context of a specific robust network design question), by Olver and Shepherd
The H2 control problem: a general transfer-function solution
Czech Academy of Sciences Publication Activity Database
Kučera, Vladimír
2007-01-01
Roč. 80, č. 5 (2007), s. 800-815 ISSN 0020-7179 Institutional research plan: CEZ:AV0Z10750506 Keywords : linear system * polynomial design methods * H_2 control problem Subject RIV: BC - Control Systems Theory Impact factor: 0.861, year: 2007
Bazo, Plácido; Rodríguez, Romén; Fumero, Dácil
2016-01-01
In this paper, we will introduce an innovative software platform that can be especially useful in a Content and Language Integrated Learning (CLIL) context. This tool is called Vocabulary Notebook, and has been developed to solve all the problems that traditional (paper) vocabulary notebooks have. This tool keeps focus on the personalisation of…
DEFF Research Database (Denmark)
Bendtsen, Claus; Nielsen, Ole Holm; Hansen, Lars Bruno
2001-01-01
The quantum mechanical ground state of electrons is described by Density Functional Theory, which leads to large minimization problems. An efficient minimization method uses a self-consistent field (SCF) solution of large eigenvalue problems. The iterative Davidson algorithm is often used, and we...... works well on both serial and parallel computers, and good scalability of the algorithm is obtained. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.......The quantum mechanical ground state of electrons is described by Density Functional Theory, which leads to large minimization problems. An efficient minimization method uses a self-consistent field (SCF) solution of large eigenvalue problems. The iterative Davidson algorithm is often used, and we...... propose a new algorithm of this kind which is well suited for the SCF method, since the accuracy of the eigensolution is gradually improved along with the outer SCF-iterations. Best efficiency is obtained for small-block-size iterations, and the algorithm is highly memory efficient. The implementation...
Foot problems in children presented to the general practitioner: a comparison between 1987 and 2001.
Krul, M.; Wouden, J.C. van der; Schellevis, F.G.; Suijlekom-Smit, L.W.A. van; Koes, B.W.
2009-01-01
BACKGROUND: In recent decades, studies on the management of common foot problems in children have suggested that in many cases, there is no indication for treatment. It is not known whether these studies have changed daily practice. OBJECTIVE: Our aim was to establish and compare incidence and
Jensen, Natasja Koitzsch; Norredam, Marie; Priebe, Stefan; Krasnik, Allan
2013-01-28
Refugees are a particularly vulnerable group in relation to the development of mental illness and many may have been subjected to torture or other traumatic experiences. General practitioners are gatekeepers for access to several parts of the psychiatric system and knowledge of their patients' refugee background is crucial to secure adequate care. The aim of this study is to investigate how general practitioners experience providing care to refugees with mental health problems. The study was conducted as part of an EU project on European Best Practices in Access, Quality and Appropriateness of Health Services for Immigrants in Europe (EUGATE). Semi-structured interviews were carried out with nine general practitioners in the vicinity of Copenhagen purposively selected from areas with a high proportion of immigrants. The analysis of the interviews is inspired by qualitative content analysis. One of the main themes identified in the analysis is communication. This includes the use of professional interpreters and that communication entails more than sharing a common language. Quality of care is another theme that emerges and includes awareness of possible trauma history, limited possibilities for refugees to participate in certain treatments due to language barriers and feelings of hopelessness in the general practitioners. The general practitioners may also choose different referral pathways for refugees and they report that their patients lack understanding regarding the differences between psychological problems and physical symptoms. General practitioners experience that providing care to refugees differs from providing care for patients from the majority population. The different strategies employed by the general practitioners in the health care treatment of refugees may be the result of the great diversity in the organisation of general practice in Denmark and the lack of a national strategy in the health care management of refugees. The findings from this
Common mental health problems in immigrants and refugees: general approach in primary care.
