Fast Solvers for Dense Linear Systems
Energy Technology Data Exchange (ETDEWEB)
Kauers, Manuel [Research Institute for Symbolic Computation (RISC), Altenbergerstrasse 69, A4040 Linz (Austria)
2008-10-15
It appears that large scale calculations in particle physics often require to solve systems of linear equations with rational number coefficients exactly. If classical Gaussian elimination is applied to a dense system, the time needed to solve such a system grows exponentially in the size of the system. In this tutorial paper, we present a standard technique from computer algebra that avoids this exponential growth: homomorphic images. Using this technique, big dense linear systems can be solved in a much more reasonable time than using Gaussian elimination over the rationals.
Application of Nearly Linear Solvers to Electric Power System Computation
Grant, Lisa L.
To meet the future needs of the electric power system, improvements need to be made in the areas of power system algorithms, simulation, and modeling, specifically to achieve a time frame that is useful to industry. If power system time-domain simulations could run in real-time, then system operators would have situational awareness to implement online control and avoid cascading failures, significantly improving power system reliability. Several power system applications rely on the solution of a very large linear system. As the demands on power systems continue to grow, there is a greater computational complexity involved in solving these large linear systems within reasonable time. This project expands on the current work in fast linear solvers, developed for solving symmetric and diagonally dominant linear systems, in order to produce power system specific methods that can be solved in nearly-linear run times. The work explores a new theoretical method that is based on ideas in graph theory and combinatorics. The technique builds a chain of progressively smaller approximate systems with preconditioners based on the system's low stretch spanning tree. The method is compared to traditional linear solvers and shown to reduce the time and iterations required for an accurate solution, especially as the system size increases. A simulation validation is performed, comparing the solution capabilities of the chain method to LU factorization, which is the standard linear solver for power flow. The chain method was successfully demonstrated to produce accurate solutions for power flow simulation on a number of IEEE test cases, and a discussion on how to further improve the method's speed and accuracy is included.
Linear optical response of finite systems using multishift linear system solvers
Energy Technology Data Exchange (ETDEWEB)
Hübener, Hannes; Giustino, Feliciano [Department of Materials, University of Oxford, Oxford OX1 3PH (United Kingdom)
2014-07-28
We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.
A parallel solver for huge dense linear systems
Badia, J. M.; Movilla, J. L.; Climente, J. I.; Castillo, M.; Marqués, M.; Mayo, R.; Quintana-Ortí, E. S.; Planelles, J.
2011-11-01
HDSS (Huge Dense Linear System Solver) is a Fortran Application Programming Interface (API) to facilitate the parallel solution of very large dense systems to scientists and engineers. The API makes use of parallelism to yield an efficient solution of the systems on a wide range of parallel platforms, from clusters of processors to massively parallel multiprocessors. It exploits out-of-core strategies to leverage the secondary memory in order to solve huge linear systems O(100.000). The API is based on the parallel linear algebra library PLAPACK, and on its Out-Of-Core (OOC) extension POOCLAPACK. Both PLAPACK and POOCLAPACK use the Message Passing Interface (MPI) as the communication layer and BLAS to perform the local matrix operations. The API provides a friendly interface to the users, hiding almost all the technical aspects related to the parallel execution of the code and the use of the secondary memory to solve the systems. In particular, the API can automatically select the best way to store and solve the systems, depending of the dimension of the system, the number of processes and the main memory of the platform. Experimental results on several parallel platforms report high performance, reaching more than 1 TFLOP with 64 cores to solve a system with more than 200 000 equations and more than 10 000 right-hand side vectors. New version program summaryProgram title: Huge Dense System Solver (HDSS) Catalogue identifier: AEHU_v1_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHU_v1_1.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 87 062 No. of bytes in distributed program, including test data, etc.: 1 069 110 Distribution format: tar.gz Programming language: Fortran90, C Computer: Parallel architectures: multiprocessors, computer clusters Operating system
Sparse Linear Solver for Power System Analysis Using FPGA
National Research Council Canada - National Science Library
Johnson, J. R; Nagvajara, P; Nwankpa, C
2005-01-01
.... Numerical solution to load flow equations are typically computed using Newton-Raphson iteration, and the most time consuming component of the computation is the solution of a sparse linear system...
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.
IMPROVING THE PERFORMANCE OF THE LINEAR SYSTEMS SOLVERS USING CUDA
Directory of Open Access Journals (Sweden)
BOGDAN OANCEA
2012-05-01
Full Text Available Parallel computing can offer an enormous advantage regarding the performance for very large applications in almost any field: scientific computing, computer vision, databases, data mining, and economics. GPUs are high performance many-core processors that can obtain very high FLOP rates. Since the first idea of using GPU for general purpose computing, things have evolved and now there are several approaches to GPU programming: CUDA from NVIDIA and Stream from AMD. CUDA is now a popular programming model for general purpose computations on GPU for C/C++ programmers. A great number of applications were ported to CUDA programming model and they obtain speedups of orders of magnitude comparing to optimized CPU implementations. In this paper we present an implementation of a library for solving linear systems using the CCUDA framework. We present the results of performance tests and show that using GPU one can obtain speedups of about of approximately 80 times comparing with a CPU implementation.
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.
Accelerated Cyclic Reduction: A Distributed-Memory Fast Solver for Structured Linear Systems
Chá vez, Gustavo; Turkiyyah, George; Zampini, Stefano; Ltaief, Hatem; Keyes, David E.
2017-01-01
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.
Balancing Energy and Performance in Dense Linear System Solvers for Hybrid ARM+GPU platforms
Directory of Open Access Journals (Sweden)
Juan P. Silva
2016-04-01
Full Text Available The high performance computing community has traditionally focused uniquely on the reduction of execution time, though in the last years, the optimization of energy consumption has become a main issue. A reduction of energy usage without a degradation of performance requires the adoption of energy-efficient hardware platforms accompanied by the development of energy-aware algorithms and computational kernels. The solution of linear systems is a key operation for many scientific and engineering problems. Its relevance has motivated an important amount of work, and consequently, it is possible to find high performance solvers for a wide variety of hardware platforms. In this work, we aim to develop a high performance and energy-efficient linear system solver. In particular, we develop two solvers for a low-power CPU-GPU platform, the NVIDIA Jetson TK1. These solvers implement the Gauss-Huard algorithm yielding an efficient usage of the target hardware as well as an efficient memory access. The experimental evaluation shows that the novel proposal reports important savings in both time and energy-consumption when compared with the state-of-the-art solvers of the platform.
Linear systems solvers - recent developments and implications for lattice computations
International Nuclear Information System (INIS)
Frommer, A.
1996-01-01
We review the numerical analysis' understanding of Krylov subspace methods for solving (non-hermitian) systems of equations and discuss its implications for lattice gauge theory computations using the example of the Wilson fermion matrix. Our thesis is that mature methods like QMR, BiCGStab or restarted GMRES are close to optimal for the Wilson fermion matrix. Consequently, preconditioning appears to be the crucial issue for further improvements. (orig.)
Improving the energy efficiency of sparse linear system solvers on multicore and manycore systems.
Anzt, H; Quintana-Ortí, E S
2014-06-28
While most recent breakthroughs in scientific research rely on complex simulations carried out in large-scale supercomputers, the power draft and energy spent for this purpose is increasingly becoming a limiting factor to this trend. In this paper, we provide an overview of the current status in energy-efficient scientific computing by reviewing different technologies used to monitor power draft as well as power- and energy-saving mechanisms available in commodity hardware. For the particular domain of sparse linear algebra, we analyse the energy efficiency of a broad collection of hardware architectures and investigate how algorithmic and implementation modifications can improve the energy performance of sparse linear system solvers, without negatively impacting their performance. © 2014 The Author(s) Published by the Royal Society. All rights reserved.
Wu, Jiayang; Cao, Pan; Hu, Xiaofeng; Jiang, Xinhong; Pan, Ting; Yang, Yuxing; Qiu, Ciyuan; Tremblay, Christine; Su, Yikai
2014-10-20
We propose and experimentally demonstrate an all-optical temporal differential-equation solver that can be used to solve ordinary differential equations (ODEs) characterizing general linear time-invariant (LTI) systems. The photonic device implemented by an add-drop microring resonator (MRR) with two tunable interferometric couplers is monolithically integrated on a silicon-on-insulator (SOI) wafer with a compact footprint of ~60 μm × 120 μm. By thermally tuning the phase shifts along the bus arms of the two interferometric couplers, the proposed device is capable of solving first-order ODEs with two variable coefficients. The operation principle is theoretically analyzed, and system testing of solving ODE with tunable coefficients is carried out for 10-Gb/s optical Gaussian-like pulses. The experimental results verify the effectiveness of the fabricated device as a tunable photonic ODE solver.
ALPS - A LINEAR PROGRAM SOLVER
Viterna, L. A.
1994-01-01
Linear programming is a widely-used engineering and management tool. Scheduling, resource allocation, and production planning are all well-known applications of linear programs (LP's). Most LP's are too large to be solved by hand, so over the decades many computer codes for solving LP's have been developed. ALPS, A Linear Program Solver, is a full-featured LP analysis program. ALPS can solve plain linear programs as well as more complicated mixed integer and pure integer programs. ALPS also contains an efficient solution technique for pure binary (0-1 integer) programs. One of the many weaknesses of LP solvers is the lack of interaction with the user. ALPS is a menu-driven program with no special commands or keywords to learn. In addition, ALPS contains a full-screen editor to enter and maintain the LP formulation. These formulations can be written to and read from plain ASCII files for portability. For those less experienced in LP formulation, ALPS contains a problem "parser" which checks the formulation for errors. ALPS creates fully formatted, readable reports that can be sent to a printer or output file. ALPS is written entirely in IBM's APL2/PC product, Version 1.01. The APL2 workspace containing all the ALPS code can be run on any APL2/PC system (AT or 386). On a 32-bit system, this configuration can take advantage of all extended memory. The user can also examine and modify the ALPS code. The APL2 workspace has also been "packed" to be run on any DOS system (without APL2) as a stand-alone "EXE" file, but has limited memory capacity on a 640K system. A numeric coprocessor (80X87) is optional but recommended. The standard distribution medium for ALPS is a 5.25 inch 360K MS-DOS format diskette. IBM, IBM PC and IBM APL2 are registered trademarks of International Business Machines Corporation. MS-DOS is a registered trademark of Microsoft Corporation.
Directory of Open Access Journals (Sweden)
Syafii
2017-03-01
Full Text Available This paper presents the assessment of fast decoupled load flow computation using three linear system solver scheme. The full matrix version of the fast decoupled load flow based on XB methods used in this study. The numerical investigations are carried out on the small and large test systems. The execution time of small system such as IEEE 14, 30, and 57 are very fast, therefore the computation time can not be compared for these cases. Another cases IEEE 118, 300 and TNB 664 produced significant execution speedup. The superLU factorization sparse matrix solver has best performance and speedup of load flow solution as well as in contigency analysis. The invers full matrix solver can solved only for IEEE 118 bus test system in 3.715 second and for another cases take too long time. However for superLU factorization linear solver can solved all of test system in 7.832 second for a largest of test system. Therefore the superLU factorization linear solver can be a viable alternative applied in contingency analysis.
Ferencz, Donald C.; Viterna, Larry A.
1991-01-01
ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.
GPU TECHNOLOGIES EMBODIED IN PARALLEL SOLVERS OF LINEAR ALGEBRAIC EQUATION SYSTEMS
Directory of Open Access Journals (Sweden)
Sidorov Alexander Vladimirovich
2012-10-01
Full Text Available The author reviews existing shareware solvers that are operated by graphical computer devices. The purpose of this review is to explore the opportunities and limitations of the above parallel solvers applicable for resolution of linear algebraic problems that arise at Research and Educational Centre of Computer Modeling at MSUCE, and Research and Engineering Centre STADYO. The author has explored new applications of the GPU in the PETSc suite and compared them with the results generated absent of the GPU. The research is performed within the CUSP library developed to resolve the problems of linear algebra through the application of GPU. The author has also reviewed the new MAGMA project which is analogous to LAPACK for the GPU.
SuperLU{_}DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
Energy Technology Data Exchange (ETDEWEB)
Li, Xiaoye S.; Demmel, James W.
2002-03-27
In this paper, we present the main algorithmic features in the software package SuperLU{_}DIST, a distributed-memory sparse direct solver for large sets of linear equations. We give in detail our parallelization strategies, with focus on scalability issues, and demonstrate the parallel performance and scalability on current machines. The solver is based on sparse Gaussian elimination, with an innovative static pivoting strategy proposed earlier by the authors. The main advantage of static pivoting over classical partial pivoting is that it permits a priori determination of data structures and communication pattern for sparse Gaussian elimination, which makes it more scalable on distributed memory machines. Based on this a priori knowledge, we designed highly parallel and scalable algorithms for both LU decomposition and triangular solve and we show that they are suitable for large-scale distributed memory machines.
PCX, Interior-Point Linear Programming Solver
International Nuclear Information System (INIS)
Czyzyk, J.
2004-01-01
1 - Description of program or function: PCX solves linear programming problems using the Mehrota predictor-corrector interior-point algorithm. PCX can be called as a subroutine or used in stand-alone mode, with data supplied from an MPS file. The software incorporates modules that can be used separately from the linear programming solver, including a pre-solve routine and data structure definitions. 2 - Methods: The Mehrota predictor-corrector method is a primal-dual interior-point method for linear programming. The starting point is determined from a modified least squares heuristic. Linear systems of equations are solved at each interior-point iteration via a sparse Cholesky algorithm native to the code. A pre-solver is incorporated in the code to eliminate inefficiencies in the user's formulation of the problem. 3 - Restriction on the complexity of the problem: There are no size limitations built into the program. The size of problem solved is limited by RAM and swap space on the user's computer
Comparison of open-source linear programming solvers.
Energy Technology Data Exchange (ETDEWEB)
Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin David.; Jones, Katherine A.; Martin, Nathaniel; Detry, Richard Joseph
2013-10-01
When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modular In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.
GPU acceleration of preconditioned solvers for ill-conditioned linear systems
Gupta, R.
2015-01-01
In this work we study the implementations of deflation and preconditioning techniques for solving ill-conditioned linear systems using iterative methods. Solving such systems can be a time-consuming process because of the jumps in the coefficients due to large difference in material properties. We
Development of an efficient iterative solver for linear systems in FE structural analysis
International Nuclear Information System (INIS)
Saint-Georges, P.; Warzee, G.; Beauwens, R.; Notay, Y.
1993-01-01
The preconditioned conjugate gradient is a well-known and powerful method to solve sparse symmetric positive definite systems of linear equations. Such systems are generated by the finite element discretization in structural analysis but users of finite element in this context generally still rely on direct methods. It is our purpose in the present paper to highlight the improvement brought forward by some new preconditioning techniques and show that the preconditioned conjugate gradient method is more performant than any direct method. (author)
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)
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.
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.
Simplified Linear Equation Solvers users manual
Energy Technology Data Exchange (ETDEWEB)
Gropp, W. [Argonne National Lab., IL (United States); Smith, B. [California Univ., Los Angeles, CA (United States)
1993-02-01
The solution of large sparse systems of linear equations is at the heart of many algorithms in scientific computing. The SLES package is a set of easy-to-use yet powerful and extensible routines for solving large sparse linear systems. The design of the package allows new techniques to be used in existing applications without any source code changes in the applications.
Application of alternating decision trees in selecting sparse linear solvers
Bhowmick, Sanjukta; Eijkhout, Victor; Freund, Yoav; Fuentes, Erika; Keyes, David E.
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.
Menu-Driven Solver Of Linear-Programming Problems
Viterna, L. A.; Ferencz, D.
1992-01-01
Program assists inexperienced user in formulating linear-programming problems. A Linear Program Solver (ALPS) computer program is full-featured LP analysis program. Solves plain linear-programming problems as well as more-complicated mixed-integer and pure-integer programs. Also contains efficient technique for solution of purely binary linear-programming problems. Written entirely in IBM's APL2/PC software, Version 1.01. Packed program contains licensed material, property of IBM (copyright 1988, all rights reserved).
Energy Technology Data Exchange (ETDEWEB)
Alleon, G. [EADS-CCR, 31 - Blagnac (France); Carpentieri, B.; Du, I.S.; Giraud, L.; Langou, J.; Martin, E. [Cerfacs, 31 - Toulouse (France)
2003-07-01
The boundary element method has become a popular tool for the solution of Maxwell's equations in electromagnetism. It discretizes only the surface of the radiating object and gives rise to linear systems that are smaller in size compared to those arising from finite element or finite difference discretizations. However, these systems are prohibitively demanding in terms of memory for direct methods and challenging to solve by iterative methods. In this paper we address the iterative solution via preconditioned Krylov methods of electromagnetic scattering problems expressed in an integral formulation, with main focus on the design of the pre-conditioner. We consider an approximate inverse method based on the Frobenius-norm minimization with a pattern prescribed in advance. The pre-conditioner is constructed from a sparse approximation of the dense coefficient matrix, and the patterns both for the pre-conditioner and for the coefficient matrix are computed a priori using geometric information from the mesh. We describe the implementation of the approximate inverse in an out-of-core parallel code that uses multipole techniques for the matrix-vector products, and show results on the numerical scalability of our method on systems of size up to one million unknowns. We propose an embedded iterative scheme based on the GMRES method and combined with multipole techniques, aimed at improving the robustness of the approximate inverse for large problems. We prove by numerical experiments that the proposed scheme enables the solution of very large and difficult problems efficiently at reduced computational and memory cost. Finally we perform a preliminary study on a spectral two-level pre-conditioner to enhance the robustness of our method. This numerical technique exploits spectral information of the preconditioned systems to build a low rank-update of the pre-conditioner. (authors)
International Nuclear Information System (INIS)
Alleon, G.; Carpentieri, B.; Du, I.S.; Giraud, L.; Langou, J.; Martin, E.
2003-01-01
The boundary element method has become a popular tool for the solution of Maxwell's equations in electromagnetism. It discretizes only the surface of the radiating object and gives rise to linear systems that are smaller in size compared to those arising from finite element or finite difference discretizations. However, these systems are prohibitively demanding in terms of memory for direct methods and challenging to solve by iterative methods. In this paper we address the iterative solution via preconditioned Krylov methods of electromagnetic scattering problems expressed in an integral formulation, with main focus on the design of the pre-conditioner. We consider an approximate inverse method based on the Frobenius-norm minimization with a pattern prescribed in advance. The pre-conditioner is constructed from a sparse approximation of the dense coefficient matrix, and the patterns both for the pre-conditioner and for the coefficient matrix are computed a priori using geometric information from the mesh. We describe the implementation of the approximate inverse in an out-of-core parallel code that uses multipole techniques for the matrix-vector products, and show results on the numerical scalability of our method on systems of size up to one million unknowns. We propose an embedded iterative scheme based on the GMRES method and combined with multipole techniques, aimed at improving the robustness of the approximate inverse for large problems. We prove by numerical experiments that the proposed scheme enables the solution of very large and difficult problems efficiently at reduced computational and memory cost. Finally we perform a preliminary study on a spectral two-level pre-conditioner to enhance the robustness of our method. This numerical technique exploits spectral information of the preconditioned systems to build a low rank-update of the pre-conditioner. (authors)
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....
Deploy production sliding mesh capability with linear solver benchmarking.
Energy Technology Data Exchange (ETDEWEB)
Domino, Stefan P. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Thomas, Stephen [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Barone, Matthew F. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Williams, Alan B. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ananthan, Shreyas [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Knaus, Robert C. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Overfelt, James [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sprague, Mike [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Rood, Jon [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2018-02-01
overall simulation time when using the full Tpetra solver stack and nearly 35% when using a mixed Tpetra- Hypre-based solver stack. The report also highlights the project achievement of surpassing the 1 billion element mesh scale for a production V27 hybrid mesh. A detailed timing breakdown is presented that again suggests work to be done in the setup events associated with the linear system. In order to mitigate these initialization costs, several application paths have been explored, all of which are designed to reduce the frequency of matrix reinitialization. Methods such as removing Jacobian entries on the dynamic matrix columns (in concert with increased inner equation iterations), and lagging of Jacobian entries have reduced setup times at the cost of numerical stability. Artificially increasing, or bloating, the matrix stencil to ensure that full Jacobians are included is developed with results suggesting that this methodology is useful in decreasing reinitialization events without loss of matrix contributions. With the above foundational advances in computational capability, the project is well positioned to begin scientific inquiry on a variety of wind-farm physics such as turbine/turbine wake interactions.
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.
Simplified Eigen-structure decomposition solver for the simulation of two-phase flow systems
International Nuclear Information System (INIS)
Kumbaro, Anela
2012-01-01
This paper discusses the development of a new solver for a system of first-order non-linear differential equations that model the dynamics of compressible two-phase flow. The solver presents a lower-complexity alternative to Roe-type solvers because it only makes use of a partial Eigen-structure information while maintaining its accuracy: the outcome is hence a good complexity-tractability trade-off to consider as relevant in a large number of situations in the scope of two-phase flow numerical simulation. A number of numerical and physical benchmarks are presented to assess the solver. Comparison between the computational results from the simplified Eigen-structure decomposition solver and the conventional Roe-type solver gives insight upon the issues of accuracy, robustness and efficiency. (authors)
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.
International Nuclear Information System (INIS)
Jia, Jingfei; Kim, Hyun K.; Hielscher, Andreas H.
2015-01-01
It is well known that radiative transfer equation (RTE) provides more accurate tomographic results than its diffusion approximation (DA). However, RTE-based tomographic reconstruction codes have limited applicability in practice due to their high computational cost. In this article, we propose a new efficient method for solving the RTE forward problem with multiple light sources in an all-at-once manner instead of solving it for each source separately. To this end, we introduce here a novel linear solver called block biconjugate gradient stabilized method (block BiCGStab) that makes full use of the shared information between different right hand sides to accelerate solution convergence. Two parallelized block BiCGStab methods are proposed for additional acceleration under limited threads situation. We evaluate the performance of this algorithm with numerical simulation studies involving the Delta–Eddington approximation to the scattering phase function. The results show that the single threading block RTE solver proposed here reduces computation time by a factor of 1.5–3 as compared to the traditional sequential solution method and the parallel block solver by a factor of 1.5 as compared to the traditional parallel sequential method. This block linear solver is, moreover, independent of discretization schemes and preconditioners used; thus further acceleration and higher accuracy can be expected when combined with other existing discretization schemes or preconditioners. - Highlights: • We solve the multiple-right-hand-side problem in DOT with a block BiCGStab method. • We examine the CPU times of the block solver and the traditional sequential solver. • The block solver is faster than the sequential solver by a factor of 1.5–3.0. • Multi-threading block solvers give additional speedup under limited threads situation.
Efficient Implementation of Solvers for Linear Model Predictive Control on Embedded Devices
DEFF Research Database (Denmark)
Frison, Gianluca; Kwame Minde Kufoalor, D.; Imsland, Lars
2014-01-01
This paper proposes a novel approach for the efficient implementation of solvers for linear MPC on embedded devices. The main focus is to explain in detail the approach used to optimize the linear algebra for selected low-power embedded devices, and to show how the high-performance implementation...
Survey on efficient linear solvers for porous media flow models on recent hardware architectures
International Nuclear Information System (INIS)
Anciaux-Sedrakian, Ani; Gratien, Jean-Marc; Guignon, Thomas; Gottschling, Peter
2014-01-01
In the past few years, High Performance Computing (HPC) technologies led to General Purpose Processing on Graphics Processing Units (GPGPU) and many-core architectures. These emerging technologies offer massive processing units and are interesting for porous media flow simulators may used for CO 2 geological sequestration or Enhanced Oil Recovery (EOR) simulation. However the crucial point is 'are current algorithms and software able to use these new technologies efficiently?' The resolution of large sparse linear systems, almost ill-conditioned, constitutes the most CPU-consuming part of such simulators. This paper proposes a survey on various solver and pre-conditioner algorithms, analyzes their efficiency and performance regarding these distinct architectures. Furthermore it proposes a novel approach based on a hybrid programming model for both GPU and many-core clusters. The proposed optimization techniques are validated through a Krylov subspace solver; BiCGStab and some pre-conditioners like ILU0 on GPU, multi-core and many-core architectures, on various large real study cases in EOR simulation. (authors)
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...
International Nuclear Information System (INIS)
Secher, Bernard; Belliard, Michel; Calvin, Christophe
2009-01-01
This paper describes a tool called 'Numerical Platon' developed by the French Atomic Energy Commission (CEA). It provides a freely available (GNU LGPL license) interface for coupling scientific computing applications to various freeware linear solver libraries (essentially PETSc, SuperLU and HyPre), together with some proprietary CEA solvers, for high-performance computers that may be used in industrial software written in various programming languages. This tool was developed as part of considerable efforts by the CEA Nuclear Energy Division in the past years to promote massively parallel software and on-shelf parallel tools to help develop new generation simulation codes. After the presentation of the package architecture and the available algorithms, we show examples of how Numerical Platon is used in sequential and parallel CEA codes. Comparing with in-house solvers, the gain in terms of increases in computation capacities or in terms of parallel performances is notable, without considerable extra development cost
Energy Technology Data Exchange (ETDEWEB)
Secher, Bernard [French Atomic Energy Commission (CEA), Nuclear Energy Division (DEN) (France); CEA Saclay DM2S/SFME/LGLS, Bat. 454, F-91191 Gif-sur-Yvette Cedex (France)], E-mail: bsecher@cea.fr; Belliard, Michel [French Atomic Energy Commission (CEA), Nuclear Energy Division (DEN) (France); CEA Cadarache DER/SSTH/LMDL, Bat. 238, F-13108 Saint-Paul-lez-Durance Cedex (France); Calvin, Christophe [French Atomic Energy Commission (CEA), Nuclear Energy Division (DEN) (France); CEA Saclay DM2S/SERMA/LLPR, Bat. 470, F-91191 Gif-sur-Yvette Cedex (France)
2009-01-15
This paper describes a tool called 'Numerical Platon' developed by the French Atomic Energy Commission (CEA). It provides a freely available (GNU LGPL license) interface for coupling scientific computing applications to various freeware linear solver libraries (essentially PETSc, SuperLU and HyPre), together with some proprietary CEA solvers, for high-performance computers that may be used in industrial software written in various programming languages. This tool was developed as part of considerable efforts by the CEA Nuclear Energy Division in the past years to promote massively parallel software and on-shelf parallel tools to help develop new generation simulation codes. After the presentation of the package architecture and the available algorithms, we show examples of how Numerical Platon is used in sequential and parallel CEA codes. Comparing with in-house solvers, the gain in terms of increases in computation capacities or in terms of parallel performances is notable, without considerable extra development cost.
Krylov solvers for linear algebraic systems
Broyden, Charles George
2004-01-01
The first four chapters of this book give a comprehensive and unified theory of the Krylov methods. Many of these are shown to be particular examples ofthe block conjugate-gradient algorithm and it is this observation thatpermits the unification of the theory. The two major sub-classes of thosemethods, the Lanczos and the Hestenes-Stiefel, are developed in parallel asnatural generalisations of the Orthodir (GCR) and Orthomin algorithms. Theseare themselves based on Arnoldi's algorithm and a generalised Gram-Schmidtalgorithm and their properties, in particular their stability properties,are det
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.
International Nuclear Information System (INIS)
Vadlamani, Srinath; Kruger, Scott; Austin, Travis
2008-01-01
Extended magnetohydrodynamic (MHD) codes are used to model the large, slow-growing instabilities that are projected to limit the performance of International Thermonuclear Experimental Reactor (ITER). The multiscale nature of the extended MHD equations requires an implicit approach. The current linear solvers needed for the implicit algorithm scale poorly because the resultant matrices are so ill-conditioned. A new solver is needed, especially one that scales to the petascale. The most successful scalable parallel processor solvers to date are multigrid solvers. Applying multigrid techniques to a set of equations whose fundamental modes are dispersive waves is a promising solution to CEMM problems. For the Phase 1, we implemented multigrid preconditioners from the HYPRE project of the Center for Applied Scientific Computing at LLNL via PETSc of the DOE SciDAC TOPS for the real matrix systems of the extended MHD code NIMROD which is a one of the primary modeling codes of the OFES-funded Center for Extended Magnetohydrodynamic Modeling (CEMM) SciDAC. We implemented the multigrid solvers on the fusion test problem that allows for real matrix systems with success, and in the process learned about the details of NIMROD data structures and the difficulties of inverting NIMROD operators. The further success of this project will allow for efficient usage of future petascale computers at the National Leadership Facilities: Oak Ridge National Laboratory, Argonne National Laboratory, and National Energy Research Scientific Computing Center. The project will be a collaborative effort between computational plasma physicists and applied mathematicians at Tech-X Corporation, applied mathematicians Front Range Scientific Computations, Inc. (who are collaborators on the HYPRE project), and other computational plasma physicists involved with the CEMM project.
A Posteriori Error Estimation for Finite Element Methods and Iterative Linear Solvers
Energy Technology Data Exchange (ETDEWEB)
Melboe, Hallgeir
2001-10-01
This thesis addresses a posteriori error estimation for finite element methods and iterative linear solvers. Adaptive finite element methods have gained a lot of popularity over the last decades due to their ability to produce accurate results with limited computer power. In these methods a posteriori error estimates play an essential role. Not only do they give information about how large the total error is, they also indicate which parts of the computational domain should be given a more sophisticated treatment in order to reduce the error. A posteriori error estimates are traditionally aimed at estimating the global error, but more recently so called goal oriented error estimators have been shown a lot of interest. The name reflects the fact that they estimate the error in user-defined local quantities. In this thesis the main focus is on global error estimators for highly stretched grids and goal oriented error estimators for flow problems on regular grids. Numerical methods for partial differential equations, such as finite element methods and other similar techniques, typically result in a linear system of equations that needs to be solved. Usually such systems are solved using some iterative procedure which due to a finite number of iterations introduces an additional error. Most such algorithms apply the residual in the stopping criterion, whereas the control of the actual error may be rather poor. A secondary focus in this thesis is on estimating the errors that are introduced during this last part of the solution procedure. The thesis contains new theoretical results regarding the behaviour of some well known, and a few new, a posteriori error estimators for finite element methods on anisotropic grids. Further, a goal oriented strategy for the computation of forces in flow problems is devised and investigated. Finally, an approach for estimating the actual errors associated with the iterative solution of linear systems of equations is suggested. (author)
Iterative linear solvers in a 2D radiation-hydrodynamics code: Methods and performance
International Nuclear Information System (INIS)
Baldwin, C.; Brown, P.N.; Falgout, R.; Graziani, F.; Jones, J.
1999-01-01
Computer codes containing both hydrodynamics and radiation play a central role in simulating both astrophysical and inertial confinement fusion (ICF) phenomena. A crucial aspect of these codes is that they require an implicit solution of the radiation diffusion equations. The authors present in this paper the results of a comparison of five different linear solvers on a range of complex radiation and radiation-hydrodynamics problems. The linear solvers used are diagonally scaled conjugate gradient, GMRES with incomplete LU preconditioning, conjugate gradient with incomplete Cholesky preconditioning, multigrid, and multigrid-preconditioned conjugate gradient. These problems involve shock propagation, opacities varying over 5--6 orders of magnitude, tabular equations of state, and dynamic ALE (Arbitrary Lagrangian Eulerian) meshes. They perform a problem size scalability study by comparing linear solver performance over a wide range of problem sizes from 1,000 to 100,000 zones. The fundamental question they address in this paper is: Is it more efficient to invert the matrix in many inexpensive steps (like diagonally scaled conjugate gradient) or in fewer expensive steps (like multigrid)? In addition, what is the answer to this question as a function of problem size and is the answer problem dependent? They find that the diagonally scaled conjugate gradient method performs poorly with the growth of problem size, increasing in both iteration count and overall CPU time with the size of the problem and also increasing for larger time steps. For all problems considered, the multigrid algorithms scale almost perfectly (i.e., the iteration count is approximately independent of problem size and problem time step). For pure radiation flow problems (i.e., no hydrodynamics), they see speedups in CPU time of factors of ∼15--30 for the largest problems, when comparing the multigrid solvers relative to diagonal scaled conjugate gradient
Numerical solution of large sparse linear systems
International Nuclear Information System (INIS)
Meurant, Gerard; Golub, Gene.
1982-02-01
This note is based on one of the lectures given at the 1980 CEA-EDF-INRIA Numerical Analysis Summer School whose aim is the study of large sparse linear systems. The main topics are solving least squares problems by orthogonal transformation, fast Poisson solvers and solution of sparse linear system by iterative methods with a special emphasis on preconditioned conjuguate gradient method [fr
Comparing direct and iterative equation solvers in a large structural analysis software system
Poole, E. L.
1991-01-01
Two direct Choleski equation solvers and two iterative preconditioned conjugate gradient (PCG) equation solvers used in a large structural analysis software system are described. The two direct solvers are implementations of the Choleski method for variable-band matrix storage and sparse matrix storage. The two iterative PCG solvers include the Jacobi conjugate gradient method and an incomplete Choleski conjugate gradient method. The performance of the direct and iterative solvers is compared by solving several representative structural analysis problems. Some key factors affecting the performance of the iterative solvers relative to the direct solvers are identified.
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.
DEFF Research Database (Denmark)
Andersen, Michael; Abel, Sarah Maria Niebe; Erleben, Kenny
2017-01-01
We address the task of computing solutions for a separating fluid-solid wall boundary condition model. We present an embarrassingly parallel, easy to implement, fluid LCP solver.We are able to use greater domain sizes than previous works have shown, due to our new solver. The solver exploits matr...
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......-direction in Interior-Point (IP) methods for MPC, and that usually are the computational bottle-neck. This strategy combines a Riccati-like solver with the use of high-performance computing techniques: in particular, in this paper we explore the performance boost given by the use of single precision computation...
PB-AM: An open-source, fully analytical linear poisson-boltzmann solver.
Felberg, Lisa E; Brookes, David H; Yap, Eng-Hui; Jurrus, Elizabeth; Baker, Nathan A; Head-Gordon, Teresa
2017-06-05
We present the open source distributed software package Poisson-Boltzmann Analytical Method (PB-AM), a fully analytical solution to the linearized PB equation, for molecules represented as non-overlapping spherical cavities. The PB-AM software package includes the generation of outputs files appropriate for visualization using visual molecular dynamics, a Brownian dynamics scheme that uses periodic boundary conditions to simulate dynamics, the ability to specify docking criteria, and offers two different kinetics schemes to evaluate biomolecular association rate constants. Given that PB-AM defines mutual polarization completely and accurately, it can be refactored as a many-body expansion to explore 2- and 3-body polarization. Additionally, the software has been integrated into the Adaptive Poisson-Boltzmann Solver (APBS) software package to make it more accessible to a larger group of scientists, educators, and students that are more familiar with the APBS framework. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
The non-linear microscale flow solver 3DWind Developments and validation
Energy Technology Data Exchange (ETDEWEB)
Undheim, Ove
2005-05-01
This PhD thesis describes the implementation of a Reynolds Stress Model in the RANS microscale solver 3DWind, which is developed to model wind flow in complex terrain. The solver is also calibrated and validated with the two-dimensional channel flow test case C18 from the ERCOFTAC Classic database and the full-scale atmospheric flow case of the Askervein hill. The implemented equations calculate both flow cases in good accordance with available experimental and numerical results. Still, the simulation experience and obtained results show that modelling of recirculation is a difficult task. The calculated flow field is very sensitive to the separation point, which is sensitive to several other factors. One important factor is the wall functions, which cause the separation zone to depend on the thickness of the first grid cell. Compared to the k-{epsilon} model, results from simulations with the Reynolds Stress Model gave improvements in the calculated turbulence upstream the C18 hill. There were also differences in the solutions in the wake of both the C18 and the Askervein hills; still, the differences are too small to make any conclusions about the quality of the models. The disadvantages of decreased stability, more wiggles in the solution and increased computational effort are considered larger than the advantages of accounting for anisotropy and historical effects in the Reynolds stresses. The solver is further used to quantify the effects of roughness and topography by generalized two-dimensional investigations of atmospheric flow. Hills and ridges are in this analysis found to increase wind velocities at 80m by up to 38%, and wind velocities above the ocean at 80m are 14% higher than corresponding open land velocities. Finally, a full wind resource assessment has been carried out at Eldsfjellet at the Norwegian island Hitra. Results were compared with measured data and simulation results from the linearized model WAsP. WAsP was found to estimate higher
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++ 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.