Kirmayer, Laurence J; Narasiah, Lavanya; Munoz, Marie; Rashid, Meb; Ryder, Andrew G; Guzder, Jaswant; Hassan, Ghayda; Rousseau, Cécile; Pottie, Kevin
2011-09-06
Recognizing and appropriately treating mental health problems among new immigrants and refugees in primary care poses a challenge because of differences in language and culture and because of specific stressors associated with migration and resettlement. We aimed to identify risk factors and strategies in the approach to mental health assessment and to prevention and treatment of common mental health problems for immigrants in primary care. We searched and compiled literature on prevalence and risk factors for common mental health problems related to migration, the effect of cultural influences on health and illness, and clinical strategies to improve mental health care for immigrants and refugees. Publications were selected on the basis of relevance, use of recent data and quality in consultation with experts in immigrant and refugee mental health. The migration trajectory can be divided into three components: premigration, migration and postmigration resettlement. Each phase is associated with specific risks and exposures. The prevalence of specific types of mental health problems is influenced by the nature of the migration experience, in terms of adversity experienced before, during and after resettlement. Specific challenges in migrant mental health include communication difficulties because of language and cultural differences; the effect of cultural shaping of symptoms and illness behaviour on diagnosis, coping and treatment; differences in family structure and process affecting adaptation, acculturation and intergenerational conflict; and aspects of acceptance by the receiving society that affect employment, social status and integration. These issues can be addressed through specific inquiry, the use of trained interpreters and culture brokers, meetings with families, and consultation with community organizations. Systematic inquiry into patients' migration trajectory and subsequent follow-up on culturally appropriate indicators of social, vocational and
Common mental health problems in immigrants and refugees: general approach in primary care
Kirmayer, Laurence J.; Narasiah, Lavanya; Munoz, Marie; Rashid, Meb; Ryder, Andrew G.; Guzder, Jaswant; Hassan, Ghayda; Rousseau, Cécile; Pottie, Kevin
2011-01-01
Background: Recognizing and appropriately treating mental health problems among new immigrants and refugees in primary care poses a challenge because of differences in language and culture and because of specific stressors associated with migration and resettlement. We aimed to identify risk factors and strategies in the approach to mental health assessment and to prevention and treatment of common mental health problems for immigrants in primary care. Methods: We searched and compiled literature on prevalence and risk factors for common mental health problems related to migration, the effect of cultural influences on health and illness, and clinical strategies to improve mental health care for immigrants and refugees. Publications were selected on the basis of relevance, use of recent data and quality in consultation with experts in immigrant and refugee mental health. Results: The migration trajectory can be divided into three components: premigration, migration and postmigration resettlement. Each phase is associated with specific risks and exposures. The prevalence of specific types of mental health problems is influenced by the nature of the migration experience, in terms of adversity experienced before, during and after resettlement. Specific challenges in migrant mental health include communication difficulties because of language and cultural differences; the effect of cultural shaping of symptoms and illness behaviour on diagnosis, coping and treatment; differences in family structure and process affecting adaptation, acculturation and intergenerational conflict; and aspects of acceptance by the receiving society that affect employment, social status and integration. These issues can be addressed through specific inquiry, the use of trained interpreters and culture brokers, meetings with families, and consultation with community organizations. Interpretation: Systematic inquiry into patients’ migration trajectory and subsequent follow-up on culturally
Yu, Peicheng; Li, Fei; Dalichaouch, Thamine; Fiuza, Frederico; Decyk, Viktor; Davidson, Asher; Tableman, Adam; An, Weiming; Tsung, Frank; Fonseca, Ricardo; Lu, Wei; Vieira, Jorge; Silva, Luis; Mori, Warren
2016-10-01
we present a finite-difference-time-domain (FDTD) Maxwell solver for the particle-in-cell (PIC) algorithm, which is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or non-neutral) relativistically drifts on a grid when using the PIC algorithm. We control the EM dispersion curve in the direction of the plasma drift of a FDTD Maxwell solver by using a customized higher order finite difference operator for the spatial derivative along the direction of the drift (1& circ; direction). We show that this eliminates the main NCI modes with moderate | k1 | , while keeps additional main NCI modes well outside the range of physical interest with higher | k1 | . These main NCI modes can be easily filtered out along with first spatial aliasing NCI modes which are also at the edge of the fundamental Brillouin zone. The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along 1& circ; which typically has many more cells than other directions for the problems of interest.
Application of a fast Newton-Krylov solver for equilibrium simulations of phosphorus and oxygen
Fu, Weiwei; Primeau, François
2017-11-01
Model drift due to inadequate spinup is a serious problem that complicates the interpretation of climate change simulations. Even after a 300 year spinup we show that solutions are not only still drifting but often drifting away from their eventual equilibrium over large parts of the ocean. Here we present a Newton-Krylov solver for computing cyclostationary equilibrium solutions of a biogeochemical model for the cycling of phosphorus and oxygen. In addition to using previously developed preconditioning strategies - time-averaging and coarse-graining the Jacobian matrix - we also introduce a new strategy: the adiabatic elimination of a fast variable (particulate organic phosphorus) by slaving it to a slow variable (dissolved inorganic phosphorus). We use transport matrices derived from the Community Earth System Model (CESM) with a nominal horizontal resolution of 1° × 1° and 60 vertical levels to implement and test the solver. We find that the new solver obtains seasonally-varying equilibrium solutions with no visible drift using no more than 80 simulation years.
International Nuclear Information System (INIS)
Boucker, M.; Laviaville, J.; Martin, A.; Bechaud, C.; Bestion, D.; Coste, P.
2004-01-01
The objective of this communication is to present some preliminary applications to pressurized thermal shock (PTS) investigations of the CFD (Computational Fluid Dynamics) two-phase flow solver of the new NEPTUNE thermal-hydraulics platform. In the framework of plant life extension, the Reactor Pressure Vessel (RPV) integrity is a major concern, and an important part of RPV integrity assessment is related to PTS analysis. In the case where the cold legs are partially filled with steam, it becomes a two-phase problem and new important effects occur, such as condensation due to the Emergency Core Cooling (ECC) injections of sub-cooled water. Thus, an advanced prediction of RPV thermal loading during these transients requires sophisticated two-phase, local scale, 3-dimensional codes. In that purpose, a program has been set up to extend the capabilities of the NEPTUNE two-phase CFD solver. A simple set of turbulence and condensation model for free surface steam-water flow has been tested in simulation of an ECC high pressure injection representing facility, using a full 3-dimensional mesh and the new NEPTUNE solver. Encouraging results have been obtained but it should be noticed that several sources of error can compensate for one another. Nevertheless, the computation presented here allows to be reasonable confident in the use of two-phase CFD in order to carry out refined analysis of two-phase PTS scenarios within the next years
Directory of Open Access Journals (Sweden)
Zhaoli Ma
2012-01-01
Full Text Available We introduce an iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of fixed points for countable families of total quasi-ϕ-asymptotically nonexpansive mappings in Banach spaces. We prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm in an uniformly smooth and strictly convex Banach space which also enjoys the Kadec-Klee property. The results presented in this paper improve and extend some recent corresponding results.
Analytic theory of curvature effects for wave problems with general boundary conditions
DEFF Research Database (Denmark)
Willatzen, Morten; Gravesen, Jens; Voon, L. C. Lew Yan
2010-01-01
A formalism based on a combination of differential geometry and perturbation theory is used to obtain analytic expressions for confined eigenmode changes due to general curvature effects. In cases of circular-shaped and helix-shaped structures, where alternative analytic solutions can be found......, the perturbative solution is shown to yield the same result. The present technique allows the generalization of earlier results to arbitrary boundary conditions. The power of the method is illustrated using examples based on Maxwell’s and Schrödinger’s equations for applications in photonics and nanoelectronics....
Indian Academy of Sciences (India)
Page S20: NMR compound 4i. Page S22: NMR compound 4j. General: Chemicals were purchased from Fluka, Merck and Aldrich Chemical Companies. All the products were characterized by comparison of their IR, 1H NMR and 13C NMR spectroscopic data and their melting points with reported values. General procedure ...
Pannier, S.; Waurick, M.; Graf, W.; Kaliske, M.
2013-05-01
The present paper is about data corrupted by both aleatoric and epistemic uncertainty. A unification of randomness, which represents aleatoric uncertainty, and fuzziness, which represents epistemic uncertainty, is dicussed in detail. As a result, the main uncertainty characteristics, i.e., variability, incompleteness and imprecision, can be described. With a focus on engineering problems the aim is to bridge the imprecision of data to the decision making process. Suitable fields of applications are highlighted; remarks on the numerical treatment are given.
ABAQUS-EPGEN: a general-purpose finite element code. Volume 3. Example problems manual
International Nuclear Information System (INIS)
Hibbitt, H.D.; Karlsson, B.I.; Sorensen, E.P.