Non linear system become linear system
Directory of Open Access Journals (Sweden)
Petre Bucur
2007-01-01
Full Text Available The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding features.
Woźniak, M.
2016-06-02
We study the features of a new mixed integration scheme dedicated to solving the non-stationary variational problems. The scheme is composed of the FEM approximation with respect to the space variable coupled with a 3-leveled time integration scheme with a linearized right-hand side operator. It was applied in solving the Cahn-Hilliard parabolic equation with a nonlinear, fourth-order elliptic part. The second order of the approximation along the time variable was proven. Moreover, the good scalability of the software based on this scheme was confirmed during simulations. We verify the proposed time integration scheme by monitoring the Ginzburg-Landau free energy. The numerical simulations are performed by using a parallel multi-frontal direct solver executed over STAMPEDE Linux cluster. Its scalability was compared to the results of the three direct solvers, including MUMPS, SuperLU and PaSTiX.
DEFF Research Database (Denmark)
Amini Afshar, Mostafa; Bingham, Harry B.; Read, Robert
During recent years a computational strategy has been developed at the Technical University of Denmark for numerical simulation of water wave problems based on the high-order nite-dierence method, [2],[4]. These methods exhibit a linear scaling of the computational eort as the number of grid points...... increases. This understanding is being applied to develop a tool for predicting the added resistance (drift force) of ships in ocean waves. We expect that the optimal scaling properties of this solver will allow us to make a convincing demonstration of convergence of the added resistance calculations based...... on both near-eld and far-eld methods. The solver has been written inside a C++ library known as Overture [3], which can be used to solve partial dierential equations on overlapping grids based on the high-order nite-dierence method. The resulting code is able to solve, in the time domain, the linearised...
Minos: a SPN solver for core calculation in the DESCARTES system
International Nuclear Information System (INIS)
Baudron, A.M.; Lautard, J.J.
2005-01-01
This paper describes a new development of a neutronic core solver done in the context of a new generation neutronic reactor computational system, named DESCARTES. 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. The solver takes into account assembly discontinuity coefficients (ADF) in the simplified transport equation (SPN) 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 performances of the old version have 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)
High performance simplex solver
Huangfu, Qi
2013-01-01
The dual simplex method is frequently the most efficient technique for solving linear programming (LP) problems. This thesis describes an efficient implementation of the sequential dual simplex method and the design and development of two parallel dual simplex solvers. In serial, many advanced techniques for the (dual) simplex method are implemented, including sparse LU factorization, hyper-sparse linear system solution technique, efficient approaches to updating LU factors and...
International Nuclear Information System (INIS)
Hindmarsh, A.D.; Brown, P.N.
1996-01-01
1 - Description of program or function: LSODKR is a new initial value ODE solver for stiff and non-stiff systems. It is a variant of the LSODPK and LSODE solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE are the following: a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, b) within the corrector iteration, LSODKR does automatic switching between functional (fix point) iteration and modified Newton iteration, c) LSODKR includes the ability to find roots of given functions of the solution during the integration. 2 - Method of solution: Integration is by Adams or BDF (Backward Differentiation Formula) methods, at user option. Corrector iteration is by Newton or fix point iteration, determined dynamically. Linear system solution is by a preconditioned Krylov iteration, selected by user from Incomplete Orthogonalization Method, Generalized Minimum Residual Method, and two variants of Preconditioned Conjugate Gradient Method. Preconditioning is to be supplied by the user. 3 - Restrictions on the complexity of the problem: None
SLAP, Large Sparse Linear System Solution Package
International Nuclear Information System (INIS)
Greenbaum, A.
1987-01-01
1 - Description of program or function: SLAP is a set of routines for solving large sparse systems of linear equations. One need not store the entire matrix - only the nonzero elements and their row and column numbers. Any nonzero structure is acceptable, so the linear system solver need not be modified when the structure of the matrix changes. Auxiliary storage space is acquired and released within the routines themselves by use of the LRLTRAN POINTER statement. 2 - Method of solution: SLAP contains one direct solver, a band matrix factorization and solution routine, BAND, and several interactive solvers. The iterative routines are as follows: JACOBI, Jacobi iteration; GS, Gauss-Seidel Iteration; ILUIR, incomplete LU decomposition with iterative refinement; DSCG and ICCG, diagonal scaling and incomplete Cholesky decomposition with conjugate gradient iteration (for symmetric positive definite matrices only); DSCGN and ILUGGN, diagonal scaling and incomplete LU decomposition with conjugate gradient interaction on the normal equations; DSBCG and ILUBCG, diagonal scaling and incomplete LU decomposition with bi-conjugate gradient iteration; and DSOMN and ILUOMN, diagonal scaling and incomplete LU decomposition with ORTHOMIN iteration
Callier, Frank M.; Desoer, Charles A.
1991-01-01
The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.
Development of RBDGG Solver and Its Application to System Reliability Analysis
International Nuclear Information System (INIS)
Kim, Man Cheol
2010-01-01
For the purpose of making system reliability analysis easier and more intuitive, RBDGG (Reliability Block diagram with General Gates) methodology was introduced as an extension of the conventional reliability block diagram. The advantage of the RBDGG methodology is that the structure of a RBDGG model is very similar to the actual structure of the analyzed system, and therefore the modeling of a system for system reliability and unavailability analysis becomes very intuitive and easy. The main idea of the development of the RBDGG methodology is similar with that of the development of the RGGG (Reliability Graph with General Gates) methodology, which is an extension of a conventional reliability graph. The newly proposed methodology is now implemented into a software tool, RBDGG Solver. RBDGG Solver was developed as a WIN32 console application. RBDGG Solver receives information on the failure modes and failure probabilities of each component in the system, along with the connection structure and connection logics among the components in the system. Based on the received information, RBDGG Solver automatically generates a system reliability analysis model for the system, and then provides the analysis results. In this paper, application of RBDGG Solver to the reliability analysis of an example system, and verification of the calculation results are provided for the purpose of demonstrating how RBDGG Solver is used for system reliability analysis
International Nuclear Information System (INIS)
Hindmarsh, A.C.; Petzold, L.R.
2005-01-01
1 - Description of program or function: LSODKR is a new initial value ODE solver for stiff and non-stiff systems. It is a variant of the LSODPK and LSODE solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE are the following: a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, b) within the corrector iteration, LSODKR does automatic switching between functional (fix point) iteration and modified Newton iteration, The nonlinear iteration method-switching differs from the method-switching in LSODA and LSODAR, but provides similar savings by using the cheaper method in the non-stiff regions of the problem. c) LSODKR includes the ability to find roots of given functions of the solution during the integration. d) LSODKR also improves on the Krylov methods in LSODPK by offering the option to save and reuse the approximate Jacobian data underlying the pre-conditioner. The LSODKR source is commented extensively to facilitate modification. Both a single-precision version and a double-precision version are available. 2 - Methods: It is assumed that the ODEs are given explicitly, so that the system can be written in the form dy/dt = f(t,y), where y is the vector of dependent variables, and t is the independent variable. Integration is by Adams or BDF (Backward Differentiation Formula) methods, at user option. Corrector iteration is by Newton or fix point iteration, determined dynamically. Linear system solution is by a preconditioned Krylov iteration, selected by user from Incomplete Orthogonalization Method, Generalized Minimum Residual Method, and two variants of Preconditioned Conjugate Gradient Method. Preconditioning is to be supplied by the user
International Nuclear Information System (INIS)
Blanchard, M.; Schuller, T.; Sipp, D.; Schmid, P. J.
2015-01-01
The response of a laminar premixed methane-air flame subjected to flow perturbations around a steady state is examined experimentally and using a linearized compressible Navier-Stokes solver with a one-step chemistry mechanism to describe combustion. The unperturbed flame takes an M-shape stabilized both by a central bluff body and by the external rim of a cylindrical nozzle. This base flow is computed by a nonlinear direct simulation of the steady reacting flow, and the flame topology is shown to qualitatively correspond to experiments conducted under comparable conditions. The flame is then subjected to acoustic disturbances produced at different locations in the numerical domain, and its response is examined using the linearized solver. This linear numerical model then allows the componentwise investigation of the effects of flow disturbances on unsteady combustion and the feedback from the flame on the unsteady flow field. It is shown that a wrinkled reaction layer produces hydrodynamic disturbances in the fresh reactant flow field that superimpose on the acoustic field. This phenomenon, observed in several experiments, is fully interpreted here. The additional perturbations convected by the mean flow stem from the feedback of the perturbed flame sheet dynamics onto the flow field by a mechanism similar to that of a perturbed vortex sheet. The different regimes where this mechanism prevails are investigated by examining the phase and group velocities of flow disturbances along an axis oriented along the main direction of the flow in the fresh reactant flow field. It is shown that this mechanism dominates the low-frequency response of the wrinkled shape taken by the flame and, in particular, that it fully determines the dynamics of the flame tip from where the bulk of noise is radiated
Evaluating Sparse Linear System Solvers on Scalable Parallel Architectures
National Research Council Canada - National Science Library
Grama, Ananth; Manguoglu, Murat; Koyuturk, Mehmet; Naumov, Maxim; Sameh, Ahmed
2008-01-01
.... The study was motivated primarily by the lack of robustness of Krylov subspace iterative schemes with generic, black-box, pre-conditioners such as approximate (or incomplete) LU-factorizations...
International Nuclear Information System (INIS)
Suzuki, Yoshio; Kushida, Noriyuki; Tatekawa, Takayuki; Teshima, Naoya; Caniou, Yves; Guivarch, Ronan; Dayde, Michel; Ramet, Pierre
2010-01-01
The 'Research and Development of International Matrix-Solver Prediction System (REDIMPS)' project aimed at improving the TLSE sparse linear algebra expert website by establishing an international grid computing environment between Japan and France. To help users in identifying the best solver or sparse linear algebra tool for their problems, we have developed an interoperable environment between French and Japanese grid infrastructures (respectively managed by DIET and AEGIS). Two main issues were considered. The first issue is how to submit a job from DIET to AEGIS. The second issue is how to bridge the difference of security between DIET and AEGIS. To overcome these issues, we developed APIs to communicate between different grid infrastructures by improving the client API of AEGIS. By developing a server deamon program (SeD) of DIET which behaves like an AEGIS user, DIET can call functions in AEGIS: authentication, file transfer, job submission, and so on. To intensify the security, we also developed functionalities to authenticate DIET sites and DIET users in order to access AEGIS computing resources. By this study, the set of software and computers available within TLSE to find an appropriate solver is enlarged over France (DIET) and Japan (AEGIS). (author)
A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation
Diosady, Laslo T.; Murman, Scott M.
2018-01-01
A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.
Energy Technology Data Exchange (ETDEWEB)
Lloyd, S. A. M.; Ansbacher, W. [Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia V8W 3P6 (Canada); Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia V8W 3P6 (Canada) and Department of Medical Physics, British Columbia Cancer Agency-Vancouver Island Centre, Victoria, British Columbia V8R 6V5 (Canada)
2013-01-15
Purpose: Acuros external beam (Acuros XB) is a novel dose calculation algorithm implemented through the ECLIPSE treatment planning system. The algorithm finds a deterministic solution to the linear Boltzmann transport equation, the same equation commonly solved stochastically by Monte Carlo methods. This work is an evaluation of Acuros XB, by comparison with Monte Carlo, for dose calculation applications involving high-density materials. Existing non-Monte Carlo clinical dose calculation algorithms, such as the analytic anisotropic algorithm (AAA), do not accurately model dose perturbations due to increased electron scatter within high-density volumes. Methods: Acuros XB, AAA, and EGSnrc based Monte Carlo are used to calculate dose distributions from 18 MV and 6 MV photon beams delivered to a cubic water phantom containing a rectangular high density (4.0-8.0 g/cm{sup 3}) volume at its center. The algorithms are also used to recalculate a clinical prostate treatment plan involving a unilateral hip prosthesis, originally evaluated using AAA. These results are compared graphically and numerically using gamma-index analysis. Radio-chromic film measurements are presented to augment Monte Carlo and Acuros XB dose perturbation data. Results: Using a 2% and 1 mm gamma-analysis, between 91.3% and 96.8% of Acuros XB dose voxels containing greater than 50% the normalized dose were in agreement with Monte Carlo data for virtual phantoms involving 18 MV and 6 MV photons, stainless steel and titanium alloy implants and for on-axis and oblique field delivery. A similar gamma-analysis of AAA against Monte Carlo data showed between 80.8% and 87.3% agreement. Comparing Acuros XB and AAA evaluations of a clinical prostate patient plan involving a unilateral hip prosthesis, Acuros XB showed good overall agreement with Monte Carlo while AAA underestimated dose on the upstream medial surface of the prosthesis due to electron scatter from the high-density material. Film measurements
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).
A coupled systems code-CFD MHD solver for fusion blanket design
Energy Technology Data Exchange (ETDEWEB)
Wolfendale, Michael J., E-mail: m.wolfendale11@imperial.ac.uk; Bluck, Michael J.
2015-10-15
Highlights: • A coupled systems code-CFD MHD solver for fusion blanket applications is proposed. • Development of a thermal hydraulic systems code with MHD capabilities is detailed. • A code coupling methodology based on the use of TCP socket communications is detailed. • Validation cases are briefly discussed for the systems code and coupled solver. - Abstract: The network of flow channels in a fusion blanket can be modelled using a 1D thermal hydraulic systems code. For more complex components such as junctions and manifolds, the simplifications employed in such codes can become invalid, requiring more detailed analyses. For magnetic confinement reactor blanket designs using a conducting fluid as coolant/breeder, the difficulties in flow modelling are particularly severe due to MHD effects. Blanket analysis is an ideal candidate for the application of a code coupling methodology, with a thermal hydraulic systems code modelling portions of the blanket amenable to 1D analysis, and CFD providing detail where necessary. A systems code, MHD-SYS, has been developed and validated against existing analyses. The code shows good agreement in the prediction of MHD pressure loss and the temperature profile in the fluid and wall regions of the blanket breeding zone. MHD-SYS has been coupled to an MHD solver developed in OpenFOAM and the coupled solver validated for test geometries in preparation for modelling blanket systems.
Esmaily, M.; Jofre, L.; Mani, A.; Iaccarino, G.
2018-03-01
A geometric multigrid algorithm is introduced for solving nonsymmetric linear systems resulting from the discretization of the variable density Navier-Stokes equations on nonuniform structured rectilinear grids and high-Reynolds number flows. The restriction operation is defined such that the resulting system on the coarser grids is symmetric, thereby allowing for the use of efficient smoother algorithms. To achieve an optimal rate of convergence, the sequence of interpolation and restriction operations are determined through a dynamic procedure. A parallel partitioning strategy is introduced to minimize communication while maintaining the load balance between all processors. To test the proposed algorithm, we consider two cases: 1) homogeneous isotropic turbulence discretized on uniform grids and 2) turbulent duct flow discretized on stretched grids. Testing the algorithm on systems with up to a billion unknowns shows that the cost varies linearly with the number of unknowns. This O (N) behavior confirms the robustness of the proposed multigrid method regarding ill-conditioning of large systems characteristic of multiscale high-Reynolds number turbulent flows. The robustness of our method to density variations is established by considering cases where density varies sharply in space by a factor of up to 104, showing its applicability to two-phase flow problems. Strong and weak scalability studies are carried out, employing up to 30,000 processors, to examine the parallel performance of our implementation. Excellent scalability of our solver is shown for a granularity as low as 104 to 105 unknowns per processor. At its tested peak throughput, it solves approximately 4 billion unknowns per second employing over 16,000 processors with a parallel efficiency higher than 50%.
Modelling dynamic liquid-gas systems: Extensions to the volume-of-fluid solver
CSIR Research Space (South Africa)
Heyns, Johan A
2013-06-01
Full Text Available This study presents the extension of the volume-of-fluid solver, interFoam, for improved accuracy and efficiency when modelling dynamic liquid-gas systems. Examples of these include the transportation of liquids, such as in the case of fuel carried...
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...
Energy Technology Data Exchange (ETDEWEB)
Domino, Stefan P. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-12-01
This milestone was focused on deploying and verifying a “sliding-mesh interface,” and establishing baseline timings for blade-resolved simulations of a sub-MW-scale turbine. In the ExaWind project, we are developing both sliding-mesh and overset-mesh approaches for handling the rotating blades in an operating wind turbine. In the sliding-mesh approach, the turbine rotor and its immediate surrounding fluid are captured in a “disk” that is embedded in the larger fluid domain. The embedded fluid is simulated in a coordinate system that rotates with the rotor. It is important that the coupling algorithm (and its implementation) between the rotating and inertial discrete models maintains the accuracy of the numerical methods on either side of the interface, i.e., the interface is “design order.”