1983-03-01
This volume is the Example and Verification Problems Manual for ABAQUS/EPGEN. Companion volumes are the User's, Theory and Systems Manuals. This volume contains two major parts. The bulk of the manual (Sections 1-8) contains worked examples that are discussed in detail, while Appendix A documents a large set of basic verification cases that provide the fundamental check of the elements in the code. The examples in Sections 1-8 illustrate and verify significant aspects of the program's capability. Most of these problems provide verification, but they have also been chosen to allow discussion of modeling and analysis techniques. Appendix A contains basic verification cases. Each of these cases verifies one element in the program's library. The verification consists of applying all possible load or flux types (including thermal loading of stress elements), and all possible foundation or film/radiation conditions, and checking the resulting force and stress solutions or flux and temperature results. This manual provides program verification. All of the problems described in the manual are run and the results checked, for each release of the program, and these verification results are made available
Koka, Betty E; Deane, Frank P; Lyons, Geoffrey Cb; Lambert, Gordon
2014-11-01
Papua New Guinea is a developing country with limited resources for specialist mental health services. Little is known about the mental health and treatment services of Papua New Guinea. The aim of this study was to clarify the presenting mental health problems encountered by Papua New Guinean health workers and the common treatment approaches used. A total of 203 Papua New Guinean health workers completed a retrospective quantitative survey about their three most recent mental health patients. The survey asked about presenting symptomatology, diagnoses (including culture-bound diagnoses) and treatment approaches. The major presenting mental health problems for males included schizophrenia, substance use disorder, sorcery and spirit possession. Depression was the most common diagnoses for women, followed by sorcery and somatisation. Over 65% of patients were prescribed psychotropic medication, over 50% received some form of psychological intervention and 28% were receiving traditional treatments. Somatic symptoms are common among both male and female Papua New Guineans; however, males may be more likely to present with psychotic symptoms and females with mood-related problems. Schizophrenia and depression are commonly identified with substance use disorder more problematic among males. Culture-specific explanations and treatment are commonly used. © The Author(s) 2013.
Sobolev spaces, their generalizations and elliptic problems in smooth and Lipschitz domains
Agranovich, Mikhail S
2015-01-01
This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic partial differential equations. Its main focus is on problems in non-smooth (Lipschitz) domains for strongly elliptic systems. The author, who is a prominent expert in the theory of linear partial differential equations, spectral theory, and pseudodifferential operators, has included his own very recent findings in the present book. The book is well suited as a modern graduate textbook, utilizing a thorough and clear format that strikes a good balance between the choice of material and the style of exposition. It can be used both as an introduction to recent advances in elliptic equations and boundary value problems, and as a valuable survey and reference work. It also includes a good deal of new and extremely useful material not available in standard textbooks to date. Graduate and post-graduate student...
The Problems and Prospects of General Education in an Information Society
Rusetskii, V. F.
2014-01-01
Russian education faces a difficult task in defining what its education system needs to be achieving to maximize its effectiveness in a changing society. Both educational officials and the general public need to be more aware of this challenge and how to deal with it. [This article was translated by Kim Braithwaite.
Children with Generalized Anxiety Disorder Do Not Have Peer Problems, Just Fewer Friends
Scharfstein, Lindsay; Alfano, Candice; Beidel, Deborah; Wong, Nina
2011-01-01
A common assumption is that all youth with anxiety disorders (AD) experience impaired peer relationships relative to healthy control children. Social impairments have been identified among youth with certain AD (e.g., social anxiety disorder; SAD), but less is known about the peer relationships of children with generalized anxiety disorder (GAD).…
Czech Academy of Sciences Publication Activity Database
Daněk, Josef; Hlaváček, Ivan; Nedoma, Jiří
2005-01-01
Roč. 68, č. 3 (2005), s. 271-300 ISSN 0378-4754 R&D Projects: GA MPO FT-TA/087 Keywords : domain decomposition * unilateral contact * Tresca's friction model * formulation in displacements * linear finite elements Subject RIV: BA - General Mathematics Impact factor: 0.554, year: 2005
Navajo Community College Funding Problems. Report by the Comptroller General of the United States.
Comptroller General of the U.S., Washington, DC.
Funding for the Navajo Community College was reviewed by the Comptroller General of the United States to determine if the Bureau of Indian Affairs' (BIA) regulations and method of computing full-time equivalent enrollments were consistent with the Tribally Controlled Community College Assistance Act of 1978 (P.L. 95-471). The investigation…