Linearization of the Lorenz system
International Nuclear Information System (INIS)
Li, Chunbiao; Sprott, Julien Clinton; Thio, Wesley
2015-01-01
A partial and complete piecewise linearized version of the Lorenz system is proposed. The linearized versions have an independent total amplitude control parameter. Additional further linearization leads naturally to a piecewise linear version of the diffusionless Lorenz system. A chaotic circuit with a single amplitude controller is then implemented using a new switch element, producing a chaotic oscillation that agrees with the numerical calculation for the piecewise linear diffusionless Lorenz system. - Highlights: • A partial and complete piecewise linearized version of the Lorenz system are addressed. • The linearized versions have an independent total amplitude control parameter. • A piecewise linear version of the diffusionless Lorenz system is derived by further linearization. • A corresponding chaotic circuit without any multiplier is implemented for the chaotic oscillation
Linearization of the Lorenz system
Energy Technology Data Exchange (ETDEWEB)
Li, Chunbiao, E-mail: goontry@126.com [School of Electronic & Information Engineering, Nanjing University of Information Science & Technology, Nanjing 210044 (China); Engineering Technology Research and Development Center of Jiangsu Circulation Modernization Sensor Network, Jiangsu Institute of Commerce, Nanjing 211168 (China); Sprott, Julien Clinton [Department of Physics, University of Wisconsin–Madison, Madison, WI 53706 (United States); Thio, Wesley [Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210 (United States)
2015-05-08
A partial and complete piecewise linearized version of the Lorenz system is proposed. The linearized versions have an independent total amplitude control parameter. Additional further linearization leads naturally to a piecewise linear version of the diffusionless Lorenz system. A chaotic circuit with a single amplitude controller is then implemented using a new switch element, producing a chaotic oscillation that agrees with the numerical calculation for the piecewise linear diffusionless Lorenz system. - Highlights: • A partial and complete piecewise linearized version of the Lorenz system are addressed. • The linearized versions have an independent total amplitude control parameter. • A piecewise linear version of the diffusionless Lorenz system is derived by further linearization. • A corresponding chaotic circuit without any multiplier is implemented for the chaotic oscillation.
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.
Dynamical systems and linear algebra
Colonius, Fritz (Prof.)
2007-01-01
Dynamical systems and linear algebra / F. Colonius, W. Kliemann. - In: Handbook of linear algebra / ed. by Leslie Hogben. - Boca Raton : Chapman & Hall/CRC, 2007. - S. 56,1-56,22. - (Discrete mathematics and its applications)
Bernede, Adrien; Poëtte, Gaël
2018-02-01
In this paper, we are interested in the resolution of the time-dependent problem of particle transport in a medium whose composition evolves with time due to interactions. As a constraint, we want to use of Monte-Carlo (MC) scheme for the transport phase. A common resolution strategy consists in a splitting between the MC/transport phase and the time discretization scheme/medium evolution phase. After going over and illustrating the main drawbacks of split solvers in a simplified configuration (monokinetic, scalar Bateman problem), we build a new Unsplit MC (UMC) solver improving the accuracy of the solutions, avoiding numerical instabilities, and less sensitive to time discretization. The new solver is essentially based on a Monte Carlo scheme with time dependent cross sections implying the on-the-fly resolution of a reduced model for each MC particle describing the time evolution of the matter along their flight path.
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.
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.
Feedback systems for linear colliders
Hendrickson, L; Himel, Thomas M; Minty, Michiko G; Phinney, N; Raimondi, Pantaleo; Raubenheimer, T O; Shoaee, H; Tenenbaum, P G
1999-01-01
Feedback systems are essential for stable operation of a linear collider, providing a cost-effective method for relaxing tight tolerances. In the Stanford Linear Collider (SLC), feedback controls beam parameters such as trajectory, energy, and intensity throughout the accelerator. A novel dithering optimization system which adjusts final focus parameters to maximize luminosity contributed to achieving record performance in the 1997-98 run. Performance limitations of the steering feedback have been investigated, and improvements have been made. For the Next Linear Collider (NLC), extensive feedback systems are planned as an intregal part of the design. Feedback requiremetns for JLC (the Japanese Linear Collider) are essentially identical to NLC; some of the TESLA requirements are similar but there are significant differences. For NLC, algorithms which incorporate improvements upon the SLC implementation are being prototyped. Specialized systems for the damping rings, rf and interaction point will operate at hi...
Hou, Jie; Dong, Jianji; Zhang, Xinliang
2017-06-15
Systems of ordinary differential equations (SODEs) are crucial for describing the dynamic behaviors in various systems such as modern control systems which require observability and controllability. In this Letter, we propose and experimentally demonstrate an all-optical SODE solver based on the silicon-on-insulator platform. We use an add/drop microring resonator to construct two different ordinary differential equations (ODEs) and then introduce two external feedback waveguides to realize the coupling between these ODEs, thus forming the SODE solver. A temporal coupled mode theory is used to deduce the expression of the SODE. A system experiment is carried out for further demonstration. For the input 10 GHz NRZ-like pulses, the measured output waveforms of the SODE solver agree well with the calculated results.
IRMHD: an implicit radiative and magnetohydrodynamical solver for self-gravitating systems
Hujeirat, A.
1998-07-01
The 2D implicit hydrodynamical solver developed by Hujeirat & Rannacher is now modified to include the effects of radiation, magnetic fields and self-gravity in different geometries. The underlying numerical concept is based on the operator splitting approach, and the resulting 2D matrices are inverted using different efficient preconditionings such as ADI (alternating direction implicit), the approximate factorization method and Line-Gauss-Seidel or similar iteration procedures. Second-order finite volume with third-order upwinding and second-order time discretization is used. To speed up convergence and enhance efficiency we have incorporated an adaptive time-step control and monotonic multilevel grid distributions as well as vectorizing the code. Test calculations had shown that it requires only 38 per cent more computational effort than its explicit counterpart, whereas its range of application to astrophysical problems is much larger. For example, strongly time-dependent, quasi-stationary and steady-state solutions for the set of Euler and Navier-Stokes equations can now be sought on a non-linearly distributed and strongly stretched mesh. As most of the numerical techniques used to build up this algorithm have been described by Hujeirat & Rannacher in an earlier paper, we focus in this paper on the inclusion of self-gravity, radiation and magnetic fields. Strategies for satisfying the condition ∇.B=0 in the implicit evolution of MHD flows are given. A new discretization strategy for the vector potential which allows alternating use of the direct method is prescribed. We investigate the efficiencies of several 2D solvers for a Poisson-like equation and compare their convergence rates. We provide a splitting approach for the radiative flux within the FLD (flux-limited diffusion) approximation to enhance consistency and accuracy between regions of different optical depths. The results of some test problems are presented to demonstrate the accuracy and
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.
Feedback Systems for Linear Colliders
International Nuclear Information System (INIS)
1999-01-01
Feedback systems are essential for stable operation of a linear collider, providing a cost-effective method for relaxing tight tolerances. In the Stanford Linear Collider (SLC), feedback controls beam parameters such as trajectory, energy, and intensity throughout the accelerator. A novel dithering optimization system which adjusts final focus parameters to maximize luminosity contributed to achieving record performance in the 1997-98 run. Performance limitations of the steering feedback have been investigated, and improvements have been made. For the Next Linear Collider (NLC), extensive feedback systems are planned as an integral part of the design. Feedback requirements for JLC (the Japanese Linear Collider) are essentially identical to NLC; some of the TESLA requirements are similar but there are significant differences. For NLC, algorithms which incorporate improvements upon the SLC implementation are being prototyped. Specialized systems for the damping rings, rf and interaction point will operate at high bandwidth and fast response. To correct for the motion of individual bunches within a train, both feedforward and feedback systems are planned. SLC experience has shown that feedback systems are an invaluable operational tool for decoupling systems, allowing precision tuning, and providing pulse-to-pulse diagnostics. Feedback systems for the NLC will incorporate the key SLC features and the benefits of advancing technologies
Window observers for linear systems
Directory of Open Access Journals (Sweden)
Utkin Vadim
2000-01-01
Full Text Available Given a linear system x ˙ = A x + B u with output y = C x and a window function ω ( t , i.e., ∀ t , ω ( t ∈ {0,1 }, and assuming that the window function is Lebesgue measurable, we refer to the following observer, x ˆ = A x + B u + ω ( t L C ( x − x ˆ as a window observer. The stability issue is treated in this paper. It is proven that for linear time-invariant systems, the window observer can be stabilized by an appropriate design under a very mild condition on the window functions, albeit for linear time-varying system, some regularity of the window functions is required to achieve observer designs with the asymptotic stability. The corresponding design methods are developed. An example is included to illustrate the possible applications
Boku, Taisuke; Ishikawa, Ken-Ichi; Kuramashi, Yoshinobu; Meadows, Lawrence
2017-01-01
Lattice Quantum Chromodynamics (Lattice QCD) is a quantum field theory on a finite discretized space-time box so as to numerically compute the dynamics of quarks and gluons to explore the nature of subatomic world. Solving the equation of motion of quarks (quark solver) is the most compute-intensive part of the lattice QCD simulations and is one of the legacy HPC applications. We have developed a mixed-precision quark solver for a large Intel Xeon Phi (KNL) system named "Oakforest-PACS", empl...
Systems of Inhomogeneous Linear Equations
Scherer, Philipp O. J.
Many problems in physics and especially computational physics involve systems of linear equations which arise e.g. from linearization of a general nonlinear problem or from discretization of differential equations. If the dimension of the system is not too large standard methods like Gaussian elimination or QR decomposition are sufficient. Systems with a tridiagonal matrix are important for cubic spline interpolation and numerical second derivatives. They can be solved very efficiently with a specialized Gaussian elimination method. Practical applications often involve very large dimensions and require iterative methods. Convergence of Jacobi and Gauss-Seidel methods is slow and can be improved by relaxation or over-relaxation. An alternative for large systems is the method of conjugate gradients.
Scalable Newton-Krylov solver for very large power flow problems
Idema, R.; Lahaye, D.J.P.; Vuik, C.; Van der Sluis, L.
2010-01-01
The power flow problem is generally solved by the Newton-Raphson method with a sparse direct solver for the linear system of equations in each iteration. While this works fine for small power flow problems, we will show that for very large problems the direct solver is very slow and we present
Linear collider systems and costs
International Nuclear Information System (INIS)
Loew, G.A.
1993-05-01
The purpose of this paper is to examine some of the systems and sub-systems involved in so-called ''conventional'' e + e - linear colliders and to study how their design affects the overall cost of these machines. There are presently a total of at least six 500 GeV c. of m. linear collider projects under study in the world. Aside from TESLA (superconducting linac at 1.3 GHz) and CLIC (two-beam accelerator with main linac at 30GHz), the other four proposed e + e - linear colliders can be considered ''conventional'' in that their main linacs use the proven technique of driving room temperature accelerator sections with pulsed klystrons and modulators. The centrally distinguishing feature between these projects is their main linac rf frequency: 3 GHz for the DESY machine, 11.424 GHz for the SLAC and JLC machines, and 14 GHz for the VLEPP machine. The other systems, namely the electron and positron sources, preaccelerators, compressors, damping rings and final foci, are fairly similar from project to project. Probably more than 80% of the cost of these linear colliders will be incurred in the two main linacs facing each other and it is therefore in their design and construction that major savings or extra costs may be found
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.
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.
Duncan, Comer; Jones, Jim
1993-01-01
A key ingredient in the simulation of self-gravitating astrophysical fluid dynamical systems is the gravitational potential and its gradient. This paper focuses on the development of a mixed method multigrid solver of the Poisson equation formulated so that both the potential and the Cartesian components of its gradient are self-consistently and accurately generated. The method achieves this goal by formulating the problem as a system of four equations for the gravitational potential and the three Cartesian components of the gradient and solves them using a distributed relaxation technique combined with conventional full multigrid V-cycles. The method is described, some tests are presented, and the accuracy of the method is assessed. We also describe how the method has been incorporated into our three-dimensional hydrodynamics code and give an example of an application to the collision of two stars. We end with some remarks about the future developments of the method and some of the applications in which it will be used in astrophysics.
Linear operator inequalities for strongly stable weakly regular linear systems
Curtain, RF
2001-01-01
We consider the question of the existence of solutions to certain linear operator inequalities (Lur'e equations) for strongly stable, weakly regular linear systems with generating operators A, B, C, 0. These operator inequalities are related to the spectral factorization of an associated Popov
Parallelized preconditioned BiCGStab solution of sparse linear system equations in F-COBRA-TF
International Nuclear Information System (INIS)
Geemert, Rene van; Glück, Markus; Riedmann, Michael; Gabriel, Harry
2011-01-01
Recently, the in-house development of a preconditioned and parallelized BiCGStab solver has been pursued successfully in AREVA’s advanced sub-channel code F-COBRA-TF. This solver can be run either in a sequential computation mode on a single CPU, or in a parallel computation mode on multiple parallel CPUs. The developed procedure enables the computation of several thousands of successive sparse linear system solutions in F-COBRA-TF with acceptable wall clock run times. The current paper provides general information about F-COBRA-TF in terms of modeling capabilities and application areas, and points out where the relevance arises for the efficient iterative solution of sparse linear systems. Furthermore, the preconditioning and parallelization strategies in the developed BiCGStab iterative solution approach are discussed. The paper is concluded with a number of verification examples. (author)
VCODE, Ordinary Differential Equation Solver for Stiff and Non-Stiff Problems
International Nuclear Information System (INIS)
Cohen, Scott D.; Hindmarsh, Alan C.
2001-01-01
1 - Description of program or function: CVODE is a package written in ANSI standard C for solving initial value problems for ordinary differential equations. It solves both stiff and non stiff systems. In the stiff case, it includes a variety of options for treating the Jacobian of the system, including dense and band matrix solvers, and a preconditioned Krylov (iterative) solver. 2 - Method of solution: Integration is by Adams or BDF (Backward Differentiation Formula) methods, at user option. Corrector iteration is by functional iteration or Newton iteration. For the solution of linear systems within Newton iteration, users can select a dense solver, a band solver, a diagonal approximation, or a preconditioned Generalized Minimal Residual (GMRES) solver. In the dense and band cases, the user can supply a Jacobian approximation or let CVODE generate it internally. In the GMRES case, the pre-conditioner is user-supplied
International Nuclear Information System (INIS)
Yokoyama, Kenji; Numata, Kazuyuki
2008-01-01
A new cross section adjustment and nuclear design accuracy evaluation solver was developed as a set of modules for MARBLE (multi-purpose advanced reactor physics analysis system based on language of engineering). In order to enhance the system extendibility and flexibility, the object-oriented design and analysis technique was adopted to the development. In the new system, it is easy to add a new design accuracy evaluation method because a new numerical calculation module is independent from other modules. Further, several new functions such as searching and editing calculation data are provided in the new solver. These functions can be easily customised by users because they are designed to work cooperatively with Python scripting language, which is used as a user interface of the MARBLE system. In order to validate the new solver, a test calculation was performed for a realistic calculation case of creating a new unified cross section library. In the test calculation, results calculated by the new solver agreed well with those by the conventional code system. In addition, it is possible to reuse existing input data files prepared for the conventional code system because the new solver utilities support the conventional formats. Because the new solver implements all main functions of the conventional code system, MARBLE can be used as a new calculation code system for cross section adjustment and nuclear design accuracy evaluation
Implementing parallel elliptic solver on a Beowulf cluster
Directory of Open Access Journals (Sweden)
Marcin Paprzycki
1999-12-01
Full Text Available In a recent paper cite{zara} a parallel direct solver for the linear systems arising from elliptic partial differential equations has been proposed. The aim of this note is to present the initial evaluation of the performance characteristics of this algorithm on Beowulf-type cluster. In this context the performance of PVM and MPI based implementations is compared.
Calo, Victor M.; Collier, Nathan; Pardo, David; Paszyński, Maciej R.
2011-01-01
The multi-frontal direct solver is the state of the art for the direct solution of linear systems. This paper provides computational complexity and memory usage estimates for the application of the multi-frontal direct solver algorithm on linear systems resulting from p finite elements. Specifically we provide the estimates for systems resulting from C0 polynomial spaces spanned by B-splines. The structured grid and uniform polynomial order used in isogeometric meshes simplifies the analysis.
Calo, Victor M.
2011-05-14
The multi-frontal direct solver is the state of the art for the direct solution of linear systems. This paper provides computational complexity and memory usage estimates for the application of the multi-frontal direct solver algorithm on linear systems resulting from p finite elements. Specifically we provide the estimates for systems resulting from C0 polynomial spaces spanned by B-splines. The structured grid and uniform polynomial order used in isogeometric meshes simplifies the analysis.
Dynamic linearization system for a radiation gauge
International Nuclear Information System (INIS)
Panarello, J.A.
1977-01-01
The linearization system and process converts a high resolution non-linear analog input signal, representative of the thickness of an object, into a high resolution linear analog output signal suitable for use in driving a variety of output devices. The system requires only a small amount of memory for storing pre-calculated non-linear correction coefficients. The system channels the input signal to separate circuit paths so that it may be used directly to; locate an appropriate correction coefficient; develop a correction term after an appropriate correction coefficient is located; and develop a linearized signal having the same high resolution inherent in the input signal. The system processes the linearized signal to compensate for the possible errors introduced by radiation source noise. The processed linearized signal is the high resolution linear analog output signal which accurately represents the thickness of the object being gauged
Linear quadratic optimization for positive LTI system
Muhafzan, Yenti, Syafrida Wirma; Zulakmal
2017-05-01
Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.
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.
T2CG1, a package of preconditioned conjugate gradient solvers for TOUGH2
International Nuclear Information System (INIS)
Moridis, G.; Pruess, K.; Antunez, E.
1994-03-01
Most of the computational work in the numerical simulation of fluid and heat flows in permeable media arises in the solution of large systems of linear equations. The simplest technique for solving such equations is by direct methods. However, because of large storage requirements and accumulation of roundoff errors, the application of direct solution techniques is limited, depending on matrix bandwidth, to systems of a few hundred to at most a few thousand simultaneous equations. T2CG1, a package of preconditioned conjugate gradient solvers, has been added to TOUGH2 to complement its direct solver and significantly increase the size of problems tractable on PCs. T2CG1 includes three different solvers: a Bi-Conjugate Gradient (BCG) solver, a Bi-Conjugate Gradient Squared (BCGS) solver, and a Generalized Minimum Residual (GMRES) solver. Results from six test problems with up to 30,000 equations show that T2CG1 (1) is significantly (and invariably) faster and requires far less memory than the MA28 direct solver, (2) it makes possible the solution of very large three-dimensional problems on PCs, and (3) that the BCGS solver is the fastest of the three in the tested problems. Sample problems are presented related to heat and fluid flow at Yucca Mountain and WIPP, environmental remediation by the Thermal Enhanced Vapor Extraction System, and geothermal resources
On pole structure assignment in linear systems
Czech Academy of Sciences Publication Activity Database
Loiseau, J.-J.; Zagalak, Petr
2009-01-01
Roč. 82, č. 7 (2009), s. 1179-1192 ISSN 0020-7179 R&D Projects: GA ČR(CZ) GA102/07/1596 Institutional research plan: CEZ:AV0Z10750506 Keywords : linear systems * linear state feedback * pole structure assignment Subject RIV: BC - Control Systems Theory Impact factor: 1.124, year: 2009 http://library.utia.cas.cz/separaty/2009/AS/zagalak-on pole structure assignment in linear systems.pdf
Displacement measurement system for linear array detector
International Nuclear Information System (INIS)
Zhang Pengchong; Chen Ziyu; Shen Ji
2011-01-01
It presents a set of linear displacement measurement system based on encoder. The system includes displacement encoders, optical lens and read out circuit. Displacement read out unit includes linear CCD and its drive circuit, two amplifier circuits, second order Butterworth low-pass filter and the binarization circuit. The coding way is introduced, and various parts of the experimental signal waveforms are given, and finally a linear experimental test results are given. The experimental results are satisfactory. (authors)
Balanced truncation for linear switched systems
DEFF Research Database (Denmark)
Petreczky, Mihaly; Wisniewski, Rafal; Leth, John-Josef
2013-01-01
In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems from Shaker and Wisniewski (2011, 2009) and . This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems (Wood et al., 1996) [3]. Specifically...
Observability of linear systems with saturated outputs
Koplon, R.; Sontag, E.D.; Hautus, M.L.J.
1994-01-01
We present necessary and sufficient conditions for observability of the class of output-saturated systems. These are linear systems whose output passes through a saturation function before it can be measured.
Isolators Including Main Spring Linear Guide Systems
Goold, Ryan (Inventor); Buchele, Paul (Inventor); Hindle, Timothy (Inventor); Ruebsamen, Dale Thomas (Inventor)
2017-01-01
Embodiments of isolators, such as three parameter isolators, including a main spring linear guide system are provided. In one embodiment, the isolator includes first and second opposing end portions, a main spring mechanically coupled between the first and second end portions, and a linear guide system extending from the first end portion, across the main spring, and toward the second end portion. The linear guide system expands and contracts in conjunction with deflection of the main spring along the working axis, while restricting displacement and rotation of the main spring along first and second axes orthogonal to the working axis.
Linear systems a measurement based approach
Bhattacharyya, S P; Mohsenizadeh, D N
2014-01-01
This brief presents recent results obtained on the analysis, synthesis and design of systems described by linear equations. It is well known that linear equations arise in most branches of science and engineering as well as social, biological and economic systems. The novelty of this approach is that no models of the system are assumed to be available, nor are they required. Instead, a few measurements made on the system can be processed strategically to directly extract design values that meet specifications without constructing a model of the system, implicitly or explicitly. These new concepts are illustrated by applying them to linear DC and AC circuits, mechanical, civil and hydraulic systems, signal flow block diagrams and control systems. These applications are preliminary and suggest many open problems. The results presented in this brief are the latest effort in this direction and the authors hope these will lead to attractive alternatives to model-based design of engineering and other systems.
Final focus systems for linear colliders
International Nuclear Information System (INIS)
Erickson, R.A.
1987-11-01
The final focus system of a linear collider must perform two primary functions, it must focus the two opposing beams so that their transverse dimensions at the interaction point are small enough to yield acceptable luminosity, and it must steer the beams together to maintain collisions. In addition, the final focus system must transport the outgoing beams to a location where they can be recycled or safely dumped. Elementary optical considerations for linear collider final focus systems are discussed, followed by chromatic aberrations. The design of the final focus system of the SLAC Linear Collider (SLC) is described. Tuning and diagnostics and steering to collision are discussed. Most of the examples illustrating the concepts covered are drawn from the SLC, but the principles and conclusions are said to be generally applicable to other linear collider designs as well. 26 refs., 17 figs
On deformations of linear differential systems
Gontsov, R.R.; Poberezhnyi, V.A.; Helminck, G.F.
2011-01-01
This article concerns deformations of meromorphic linear differential systems. Problems relating to their existence and classification are reviewed, and the global and local behaviour of solutions to deformation equations in a neighbourhood of their singular set is analysed. Certain classical
Superconducting linear accelerator system for NSC
Indian Academy of Sciences (India)
59, No. 5. — journal of. November 2002 physics pp. 849–858. Superconducting linear accelerator system for NSC ... cryogenics facility, RF electronics development, facilities for fabricating niobium resonators indige- ... Prototype resonator was.
Torres, Hilario; Iaccarino, Gianluca
2017-11-01
Soleil-X is a multi-physics solver being developed at Stanford University as a part of the Predictive Science Academic Alliance Program II. Our goal is to conduct high fidelity simulations of particle laden turbulent flows in a radiation environment for solar energy receiver applications as well as to demonstrate our readiness to effectively utilize next generation Exascale machines. The novel aspect of Soleil-X is that it is built upon the Legion runtime system to enable easy portability to different parallel distributed heterogeneous architectures while also being written entirely in high-level/high-productivity languages (Ebb and Regent). An overview of the Soleil-X software architecture will be given. Results from coupled fluid flow, Lagrangian point particle tracking, and thermal radiation simulations will be presented. Performance diagnostic tools and metrics corresponding the the same cases will also be discussed. US Department of Energy, National Nuclear Security Administration.
Signals and transforms in linear systems analysis
Wasylkiwskyj, Wasyl
2013-01-01
Signals and Transforms in Linear Systems Analysis covers the subject of signals and transforms, particularly in the context of linear systems theory. Chapter 2 provides the theoretical background for the remainder of the text. Chapter 3 treats Fourier series and integrals. Particular attention is paid to convergence properties at step discontinuities. This includes the Gibbs phenomenon and its amelioration via the Fejer summation techniques. Special topics include modulation and analytic signal representation, Fourier transforms and analytic function theory, time-frequency analysis and frequency dispersion. Fundamentals of linear system theory for LTI analogue systems, with a brief account of time-varying systems, are covered in Chapter 4 . Discrete systems are covered in Chapters 6 and 7. The Laplace transform treatment in Chapter 5 relies heavily on analytic function theory as does Chapter 8 on Z -transforms. The necessary background on complex variables is provided in Appendix A. This book is intended to...
Linear integral equations and soliton systems
International Nuclear Information System (INIS)
Quispel, G.R.W.
1983-01-01
A study is presented of classical integrable dynamical systems in one temporal and one spatial dimension. The direct linearizations are given of several nonlinear partial differential equations, for example the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the sine-Gordon equation, the nonlinear Schroedinger equation, and the equation of motion for the isotropic Heisenberg spin chain; the author also discusses several relations between these equations. The Baecklund transformations of these partial differential equations are treated on the basis of a singular transformation of the measure (or equivalently of the plane-wave factor) occurring in the corresponding linear integral equations, and the Baecklund transformations are used to derive the direct linearization of a chain of so-called modified partial differential equations. Finally it is shown that the singular linear integral equations lead in a natural way to the direct linearizations of various nonlinear difference-difference equations. (Auth.)
STABILITY OF LINEAR SYSTEMS WITH MARKOVIAN JUMPS
Directory of Open Access Journals (Sweden)
Jorge Enrique Mayta Guillermo
2016-12-01
Full Text Available In this work we will analyze the stability of linear systems governed by a Markov chain, this family is known in the specialized literature as linear systems with Markov jumps or by its acronyms in English MJLS as it is denoted in [1]. Linear systems governed by a Markov chain are dynamic systems with abrupt changes. We give some denitions of stability for the MJLS system, where these types of stability are equivalent as long as the state space of the Markov chain is nite. Finally we present a theorem that characterizes the stochastic stability by means of an equation of the Lyapunov type. The result is a generalization of a theorem in classical theory.
Correlated Levy Noise in Linear Dynamical Systems
International Nuclear Information System (INIS)
Srokowski, T.
2011-01-01
Linear dynamical systems, driven by a non-white noise which has the Levy distribution, are analysed. Noise is modelled by a specific stochastic process which is defined by the Langevin equation with a linear force and the Levy distributed symmetric white noise. Correlation properties of the process are discussed. The Fokker-Planck equation driven by that noise is solved. Distributions have the Levy shape and their width, for a given time, is smaller than for processes in the white noise limit. Applicability of the adiabatic approximation in the case of the linear force is discussed. (author)
Introduction to linear systems of differential equations
Adrianova, L Ya
1995-01-01
The theory of linear systems of differential equations is one of the cornerstones of the whole theory of differential equations. At its root is the concept of the Lyapunov characteristic exponent. In this book, Adrianova presents introductory material and further detailed discussions of Lyapunov exponents. She also discusses the structure of the space of solutions of linear systems. Classes of linear systems examined are from the narrowest to widest: 1)�autonomous, 2)�periodic, 3)�reducible to autonomous, 4)�nearly reducible to autonomous, 5)�regular. In addition, Adrianova considers the following: stability of linear systems and the influence of perturbations of the coefficients on the stability the criteria of uniform stability and of uniform asymptotic stability in terms of properties of the solutions several estimates of the growth rate of solutions of a linear system in terms of its coefficients How perturbations of the coefficients change all the elements of the spectrum of the system is defin...
International Nuclear Information System (INIS)
Ikuno, Soichiro; Chen, Gong; Yamamoto, Susumu; Itoh, Taku; Abe, Kuniyoshi; Nakamura, Hiroaki
2016-01-01
Krylov subspace method and the variable preconditioned Krylov subspace method with communication avoiding technique for a linear system obtained from electromagnetic analysis are numerically investigated. In the k−skip Krylov method, the inner product calculations are expanded by Krylov basis, and the inner product calculations are transformed to the scholar operations. k−skip CG method is applied for the inner-loop solver of Variable Preconditioned Krylov subspace methods, and the converged solution of electromagnetic problem is obtained using the method. (author)
Topics in computational linear optimization
DEFF Research Database (Denmark)
Hultberg, Tim Helge
2000-01-01
Linear optimization has been an active area of research ever since the pioneering work of G. Dantzig more than 50 years ago. This research has produced a long sequence of practical as well as theoretical improvements of the solution techniques avilable for solving linear optimization problems...... of high quality solvers and the use of algebraic modelling systems to handle the communication between the modeller and the solver. This dissertation features four topics in computational linear optimization: A) automatic reformulation of mixed 0/1 linear programs, B) direct solution of sparse unsymmetric...... systems of linear equations, C) reduction of linear programs and D) integration of algebraic modelling of linear optimization problems in C++. Each of these topics is treated in a separate paper included in this dissertation. The efficiency of solving mixed 0-1 linear programs by linear programming based...
Final Focus Systems in Linear Colliders
International Nuclear Information System (INIS)
Raubenheimer, Tor
1998-01-01
In colliding beam facilities, the ''final focus system'' must demagnify the beams to attain the very small spot sizes required at the interaction points. The first final focus system with local chromatic correction was developed for the Stanford Linear Collider where very large demagnifications were desired. This same conceptual design has been adopted by all the future linear collider designs as well as the SuperConducting Supercollider, the Stanford and KEK B-Factories, and the proposed Muon Collider. In this paper, the over-all layout, physics constraints, and optimization techniques relevant to the design of final focus systems for high-energy electron-positron linear colliders are reviewed. Finally, advanced concepts to avoid some of the limitations of these systems are discussed
Generalized Cross-Gramian for Linear Systems
DEFF Research Database (Denmark)
Shaker, Hamid Reza
2012-01-01
The cross-gramian is a well-known matrix with embedded controllability and observability information. The cross-gramian is related to the Hankel operator and the Hankel singular values of a linear square system and it has several interesting properties. These properties make the cross...... square symmetric systems, the ordinary cross-gramian does not exist. To cope with this problem, a new generalized cross-gramian is introduced in this paper. In contrast to the ordinary cross-gramian, the generalized cross-gramian can be easily obtained for general linear systems and therefore can be used...
Linear dynamic coupling in geared rotor systems
David, J. W.; Mitchell, L. D.
1986-01-01
The effects of high frequency oscillations caused by the gear mesh, on components of a geared system that can be modeled as rigid discs are analyzed using linear dynamic coupling terms. The coupled, nonlinear equations of motion for a disc attached to a rotating shaft are presented. The results of a trial problem analysis show that the inclusion of the linear dynamic coupling terms can produce significant changes in the predicted response of geared rotor systems, and that the produced sideband responses are greater than the unbalanced response. The method is useful in designing gear drives for heavy-lift helicopters, industrial speed reducers, naval propulsion systems, and heavy off-road equipment.
On output regulation for linear systems
Saberi, Ali; Stoorvogel, Antonie Arij; Sannuti, Peddapullaiah
For both continuous- and discrete-time systems, we revisit the output regulation problem for linear systems. We generalize the problem formulation in order • to expand the class of reference or disturbance signals, • to utilize the derivative or feedforward information of reference signals whenever
Linear response theory for quantum open systems
Wei, J. H.; Yan, YiJing
2011-01-01
Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a quantum open system at its steady-state, which can be applied to various fields of non-equilibrium condensed matter physics.
When to call a linear system nonnegative
Nieuwenhuis, J.W.
1998-01-01
In this paper we will consider discrete time invariant linear systems that allow for an input-state-output representation with a finite dimensional state space, and that have a finite number of inputs and outputs. The basic issue in this paper is when to call these systems nonnegative. An important
Tikhonov theorem for linear hyperbolic systems
Tang , Ying; Prieur , Christophe; Girard , Antoine
2015-01-01
International audience; A class of linear systems of conservation laws with a small perturbation parameter is introduced. By setting the perturbation parameter to zero, two subsystems, the reduced system standing for the slow dynamics and the boundary-layer system representing the fast dynamics, are computed. It is first proved that the exponential stability of the full system implies the stability of both subsystems. Secondly, a counter example is given to indicate that the converse is not t...
ITMETH, Iterative Routines for Linear System
International Nuclear Information System (INIS)
Greenbaum, A.
1989-01-01
1 - Description of program or function: ITMETH is a collection of iterative routines for solving large, sparse linear systems. 2 - Method of solution: ITMETH solves general linear systems of the form AX=B using a variety of methods: Jacobi iteration; Gauss-Seidel iteration; incomplete LU decomposition or matrix splitting with iterative refinement; diagonal scaling, matrix splitting, or incomplete LU decomposition with the conjugate gradient method for the problem AA'Y=B, X=A'Y; bi-conjugate gradient method with diagonal scaling, matrix splitting, or incomplete LU decomposition; and ortho-min method with diagonal scaling, matrix splitting, or incomplete LU decomposition. ITMETH also solves symmetric positive definite linear systems AX=B using the conjugate gradient method with diagonal scaling or matrix splitting, or the incomplete Cholesky conjugate gradient method
Conduction cooling systems for linear accelerator cavities
Kephart, Robert
2017-05-02
A conduction cooling system for linear accelerator cavities. The system conducts heat from the cavities to a refrigeration unit using at least one cavity cooler interconnected with a cooling connector. The cavity cooler and cooling connector are both made from solid material having a very high thermal conductivity of approximately 1.times.10.sup.4 W m.sup.-1 K.sup.-1 at temperatures of approximately 4 degrees K. This allows for very simple and effective conduction of waste heat from the linear accelerator cavities to the cavity cooler, along the cooling connector, and thence to the refrigeration unit.
Rf system specifications for a linear accelerator
International Nuclear Information System (INIS)
Young, A.; Eaton, L.E.
1992-01-01
A linear accelerator contains many systems; however, the most complex and costly is the RF system. The goal of an RF system is usually simply stated as maintaining the phase and amplitude of the RF signal within a given tolerance to accelerate the charged particle beam. An RF system that drives a linear accelerator needs a complete system specification, which should contain specifications for all the subsystems (i.e., high-power RF, low-level RF, RF generation/distribution, and automation control). This paper defines a format for the specifications of these subsystems and discusses each RF subsystem independently to provide a comprehensive understanding of the function of each subsystem. This paper concludes with an example of a specification spreadsheet allowing one to input the specifications of a subsystem. Thus, some fundamental parameters (i.e., the cost and size) of the RF system can be determined
Chaos as an intermittently forced linear system.
Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kaiser, Eurika; Kutz, J Nathan
2017-05-30
Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth's magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.
Final focus systems for linear colliders
International Nuclear Information System (INIS)
Helm, R.; Irwin, J.
1992-08-01
Final focus systems for linear colliders present many exacting challenges in beam optics, component design, and beam quality. Efforts to resolve these problems as they relate to a new generation of linear colliders are under way at several laboratories around the world. We will outline criteria for final focus systems and discuss the current state of understanding and resolution of the outstanding problems. We will discuss tolerances on alignment, field quality and stability for optical elements, and the implications for beam parameters such as emittance, energy spread, bunch length, and stability in position and energy. Beam-based correction procedures, which in principle can alleviate many of the tolerances, will be described. Preliminary results from the Final Focus Test Beam (FFTB) under construction at SLAC will be given. Finally, we mention conclusions from operating experience at the Stanford Linear Collider (SLC)
Final focus systems for linear colliders
International Nuclear Information System (INIS)
Helm, R.; Irwing, J.
1992-01-01
Final focus systems for linear colliders present many exacting challenges in beam optics, component design, and beam quality. Efforts to resolve these problems as they relate to a new generation of linear colliders are under way at several laboratories around the world. We outline criteria for final focus systems and discuss the current state of understanding and resolution of the outstanding problems. We discuss tolerances on alignment, field quality and stability for optical elements, and the implications for beam parameters such as emittance, energy spread , bunch length, and stability in position and energy. Beam-based correction procedures, which in principle can alleviate many of the tolerances, are described. Preliminary results from the Final Focus Test Beam (FFTB) under construction at SLAC are given. Finally, we mention conclusions from operating experience at the Stanford Linear Collider (SLC). (Author) 16 refs., 4 tabs., 6 figs
Dual-range linearized transimpedance amplifier system
Wessendorf, Kurt O.
2010-11-02
A transimpedance amplifier system is disclosed which simultaneously generates a low-gain output signal and a high-gain output signal from an input current signal using a single transimpedance amplifier having two different feedback loops with different amplification factors to generate two different output voltage signals. One of the feedback loops includes a resistor, and the other feedback loop includes another resistor in series with one or more diodes. The transimpedance amplifier system includes a signal linearizer to linearize one or both of the low- and high-gain output signals by scaling and adding the two output voltage signals from the transimpedance amplifier. The signal linearizer can be formed either as an analog device using one or two summing amplifiers, or alternately can be formed as a digital device using two analog-to-digital converters and a digital signal processor (e.g. a microprocessor or a computer).
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
Consys Linear Control System Design Software Package
International Nuclear Information System (INIS)
Diamantidis, Z.
1987-01-01
This package is created in order to help engineers, researchers, students and all who work on linear control systems. The software includes all time and frequency domain analysises, spectral analysises and networks, active filters and regulators design aids. The programmes are written on Hewlett Packard computer in Basic 4.0
Disturbance Decoupling of Switched Linear Systems
Yurtseven, E.; Heemels, W.P.M.H.; Camlibel, M.K.
2010-01-01
In this paper we consider disturbance decoupling problems for switched linear systems. We will provide necessary and sufficient conditions for three different versions of disturbance decoupling, which differ based on which signals are considered to be the disturbance. In the first version the
Uzawa method for fuzzy linear system
Ke Wang
2013-01-01
An Uzawa method is presented for solving fuzzy linear systems whose coefficient matrix is crisp and the right-hand side column is arbitrary fuzzy number vector. The explicit iterative scheme is given. The convergence is analyzed with convergence theorems and the optimal parameter is obtained. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.
The solution of linear systems of equations with a structural analysis code on the NAS CRAY-2
Poole, Eugene L.; Overman, Andrea L.
1988-01-01
Two methods for solving linear systems of equations on the NAS Cray-2 are described. One is a direct method; the other is an iterative method. Both methods exploit the architecture of the Cray-2, particularly the vectorization, and are aimed at structural analysis applications. To demonstrate and evaluate the methods, they were installed in a finite element structural analysis code denoted the Computational Structural Mechanics (CSM) Testbed. A description of the techniques used to integrate the two solvers into the Testbed is given. Storage schemes, memory requirements, operation counts, and reformatting procedures are discussed. Finally, results from the new methods are compared with results from the initial Testbed sparse Choleski equation solver for three structural analysis problems. The new direct solvers described achieve the highest computational rates of the methods compared. The new iterative methods are not able to achieve as high computation rates as the vectorized direct solvers but are best for well conditioned problems which require fewer iterations to converge to the solution.
Collimation systems in the next linear collider
International Nuclear Information System (INIS)
Merminga, N.; Irwin, J.; Helm, R.; Ruth, R.D.
1991-02-01
Experience indicates that beam collimation will be an essential element of the next generation e + E - linear colliders. A proposal for using nonlinear lenses to drive beam tails to large amplitudes was presented in a previous paper. Here we study the optimization of such systems including effects of wakefields and optical aberrations. Protection and design of the scrapers in these systems are discussed. 9 refs., 7 figs
Standard diffusive systems are well-posed linear systems
Matignon, Denis; Zwart, Heiko J.
2004-01-01
The class of well-posed linear systems as introduced by Salamon has become a well-understood class of systems, see e.g. the work of Weiss and the book of Staffans. Many partial partial differential equations with boundary control and point observation can be formulated as a well-posed linear system.
Parameter identifiability of linear dynamical systems
Glover, K.; Willems, J. C.
1974-01-01
It is assumed that the system matrices of a stationary linear dynamical system were parametrized by a set of unknown parameters. The question considered here is, when can such a set of unknown parameters be identified from the observed data? Conditions for the local identifiability of a parametrization are derived in three situations: (1) when input/output observations are made, (2) when there exists an unknown feedback matrix in the system and (3) when the system is assumed to be driven by white noise and only output observations are made. Also a sufficient condition for global identifiability is derived.
Stability problems for linear hyperbolic systems
International Nuclear Information System (INIS)
Eckhoff, K.S.
1975-05-01
The stability properties for the trivial solution of a general linear hyperbolic system of partial differential equations of the first order are studied. It is shown that results may be obtained by studying the stability properties of certain systems of ordinary differential equations which can be constructed from the hyperbolic system (the so-called transport equations). In some cases the associated stability problem for the transport equations can in fact be shown to be equivalent to the stability problem for the hyperbolic system, but in general the transport equations will only give the necessary conditions for stability. (Auth.)
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.
Identification of general linear mechanical systems
Sirlin, S. W.; Longman, R. W.; Juang, J. N.
1983-01-01
Previous work in identification theory has been concerned with the general first order time derivative form. Linear mechanical systems, a large and important class, naturally have a second order form. This paper utilizes this additional structural information for the purpose of identification. A realization is obtained from input-output data, and then knowledge of the system input, output, and inertia matrices is used to determine a set of linear equations whereby we identify the remaining unknown system matrices. Necessary and sufficient conditions on the number, type and placement of sensors and actuators are given which guarantee identificability, and less stringent conditions are given which guarantee generic identifiability. Both a priori identifiability and a posteriori identifiability are considered, i.e., identifiability being insured prior to obtaining data, and identifiability being assured with a given data set.
Linear systems optimal and robust control
Sinha, Alok
2007-01-01
Introduction Overview Contents of the Book State Space Description of a Linear System Transfer Function of a Single Input/Single Output (SISO) System State Space Realizations of a SISO System SISO Transfer Function from a State Space Realization Solution of State Space Equations Observability and Controllability of a SISO System Some Important Similarity Transformations Simultaneous Controllability and Observability Multiinput/Multioutput (MIMO) Systems State Space Realizations of a Transfer Function Matrix Controllability and Observability of a MIMO System Matrix-Fraction Description (MFD) MFD of a Transfer Function Matrix for the Minimal Order of a State Space Realization Controller Form Realization from a Right MFD Poles and Zeros of a MIMO Transfer Function Matrix Stability Analysis State Feedback Control and Optimization State Variable Feedback for a Single Input System Computation of State Feedback Gain Matrix for a Multiinput System State Feedback Gain Matrix for a Multi...
Lectures on algebraic system theory: Linear systems over rings
Kamen, E. W.
1978-01-01
The presentation centers on four classes of systems that can be treated as linear systems over a ring. These are: (1) discrete-time systems over a ring of scalars such as the integers; (2) continuous-time systems containing time delays; (3) large-scale discrete-time systems; and (4) time-varying discrete-time systems.
A finite different field solver for dipole modes
International Nuclear Information System (INIS)
Nelson, E.M.
1992-08-01
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
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
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.
An injection system for a linear accelerator
International Nuclear Information System (INIS)
Santos, A.C.R.
1978-03-01
An injection system for the Linear Accelerator is developed using the parameters of machines at the Centro Brasileiro de Pesquisas Fisicas and the Instituto Militar de Engenharia. The proposed system consists basically of a prebuncher and a chopper. The pre-buncher is used to improve the energy resolution and also to increase the accelerator target current. The chopper is used to remove from the beam the electrons that have no possibility of attaining the desired energy and that are usually lost in the walls and the cavity tube, thus producing undesirable background. Theoretical development of the chopper is performed in order to obtain its dimensions for future construction. The complete design the pre-buncher and its feed supply system and the experimental verication of its performance are also presented. It is intended to give the necessary information for the design and construction of the complete injection system proposed. (Author) [pt
Operator approach to linear control systems
Cheremensky, A
1996-01-01
Within the framework of the optimization problem for linear control systems with quadratic performance index (LQP), the operator approach allows the construction of a systems theory including a number of particular infinite-dimensional optimization problems with hardly visible concreteness. This approach yields interesting interpretations of these problems and more effective feedback design methods. This book is unique in its emphasis on developing methods for solving a sufficiently general LQP. Although this is complex material, the theory developed here is built on transparent and relatively simple principles, and readers with less experience in the field of operator theory will find enough material to give them a good overview of the current state of LQP theory and its applications. Audience: Graduate students and researchers in the fields of mathematical systems theory, operator theory, cybernetics, and control systems.
CSIR Research Space (South Africa)
Heyns, Johan A
2013-05-01
Full Text Available of the gas has a noteworthy effect on predicted pressure loads in liquid–gas flow in certain instances. With the aim of providing a more accurate numerical representation of dynamic two-fluid flow, the solver is subsequently extended to account for variations...
OSIRIS: a runge kutta solver of systems of ordinary differential equations
International Nuclear Information System (INIS)
Collin, M.; Schett, A.
1983-12-01
The Code OSIRIS (Order and Step Idently Adjusting Runge-Kutta Integrator of Systems) has been developed on the basis of both explicit as well as implicit Runge-Kutta processes of various orders: 4(5), 7(8), 8(9), 10 for explicit processes and 4 and 6 for implicit processes of the Rosenbrock type. This permits an optimization of the integration procedure by choosing the appropriate type of Runge-Kutta methods (explicit or implicit) and by adjusting dynamically the order of the process as well as the step-size. The performance of the Code OSIRIS is demonstrated by some representative examples and is compared with the Code GEAR which is applying multistep methods
Multiple solutions to dense systems in radar scattering using a preconditioned block GMRES solver
Energy Technology Data Exchange (ETDEWEB)
Boyse, W.E. [Advanced Software Resources, Inc., Santa Clara, CA (United States)
1996-12-31
Multiple right-hand sides occur in radar scattering calculations in the computation of the simulated radar return from a body at a large number of angles. Each desired angle requires a right-hand side vector to be computed and the solution generated. These right-hand sides are naturally smooth functions of the angle parameters and this property is utilized in a novel way to compute solutions an order of magnitude faster than LINPACK The modeling technique addressed is the Method of Moments (MOM), i.e. a boundary element method for time harmonic Maxwell`s equations. Discretization by this method produces general complex dense systems of rank 100`s to 100,000`s. The usual way to produce the required multiple solutions is via LU factorization and solution routines such as found in LINPACK. Our method uses the block GMRES iterative method to directly iterate a subset of the desired solutions to convergence.
Domain Decomposition Solvers for Frequency-Domain Finite Element Equations
Copeland, Dylan; Kolmbauer, Michael; Langer, Ulrich
2010-01-01
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.
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.
Iterative solution of large linear systems
Young, David Matheson
1971-01-01
This self-contained treatment offers a systematic development of the theory of iterative methods. Its focal point resides in an analysis of the convergence properties of the successive overrelaxation (SOR) method, as applied to a linear system with a consistently ordered matrix. The text explores the convergence properties of the SOR method and related techniques in terms of the spectral radii of the associated matrices as well as in terms of certain matrix norms. Contents include a review of matrix theory and general properties of iterative methods; SOR method and stationary modified SOR meth
a Continuous-Time Positive Linear System
Directory of Open Access Journals (Sweden)
Kyungsup Kim
2013-01-01
Full Text Available This paper discusses a computational method to construct positive realizations with sparse matrices for continuous-time positive linear systems with multiple complex poles. To construct a positive realization of a continuous-time system, we use a Markov sequence similar to the impulse response sequence that is used in the discrete-time case. The existence of the proposed positive realization can be analyzed with the concept of a polyhedral convex cone. We provide a constructive algorithm to compute positive realizations with sparse matrices of some positive systems under certain conditions. A sufficient condition for the existence of a positive realization, under which the proposed constructive algorithm works well, is analyzed.
International Nuclear Information System (INIS)
Petrila, Iulian; Bodale, Ilie; Rotarescu, Cristian; Stancu, Alexandru
2011-01-01
A comparative analysis between linear and non-linear energy barriers used for modeling statistical thermally-excited ferromagnetic systems is presented. The linear energy barrier is obtained by new symmetry considerations about the anisotropy energy and the link with the non-linear energy barrier is also presented. For a relevant analysis we compare the effects of linear and non-linear energy barriers implemented in two different models: Preisach-Neel and Ising-Metropolis. The differences between energy barriers which are reflected in different coercive field dependence of the temperature are also presented. -- Highlights: → The linear energy barrier is obtained from symmetry considerations. → The linear and non-linear energy barriers are calibrated and implemented in Preisach-Neel and Ising-Metropolis models. → The temperature and time effects of the linear and non-linear energy barriers are analyzed.
New approach to solve symmetric fully fuzzy linear systems
Indian Academy of Sciences (India)
concepts of fuzzy set theory and then define a fully fuzzy linear system of equations. .... To represent the above problem as fully fuzzy linear system, we represent x .... Fully fuzzy linear systems can be solved by Linear programming approach, ...
Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics
Pavarino, L.F.; Scacchi, S.; Zampini, Stefano
2015-01-01
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.
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.
Direct solvers performance on h-adapted grids
Paszynski, Maciej; Pardo, David; Calo, Victor M.
2015-01-01
We analyse the performance of direct solvers when applied to a system of linear equations arising from an hh-adapted, C0C0 finite element space. Theoretical estimates are derived for typical hh-refinement patterns arising as a result of a point, edge, or face singularity as well as boundary layers. They are based on the elimination trees constructed specifically for the considered grids. Theoretical estimates are compared with experiments performed with MUMPS using the nested-dissection algorithm for construction of the elimination tree from METIS library. The numerical experiments provide the same performance for the cases where our trees are identical with those constructed by the nested-dissection algorithm, and worse performance for some cases where our trees are different. We also present numerical experiments for the cases with mixed singularities, where how to construct optimal elimination trees is unknown. In all analysed cases, the use of hh-adaptive grids significantly reduces the cost of the direct solver algorithm per unknown as compared to uniform grids. The theoretical estimates predict and the experimental data confirm that the computational complexity is linear for various refinement patterns. In most cases, the cost of the direct solver per unknown is lower when employing anisotropic refinements as opposed to isotropic ones.
Direct solvers performance on h-adapted grids
Paszynski, Maciej
2015-05-27
We analyse the performance of direct solvers when applied to a system of linear equations arising from an hh-adapted, C0C0 finite element space. Theoretical estimates are derived for typical hh-refinement patterns arising as a result of a point, edge, or face singularity as well as boundary layers. They are based on the elimination trees constructed specifically for the considered grids. Theoretical estimates are compared with experiments performed with MUMPS using the nested-dissection algorithm for construction of the elimination tree from METIS library. The numerical experiments provide the same performance for the cases where our trees are identical with those constructed by the nested-dissection algorithm, and worse performance for some cases where our trees are different. We also present numerical experiments for the cases with mixed singularities, where how to construct optimal elimination trees is unknown. In all analysed cases, the use of hh-adaptive grids significantly reduces the cost of the direct solver algorithm per unknown as compared to uniform grids. The theoretical estimates predict and the experimental data confirm that the computational complexity is linear for various refinement patterns. In most cases, the cost of the direct solver per unknown is lower when employing anisotropic refinements as opposed to isotropic ones.
ROBUST MPC FOR STABLE LINEAR SYSTEMS
Directory of Open Access Journals (Sweden)
M.A. Rodrigues
2002-03-01
Full Text Available In this paper, a new model predictive controller (MPC, which is robust for a class of model uncertainties, is developed. Systems with stable dynamics and time-invariant model uncertainty are treated. The development herein proposed is focused on real industrial systems where the controller is part of an on-line optimization scheme and works in the output-tracking mode. In addition, the system has a time-varying number of degrees of freedom since some of the manipulated inputs may become constrained. Moreover, the number of controlled outputs may also vary during system operation. Consequently, the actual system may show operating conditions with a number of controlled outputs larger than the number of available manipulated inputs. The proposed controller uses a state-space model, which is aimed at the representation of the output-predicted trajectory. Based on this model, a cost function is proposed whereby the output error is integrated along an infinite prediction horizon. It is considered the case of multiple operating points, where the controller stabilizes a set of models corresponding to different operating conditions for the system. It is shown that closed-loop stability is guaranteed by the feasibility of a linear matrix optimization problem.
Optimal Control of Switching Linear Systems
Directory of Open Access Journals (Sweden)
Ali Benmerzouga
2004-06-01
Full Text Available A solution to the control of switching linear systems with input constraints was given in Benmerzouga (1997 for both the conventional enumeration approach and the new approach. The solution given there turned out to be not unique. The main objective in this work is to determine the optimal control sequences {Ui(k , i = 1,..., M ; k = 0, 1, ..., N -1} which transfer the system from a given initial state X0 to a specific target state XT (or to be as close as possible by using the same discrete time solution obtained in Benmerzouga (1997 and minimizing a running cost-to-go function. By using the dynamic programming technique, the optimal solution is found for both approaches given in Benmerzouga (1997. The computational complexity of the modified algorithm is also given.
Well logging system with linearity control
International Nuclear Information System (INIS)
Jones, J.M.
1973-01-01
Apparatus is described for controlling the gain of a nuclear well logging system comprising: (1) means for measuring the energy spectrum of gamma rays produced by earth formation materials surrounding a well borehole; (2) means for measuring the number of counts of a gamma rays having an energy falling within each of at least two predetermined energy band portions of the gamma ray energy spectrum; (3) means for generating a signal proportional to the ratio of the gamma ray counts and for comparing the ratio signal with at least one constant ratio calibration signal; (4) means for generating an error signal representative of the difference of the ratio signal and the constant ratio calibration signal; and (5) means for using the error signal to control the linearity of the well logging system. (author)
Linear concentration system; Sistema de concentracion lineal
Energy Technology Data Exchange (ETDEWEB)
Gonzalez Lugo, J.I; Leon Rovira, N; Aguayo Tellez, H [Instituto Tecnologico y de Estudios Superiores de Monterrey, Monterrey, Nuevo Leon (Mexico)]. E-mails: a00812662@itesm.mx; noel.leon@itesm.mx; haguayo@itesm.mx
2013-03-15
Solar linear concentration technologies to generate high temperatures are limited to the ranges of 200 to 500 degrees Celsius. While its performance has been tested through prototypes and pilot plants around the world, there are still areas of opportunity that can be exploited to obtain a linear concentration that achieves temperatures above this range in order to have a better use of the available solar energy. Because of this: It is possible to develop a linear concentration system that can track the sun with minimal movement of the absorber-receiver while maintaining temperatures above 850 degrees Celsius sufficient for industrial processes that require that temperature. The methodology consists of a series of stages (conceptual design, simulation, evaluation, development concept, results and validation) through which concepts are generated that allow design and evaluation of solar concentrator configurations with the help of simulation software. We have designed a linear parabolic concentrating system which comprises a set of mirrors segments with different focal lengths that works within the range of 600 degrees Celsius; however, it is advancing in the development of a double concentration to reach 850 degrees Celsius. [Spanish] Las tecnologias de concentracion lineal solar para generar altas temperaturas se ven limitadas a los rangos de 200 a 500 grados centigrados. Si bien su funcionamiento ha sido probado a traves de prototipos y plantas piloto alrededor del mundo, aun existen areas de oportunidad que pueden ser aprovechadas para obtener un sistema de concentracion lineal que permita alcanzar temperaturas mayores a este rango para asi tener un mejor aprovechamiento de la energia solar disponible. Debido a esto: Es posible desarrollar un sistema de concentracion lineal capaz de seguir la trayectoria del Sol con minimo movimiento del absorbedor-recibidor al mismo tiempo que mantiene temperaturas superiores a los 850 grados centigrados suficientes para
Linear Actuator System for the NASA Docking System
Dick, Brandon N.; Oesch, Christopher; Rupp, Timothy W.
2017-01-01
The Linear Actuator System (LAS) is a major sub-system within the NASA Docking System (NDS). The NDS Block 1 will be used on the Boeing Crew Space Transportation (CST-100) system to achieve docking with the International Space Station. Critical functions in the Soft Capture aspect of docking are performed by the LAS. This paper describes the general function of the LAS, the system's key requirements and technical challenges, and the development and qualification approach for the system.
Relative null controllability of linear systems with multiple delays in ...
African Journals Online (AJOL)
varying multiple delays in state and control are developed. If the uncontrolled system is uniformly asymptotically stable, and if the linear system is controllable, then the linear system is null controllable. Journal of the Nigerian Association of ...
Control system analysis for the perturbed linear accelerator rf system
Sung Il Kwon
2002-01-01
This paper addresses the modeling problem of the linear accelerator RF system in SNS. Klystrons are modeled as linear parameter varying systems. The effect of the high voltage power supply ripple on the klystron output voltage and the output phase is modeled as an additive disturbance. The cavity is modeled as a linear system and the beam current is modeled as the exogenous disturbance. The output uncertainty of the low level RF system which results from the uncertainties in the RF components and cabling is modeled as multiplicative uncertainty. Also, the feedback loop uncertainty and digital signal processing signal conditioning subsystem uncertainties are lumped together and are modeled as multiplicative uncertainty. Finally, the time delays in the loop are modeled as a lumped time delay. For the perturbed open loop system, the closed loop system performance, and stability are analyzed with the PI feedback controller.
CONTROL SYSTEM ANALYSIS FOR THE PERTURBED LINEAR ACCELERATOR RF SYSTEM
International Nuclear Information System (INIS)
SUNG-IL KWON; AMY H. REGAN
2002-01-01
This paper addresses the modeling problem of the linear accelerator RF system in SNS. Klystrons are modeled as linear parameter varying systems. The effect of the high voltage power supply ripple on the klystron output voltage and the output phase is modeled as an additive disturbance. The cavity is modeled as a linear system and the beam current is modeled as the exogenous disturbance. The output uncertainty of the low level RF system which results from the uncertainties in the RF components and cabling is modeled as multiplicative uncertainty. Also, the feedback loop uncertainty and digital signal processing signal conditioning subsystem uncertainties are lumped together and are modeled as multiplicative uncertainty. Finally, the time delays in the loop are modeled as a lumped time delay. For the perturbed open loop system, the closed loop system performance, and stability are analyzed with the PI feedback controller
Iterative solution of general sparse linear systems on clusters of workstations
Energy Technology Data Exchange (ETDEWEB)
Lo, Gen-Ching; Saad, Y. [Univ. of Minnesota, Minneapolis, MN (United States)
1996-12-31
Solving sparse irregularly structured linear systems on parallel platforms poses several challenges. First, sparsity makes it difficult to exploit data locality, whether in a distributed or shared memory environment. A second, perhaps more serious challenge, is to find efficient ways to precondition the system. Preconditioning techniques which have a large degree of parallelism, such as multicolor SSOR, often have a slower rate of convergence than their sequential counterparts. Finally, a number of other computational kernels such as inner products could ruin any gains gained from parallel speed-ups, and this is especially true on workstation clusters where start-up times may be high. In this paper we discuss these issues and report on our experience with PSPARSLIB, an on-going project for building a library of parallel iterative sparse matrix solvers.
Linear-array systems for aerospace NDE
International Nuclear Information System (INIS)
Smith, Robert A.; Willsher, Stephen J.; Bending, Jamie M.
1999-01-01
Rapid large-area inspection of composite structures for impact damage and multi-layered aluminum skins for corrosion has been a recognized priority for several years in both military and civil aerospace applications. Approaches to this requirement have followed two clearly different routes: the development of novel large-area inspection systems, and the enhancement of current ultrasonic or eddy-current methods to reduce inspection times. Ultrasonic inspection is possible with standard flaw detection equipment but the addition of a linear ultrasonic array could reduce inspection times considerably. In order to investigate their potential, 9-element and 17-element linear ultrasonic arrays for composites, and 64-element arrays for aluminum skins, have been developed to DERA specifications for use with the ANDSCAN area scanning system. A 5 m 2 composite wing surface has been scanned with a scan resolution of approximately 3 mm in 6 hours. With subsequent software and hardware improvements all four composite wing surfaces (top/bottom, left/right) of a military fighter aircraft can potentially be inspected in less than a day. Array technology has been very widely used in the medical ultrasound field although rarely above 10 MHz, whereas lap-joint inspection requires a pulse center-frequency of 12 to 20 MHz in order to resolve the separate interfaces in the lap joint. A 128 mm-long multi-element array of 5 mmx2 mm ultrasonic elements for use with the ANDSCAN scanning software was produced to a DERA specification by an NDT manufacturer with experience in the medical imaging field. This paper analyses the performance of the transducers that have been produced and evaluates their use in scanning systems of different configurations
High-Order Calderón Preconditioned Time Domain Integral Equation Solvers
Valdes, Felipe
2013-05-01
Two high-order accurate Calderón preconditioned time domain electric field integral equation (TDEFIE) solvers are presented. In contrast to existing Calderón preconditioned time domain solvers, the proposed preconditioner allows for high-order surface representations and current expansions by using a novel set of fully-localized high-order div-and quasi curl-conforming (DQCC) basis functions. Numerical results demonstrate that the linear systems of equations obtained using the proposed basis functions converge rapidly, regardless of the mesh density and of the order of the current expansion. © 1963-2012 IEEE.
High-Order Calderón Preconditioned Time Domain Integral Equation Solvers
Valdes, Felipe; Ghaffari-Miab, Mohsen; Andriulli, Francesco P.; Cools, Kristof; Michielssen,
2013-01-01
Two high-order accurate Calderón preconditioned time domain electric field integral equation (TDEFIE) solvers are presented. In contrast to existing Calderón preconditioned time domain solvers, the proposed preconditioner allows for high-order surface representations and current expansions by using a novel set of fully-localized high-order div-and quasi curl-conforming (DQCC) basis functions. Numerical results demonstrate that the linear systems of equations obtained using the proposed basis functions converge rapidly, regardless of the mesh density and of the order of the current expansion. © 1963-2012 IEEE.
Collier, Nathan; Pardo, David; Dalcí n, Lisandro D.; Paszyński, Maciej R.; Calo, Victor M.
2012-01-01
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.
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.
Model Predictive Control for Linear Complementarity and Extended Linear Complementarity Systems
Directory of Open Access Journals (Sweden)
Bambang Riyanto
2005-11-01
Full Text Available In this paper, we propose model predictive control method for linear complementarity and extended linear complementarity systems by formulating optimization along prediction horizon as mixed integer quadratic program. Such systems contain interaction between continuous dynamics and discrete event systems, and therefore, can be categorized as hybrid systems. As linear complementarity and extended linear complementarity systems finds applications in different research areas, such as impact mechanical systems, traffic control and process control, this work will contribute to the development of control design method for those areas as well, as shown by three given examples.
Thermodynamics of (1-alkanol + linear monoether) systems
International Nuclear Information System (INIS)
Gonzalez, Juan Antonio; Mozo, Ismael; Garcia de la Fuente, Isaias; Cobos, Jose Carlos; Riesco, Nicolas
2008-01-01
Densities, ρ, and speeds of sound, u, of systems formed by 1-heptanol, or 1-octanol, or 1-decanol and dibutylether have been measured at a temperature of (293.15, 298.15, and 303.15) K and atmospheric pressure using a vibrating tube densimeter and sound analyser Anton Paar model DSA-5000. The ρ and u values were used to calculate excess molar volumes, V E , and deviations from the ideal behaviour of the thermal expansion coefficient, Δα p and of the isentropic compressibilities, Δκ S . The available database on molar excess enthalpies, H E , and V E for (1-alkanol + linear monoether) systems was used to investigate interactional and structural effects in such mixtures. The enthalpy of the OH...O bonds is lower for methanol solutions, and for the remainder systems, it is practically independent of the mixture compounds. The V E variation with the chain length of the 1-alkanol points out the existence of structural effects for systems including longer 1-alkanols. The ERAS model is applied to the studied mixtures. ERAS represents quite accurately H E and V E data using parameters which consistently depend on the molecular structure
A Lagrangian meshfree method applied to linear and nonlinear elasticity.
Walker, Wade A
2017-01-01
The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code.
Identification problems in linear transformation system
International Nuclear Information System (INIS)
Delforge, Jacques.
1975-01-01
An attempt was made to solve the theoretical and numerical difficulties involved in the identification problem relative to the linear part of P. Delattre's theory of transformation systems. The theoretical difficulties are due to the very important problem of the uniqueness of the solution, which must be demonstrated in order to justify the value of the solution found. Simple criteria have been found when measurements are possible on all the equivalence classes, but the problem remains imperfectly solved when certain evolution curves are unknown. The numerical difficulties are of two kinds: a slow convergence of iterative methods and a strong repercussion of numerical and experimental errors on the solution. In the former case a fast convergence was obtained by transformation of the parametric space, while in the latter it was possible, from sensitivity functions, to estimate the errors, to define and measure the conditioning of the identification problem then to minimize this conditioning as a function of the experimental conditions [fr
Directory of Open Access Journals (Sweden)
Daniel Marcsa
2015-01-01
Full Text Available The analysis and design of electromechanical devices involve the solution of large sparse linear systems, and require therefore high performance algorithms. In this paper, the primal Domain Decomposition Method (DDM with parallel forward-backward and with parallel Preconditioned Conjugate Gradient (PCG solvers are introduced in two-dimensional parallel time-stepping finite element formulation to analyze rotating machine considering the electromagnetic field, external circuit and rotor movement. The proposed parallel direct and the iterative solver with two preconditioners are analyzed concerning its computational efficiency and number of iterations of the solver with different preconditioners. Simulation results of a rotating machine is also presented.
System theory as applied differential geometry. [linear system
Hermann, R.
1979-01-01
The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented.
Normal form of linear systems depending on parameters
International Nuclear Information System (INIS)
Nguyen Huynh Phan.
1995-12-01
In this paper we resolve completely the problem to find normal forms of linear systems depending on parameters for the feedback action that we have studied for the special case of controllable linear systems. (author). 24 refs
PWR control system design using advanced linear and non-linear methodologies
International Nuclear Information System (INIS)
Rabindran, N.; Whitmarsh-Everiss, M.J.
2004-01-01
Consideration is here given to the methodology deployed for non-linear heuristic analysis in the time domain supported by multi-variable linear control system design methods for the purposes of operational dynamics and control system analysis. This methodology is illustrated by the application of structural singular value μ analysis to Pressurised Water Reactor control system design. (author)
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.
Advanced Algebraic Multigrid Solvers for Subsurface Flow Simulation
Chen, Meng-Huo; Sun, Shuyu; Salama, Amgad
2015-01-01
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
Superconducting linear accelerator system for NSC
Indian Academy of Sciences (India)
This paper reports the construction of a superconducting linear accelerator as a booster to the 15 UD Pelletron accelerator at Nuclear Science Centre, New Delhi. The LINAC will use superconducting niobium quarter wave resonators as the accelerating element. Construction of the linear accelerator has progressed ...
Safari, A.; Sharifi, M. A.; Amjadiparvar, B.
2010-05-01
The GRACE mission has substantiated the low-low satellite-to-satellite tracking (LL-SST) concept. The LL-SST configuration can be combined with the previously realized high-low SST concept in the CHAMP mission to provide a much higher accuracy. The line of sight (LOS) acceleration difference between the GRACE satellite pair is the mostly used observable for mapping the global gravity field of the Earth in terms of spherical harmonic coefficients. In this paper, mathematical formulae for LOS acceleration difference observations have been derived and the corresponding linear system of equations has been set up for spherical harmonic up to degree and order 120. The total number of unknowns is 14641. Such a linear equation system can be solved with iterative solvers or direct solvers. However, the runtime of direct methods or that of iterative solvers without a suitable preconditioner increases tremendously. This is the reason why we need a more sophisticated method to solve the linear system of problems with a large number of unknowns. Multiplicative variant of the Schwarz alternating algorithm is a domain decomposition method, which allows it to split the normal matrix of the system into several smaller overlaped submatrices. In each iteration step the multiplicative variant of the Schwarz alternating algorithm solves linear systems with the matrices obtained from the splitting successively. It reduces both runtime and memory requirements drastically. In this paper we propose the Multiplicative Schwarz Alternating Algorithm (MSAA) for solving the large linear system of gravity field recovery. The proposed algorithm has been tested on the International Association of Geodesy (IAG)-simulated data of the GRACE mission. The achieved results indicate the validity and efficiency of the proposed algorithm in solving the linear system of equations from accuracy and runtime points of view. Keywords: Gravity field recovery, Multiplicative Schwarz Alternating Algorithm, Low
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.
Brouwer-Janse, M.D.
1991-01-01
Most formal problem-solving studies use verbal protocol and observational data of problem solvers working on a task. In user-centred product-design projects, observational studies of users are frequently used too. In the latter case, however, systematic control of conditions, indepth analysis and
Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.
1988-11-01
Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.
Symmetric linear systems - An application of algebraic systems theory
Hazewinkel, M.; Martin, C.
1983-01-01
Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.
Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.
1988-11-01
Many physical problems require the solution of coupled partial differential equations on three-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect induces which is vectorizable on some of the newer scientific computers.
A study on switched linear system identification using game ...
African Journals Online (AJOL)
A study on switched linear system identification using game-theoretic strategies and neural computing. ... This study deals with application of game-theoretic strategies and neural computing to switched linear ... AJOL African Journals Online.
Reduction of Linear Functional Systems using Fuhrmann's Equivalence
Directory of Open Access Journals (Sweden)
Mohamed S. Boudellioua
2016-11-01
Full Text Available Functional systems arise in the treatment of systems of partial differential equations, delay-differential equations, multidimensional equations, etc. The problem of reducing a linear functional system to a system containing fewer equations and unknowns was first studied by Serre. Finding an equivalent presentation of a linear functional system containing fewer equations and fewer unknowns can generally simplify both the study of the structural properties of the linear functional system and of different numerical analysis issues, and it can sometimes help in solving the linear functional system. In this paper, Fuhrmann's equivalence is used to present a constructive result on the reduction of under-determined linear functional systems to a single equation involving a single unknown. This equivalence transformation has been studied by a number of authors and has been shown to play an important role in the theory of linear functional systems.
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.
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...
How to Use Linear Programming for Information System Performances Optimization
Directory of Open Access Journals (Sweden)
Hell Marko
2014-09-01
Full Text Available Background: Organisations nowadays operate in a very dynamic environment, and therefore, their ability of continuously adjusting the strategic plan to the new conditions is a must for achieving their strategic objectives. BSC is a well-known methodology for measuring performances enabling organizations to learn how well they are doing. In this paper, “BSC for IS” will be proposed in order to measure the IS impact on the achievement of organizations’ business goals. Objectives: The objective of this paper is to present the original procedure which is used to enhance the BSC methodology in planning the optimal targets of IS performances value in order to maximize the organization's effectiveness. Methods/Approach: The method used in this paper is the quantitative methodology - linear programming. In the case study, linear programming is used for optimizing organization’s strategic performance. Results: Results are shown on the example of a case study national park. An optimal performance value for the strategic objective has been calculated, as well as an optimal performance value for each DO (derived objective. Results are calculated in Excel, using Solver Add-in. Conclusions: The presentation of methodology through the case study of a national park shows that this methodology, though it requires a high level of formalisation, provides a very transparent performance calculation.
High density linear systems for fusion power
International Nuclear Information System (INIS)
Ellis, W.R.; Krakowski, R.A.
1975-01-01
The physics and technological limitations and uncertainties associated with the linear theta pinch are discussed in terms of a generalized energy balance, which has as its basis the ratio (Q/sub E/) of total electrical energy generated to net electrical energy consumed. Included in this total is the virtual energy of bred fissile fuel, if a hybrid blanket is used, as well as the actual of real energy deposited in the blanket by the fusion neutron. The advantages and disadvantages of the pulsed operation demanded by the linear theta pinch are also discussed
Bernier, Caroline; Gazzola, Mattia; Ronsse, Renaud; Chatelain, Philippe
2017-11-01
We present a 2D fluid-structure interaction simulation method with a specific focus on articulated and actuated structures. The proposed algorithm combines a viscous Vortex Particle-Mesh (VPM) method based on a penalization technique and a Multi-Body System (MBS) solver. The hydrodynamic forces and moments acting on the structure parts are not computed explicitly from the surface stresses; they are rather recovered from the projection and penalization steps within the VPM method. The MBS solver accounts for the body dynamics via the Euler-Lagrange formalism. The deformations of the structure are dictated by the hydrodynamic efforts and actuation torques. Here, we focus on simplified swimming structures composed of neutrally buoyant ellipses connected by virtual joints. The joints are actuated through a simple controller in order to reproduce the swimming patterns of an eel-like swimmer. The method enables to recover the histories of torques applied on each hinge along the body. The method is verified on several benchmarks: an impulsively started elastically mounted cylinder and free swimming articulated fish-like structures. Validation will be performed by means of an experimental swimming robot that reproduces the 2D articulated ellipses.
Java Based Symbolic Circuit Solver For Electrical Engineering Curriculum
Directory of Open Access Journals (Sweden)
Ruba Akram Amarin
2012-11-01
Full Text Available The interactive technical electronic book, TechEBook, currently under development at the University of Central Florida (UCF, introduces a paradigm shift by replacing the traditional electrical engineering course with topic-driven modules that provide a useful tool for engineers and scientists. The TechEBook comprises the two worlds of classical circuit books and interactive operating platforms such as iPads, laptops and desktops. The TechEBook provides an interactive applets screen that holds many modules, each of which has a specific application in the self learning process. This paper describes one of the interactive techniques in the TechEBook known as Symbolic Circuit Solver (SymCirc. The SymCirc develops a versatile symbolic based linear circuit with a switches solver. The solver works by accepting a Netlist and the element that the user wants to find the voltage across or current on, as input parameters. Then it either produces the plot or the time domain expression of the output. Frequency domain plots or Symbolic Transfer Functions are also produced. The solver gets its input from a Web-based GUI circuit drawer developed at UCF. Typical simulation tools that electrical engineers encounter are numerical in nature, that is, when presented with an input circuit they iteratively solve the circuit across a set of small time steps. The result is represented as a data set of output versus time, which can be plotted for further inspection. Such results do not help users understand the ultimate nature of circuits as Linear Time Invariant systems with a finite dimensional basis in the solution space. SymCirc provides all simulation results as time domain expressions composed of the basic functions that exclusively include exponentials, sines, cosines and/or t raised to any power. This paper explains the motivation behind SymCirc, the Graphical User Interface front end and how the solver actually works. The paper also presents some examples and
Analysis of Linear Hybrid Systems in CLP
DEFF Research Database (Denmark)
Banda, Gourinath; Gallagher, John Patrick
2009-01-01
In this paper we present a procedure for representing the semantics of linear hybrid automata (LHAs) as constraint logic programs (CLP); flexible and accurate analysis and verification of LHAs can then be performed using generic CLP analysis and transformation tools. LHAs provide an expressive...
Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel
El-Gebeily, M.; Yushau, B.
2008-01-01
In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…
Robust Multiscale Iterative Solvers for Nonlinear Flows in Highly Heterogeneous Media
Efendiev, Y.
2012-08-01
In this paper, we study robust iterative solvers for finite element systems resulting in approximation of steady-state Richards\\' equation in porous media with highly heterogeneous conductivity fields. It is known that in such cases the contrast, ratio between the highest and lowest values of the conductivity, can adversely affect the performance of the preconditioners and, consequently, a design of robust preconditioners is important for many practical applications. The proposed iterative solvers consist of two kinds of iterations, outer and inner iterations. Outer iterations are designed to handle nonlinearities by linearizing the equation around the previous solution state. As a result of the linearization, a large-scale linear system needs to be solved. This linear system is solved iteratively (called inner iterations), and since it can have large variations in the coefficients, a robust preconditioner is needed. First, we show that under some assumptions the number of outer iterations is independent of the contrast. Second, based on the recently developed iterative methods, we construct a class of preconditioners that yields convergence rate that is independent of the contrast. Thus, the proposed iterative solvers are optimal with respect to the large variation in the physical parameters. Since the same preconditioner can be reused in every outer iteration, this provides an additional computational savings in the overall solution process. Numerical tests are presented to confirm the theoretical results. © 2012 Global-Science Press.
A SYSTEMIC VISION OF BIOLOGY: OVERCOMING LINEARITY
Directory of Open Access Journals (Sweden)
M. Mayer
2005-07-01
were used to build a hipermedia material. This technology permit overcomes a linear communication, improving the comprehension of the network perspective. The teachers speeches revealed their conceptual con- structions along the course, showed the development of the competences in identify interconnection points in the flow and chemical cycling of energy, compatible with a systemic view of life.
Solving Fully Fuzzy Linear System of Equations in General Form
Directory of Open Access Journals (Sweden)
A. Yousefzadeh
2012-06-01
Full Text Available In this work, we propose an approach for computing the positive solution of a fully fuzzy linear system where the coefficient matrix is a fuzzy $nimes n$ matrix. To do this, we use arithmetic operations on fuzzy numbers that introduced by Kaffman in and convert the fully fuzzy linear system into two $nimes n$ and $2nimes 2n$ crisp linear systems. If the solutions of these linear systems don't satisfy in positive fuzzy solution condition, we introduce the constrained least squares problem to obtain optimal fuzzy vector solution by applying the ranking function in given fully fuzzy linear system. Using our proposed method, the fully fuzzy linear system of equations always has a solution. Finally, we illustrate the efficiency of proposed method by solving some numerical examples.
Dynamics of unsymmetric piecewise-linear/non-linear systems using finite elements in time
Wang, Yu
1995-08-01
The dynamic response and stability of a single-degree-of-freedom system with unsymmetric piecewise-linear/non-linear stiffness are analyzed using the finite element method in the time domain. Based on a Hamilton's weak principle, this method provides a simple and efficient approach for predicting all possible fundamental and sub-periodic responses. The stability of the steady state response is determined by using Floquet's theory without any special effort for calculating transition matrices. This method is applied to a number of examples, demonstrating its effectiveness even for a strongly non-linear problem involving both clearance and continuous stiffness non-linearities. Close agreement is found between available published findings and the predictions of the finite element in time approach, which appears to be an efficient and reliable alternative technique for non-linear dynamic response and stability analysis of periodic systems.
Reliability modelling and simulation of switched linear system ...
African Journals Online (AJOL)
Reliability modelling and simulation of switched linear system control using temporal databases. ... design of fault-tolerant real-time switching systems control and modelling embedded micro-schedulers for complex systems maintenance.
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.
Energy balance in a system with quasispherical linear compression
International Nuclear Information System (INIS)
Es'kov, A.G.; Kozlov, N.P.; Kurtmullaev, R.K.; Semenov, V.N.; Khvesyuk, V.I.; Yaminskii, A.V.
1983-01-01
This letter reports the resists of some experimental studies and a numerical simulation of the Tor-linear fusion system, 1 in which a heavy plasma shell with a closed magnetic structure is compressed in a quasispherical manner. The parameters of the Tor-Linear, at the Kurchatov Institute of Atomic Energy in Moscow are as follows: The energy stored in the system which accelerates the linear is E = 0.5 MJ; the linear mass is m = 0.2 kg; the working volume of the linear module is 1.5 x 10 -3 m 3 ; the linear velocity is approx.10 3 m/s; the guiding field in the toriod in the linear is 1--10 x 10 21 m -3 ; and the intial volume of the plasma in the linear chamber is 2.5 x 10 -4 m 3 . In this series of experiments, new solutions were developed for all the systems of the plasma--linear complex of the Tor-Linear: to produce a plasma toroid, to transport it, and to trap it in the linear cavity
A Proposed Method for Solving Fuzzy System of Linear Equations
Directory of Open Access Journals (Sweden)
Reza Kargar
2014-01-01
Full Text Available This paper proposes a new method for solving fuzzy system of linear equations with crisp coefficients matrix and fuzzy or interval right hand side. Some conditions for the existence of a fuzzy or interval solution of m×n linear system are derived and also a practical algorithm is introduced in detail. The method is based on linear programming problem. Finally the applicability of the proposed method is illustrated by some numerical examples.
Pilkey, W. D.; Chen, Y. H.
1974-01-01
An indirect synthesis method is used in the efficient optimal design of multi-degree of freedom, multi-design element, nonlinear, transient systems. A limiting performance analysis which requires linear programming for a kinematically linear system is presented. The system is selected using system identification methods such that the designed system responds as closely as possible to the limiting performance. The efficiency is a result of the method avoiding the repetitive systems analyses accompanying other numerical optimization methods.
Minimal solution of general dual fuzzy linear systems
International Nuclear Information System (INIS)
Abbasbandy, S.; Otadi, M.; Mosleh, M.
2008-01-01
Fuzzy linear systems of equations, play a major role in several applications in various area such as engineering, physics and economics. In this paper, we investigate the existence of a minimal solution of general dual fuzzy linear equation systems. Two necessary and sufficient conditions for the minimal solution existence are given. Also, some examples in engineering and economic are considered
Partial Linearization of Mechanical Systems with Application to Observer Design
Sarras, Ioannis; Venkatraman, Aneesh; Ortega, Romeo; Schaft, Arjan van der
2008-01-01
We consider general mechanical systems and establish a necessary and sufficient condition for the existence of a suitable change in the generalized momentum coordinates such that the new dynamics become linear in the transformed momenta. The class of systems which can be (partially) linearized by
Simultaneous Balancing and Model Reduction of Switched Linear Systems
Monshizadeh, Nima; Trentelman, Hendrikus; Camlibel, M.K.
2011-01-01
In this paper, first, balanced truncation of linear systems is revisited. Then, simultaneous balancing of multiple linear systems is investigated. Necessary and sufficient conditions are introduced to identify the case where simultaneous balancing is possible. The validity of these conditions is not
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
Linear System Control Using Stochastic Learning Automata
Ziyad, Nigel; Cox, E. Lucien; Chouikha, Mohamed F.
1998-01-01
This paper explains the use of a Stochastic Learning Automata (SLA) to control switching between three systems to produce the desired output response. The SLA learns the optimal choice of the damping ratio for each system to achieve a desired result. We show that the SLA can learn these states for the control of an unknown system with the proper choice of the error criteria. The results of using a single automaton are compared to using multiple automata.
Useful tools for non-linear systems: Several non-linear integral inequalities
Czech Academy of Sciences Publication Activity Database
Agahi, H.; Mohammadpour, A.; Mesiar, Radko; Vaezpour, M. S.
2013-01-01
Roč. 49, č. 1 (2013), s. 73-80 ISSN 0950-7051 R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : Monotone measure * Comonotone functions * Integral inequalities * Universal integral Subject RIV: BA - General Mathematics Impact factor: 3.058, year: 2013 http://library.utia.cas.cz/separaty/2013/E/mesiar-useful tools for non-linear systems several non-linear integral inequalities.pdf
Decentralized linear quadratic power system stabilizers for multi ...
Indian Academy of Sciences (India)
Introduction. Modern excitation systems considerably enhance the overall transient stability of power systems ..... to the local bus rather than the angle δ measured with respect to the remote bus. ... With this in view, the linear and nonlinear per-.
Extending the QUDA Library with the eigCG Solver
Energy Technology Data Exchange (ETDEWEB)
Strelchenko, Alexei [Fermilab; Stathopoulos, Andreas [William-Mary Coll.
2014-12-12
While the incremental eigCG algorithm [ 1 ] is included in many LQCD software packages, its realization on GPU micro-architectures was still missing. In this session we report our experi- ence of the eigCG implementation in the QUDA library. In particular, we will focus on how to employ the mixed precision technique to accelerate solutions of large sparse linear systems with multiple right-hand sides on GPUs. Although application of mixed precision techniques is a well-known optimization approach for linear solvers, its utilization for the eigenvector com- puting within eigCG requires special consideration. We will discuss implementation aspects of the mixed precision deflation and illustrate its numerical behavior on the example of the Wilson twisted mass fermion matrix inversions
A new active absorption system and its performance to linear and non-linear waves
DEFF Research Database (Denmark)
Andersen, Thomas Lykke; Clavero, M.; Frigaard, Peter Bak
2016-01-01
Highlights •An active absorption system for wavemakers has been developed. •The theory for flush mounted gauges has been extended to cover also small gaps. •The new system has been validated in a wave flume with wavemakers in both ends. •A generation and absorption procedure for highly non-linear...
On Optimal Feedback Control for Stationary Linear Systems
International Nuclear Information System (INIS)
Russell, David L.
2010-01-01
We study linear-quadratic optimal control problems for finite dimensional stationary linear systems AX+BU=Z with output Y=CX+DU from the viewpoint of linear feedback solution. We interpret solutions in relation to system robustness with respect to disturbances Z and relate them to nonlinear matrix equations of Riccati type and eigenvalue-eigenvector problems for the corresponding Hamiltonian system. Examples are included along with an indication of extensions to continuous, i.e., infinite dimensional, systems, primarily of elliptic type.
Virtual Estimator for Piecewise Linear Systems Based on Observability Analysis
Morales-Morales, Cornelio; Adam-Medina, Manuel; Cervantes, Ilse; Vela-Valdés and, Luis G.; García Beltrán, Carlos Daniel
2013-01-01
This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system's outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article proposes a set of virtual estimators that discern the commutation paths of the system and allow estimating their output. In this work a methodology in order to test the observability for piecewise linear systems with discrete time is proposed. An academic example is presented to show the obtained results. PMID:23447007
A Numerical Study of Scalable Cardiac Electro-Mechanical Solvers on HPC Architectures
Directory of Open Access Journals (Sweden)
Piero Colli Franzone
2018-04-01
Full Text Available We introduce and study some scalable domain decomposition preconditioners for cardiac electro-mechanical 3D simulations on parallel HPC (High Performance Computing architectures. The electro-mechanical model of the cardiac tissue is composed of four coupled sub-models: (1 the static finite elasticity equations for the transversely isotropic deformation of the cardiac tissue; (2 the active tension model describing the dynamics of the intracellular calcium, cross-bridge binding and myofilament tension; (3 the anisotropic Bidomain model describing the evolution of the intra- and extra-cellular potentials in the deforming cardiac tissue; and (4 the ionic membrane model describing the dynamics of ionic currents, gating variables, ionic concentrations and stretch-activated channels. This strongly coupled electro-mechanical model is discretized in time with a splitting semi-implicit technique and in space with isoparametric finite elements. The resulting scalable parallel solver is based on Multilevel Additive Schwarz preconditioners for the solution of the Bidomain system and on BDDC preconditioned Newton-Krylov solvers for the non-linear finite elasticity system. The results of several 3D parallel simulations show the scalability of both linear and non-linear solvers and their application to the study of both physiological excitation-contraction cardiac dynamics and re-entrant waves in the presence of different mechano-electrical feedbacks.
Gradient remediability in linear distributed parabolic systems ...
African Journals Online (AJOL)
The aim of this paper is the introduction of a new concept that concerned the analysis of a large class of distributed parabolic systems. It is the general concept of gradient remediability. More precisely, we study with respect to the gradient observation, the existence of an input operator (gradient efficient actuators) ensuring ...
Linearization of Nonautonomous Impulsive System with Nonuniform Exponential Dichotomy
Directory of Open Access Journals (Sweden)
Yongfei Gao
2014-01-01
Full Text Available This paper gives a version of Hartman-Grobman theorem for the impulsive differential equations. We assume that the linear impulsive system has a nonuniform exponential dichotomy. Under some suitable conditions, we proved that the nonlinear impulsive system is topologically conjugated to its linear system. Indeed, we do construct the topologically equivalent function (the transformation. Moreover, the method to prove the topological conjugacy is quite different from those in previous works (e.g., see Barreira and Valls, 2006.
On the discretization of linear fractional representations of LPV systems
Toth, R.; Lovera, M.; Heuberger, P.S.C.; Corno, M.; Hof, Van den P.M.J.
2012-01-01
Commonly, controllers for linear parameter-varying (LPV) systems are designed in continuous time using a linear fractional representation (LFR) of the plant. However, the resulting controllers are implemented on digital hardware. Furthermore, discrete-time LPV synthesis approaches require a
Automatic frequency control system for driving a linear accelerator
International Nuclear Information System (INIS)
Helgesson, A.L.
1976-01-01
An automatic frequency control system is described for maintaining the drive frequency applied to a linear accelerator to produce maximum particle output from the accelerator. The particle output amplitude is measured and the frequency of the radio frequency source powering the linear accelerator is adjusted to maximize particle output amplitude
Feedback linearizing control of a MIMO power system
Ilyes, Laszlo
Prior research has demonstrated that either the mechanical or electrical subsystem of a synchronous electric generator may be controlled using single-input single-output (SISO) nonlinear feedback linearization. This research suggests a new approach which applies nonlinear feedback linearization to a multi-input multi-output (MIMO) model of the synchronous electric generator connected to an infinite bus load model. In this way, the electrical and mechanical subsystems may be linearized and simultaneously decoupled through the introduction of a pair of auxiliary inputs. This allows well known, linear, SISO control methods to be effectively applied to the resulting systems. The derivation of the feedback linearizing control law is presented in detail, including a discussion on the use of symbolic math processing as a development tool. The linearizing and decoupling properties of the control law are validated through simulation. And finally, the robustness of the control law is demonstrated.
Portable, x-band, linear accelerator systems
International Nuclear Information System (INIS)
Schonberg, R.G.; Deruyter, H.; Fowkes, W.R.; Johnson, W.A.; Miller, R.H.; Potter, J.M.; Weaver, J.N.
1985-01-01
Three light-weight, x-band, electron accelerators have been developed to provide a series of highly portable sources of x-rays and neutrons for nondestructive testing. The 1.5 MeV x-ray unit has a 200 kW magnetron for an RF source and an air-cooled, traveling wave accelerating structure to minimize its weight. The 4 and 6 MeV units share the same drive system which contains a 1.2 MW magnetron. The 4 MeV unit uses a traveling-wave guide to produce x-rays and the 6MeV unit uses a standing-wave guide to produce x-rays or neutrons. The choice of 9.3 GHz was dictated by the availability of a high power coaxial magnetron and by the obvious dimensional and weight advantages of a higher frequency over the more common S-band frequencies around 3 GHz
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.
Structure Learning in Stochastic Non-linear Dynamical Systems
Morris, R. D.; Smelyanskiy, V. N.; Luchinsky, D. G.
2005-12-01
A great many systems can be modeled in the non-linear dynamical systems framework, as x˙ = f(x) + ξ(t), where f(x) is the potential function for the system, and ξ(t) is the driving noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications, for example in predator-prey systems, where the very structure of the coupling between predator-prey pairs can have great ecological significance.
Portable, x-band, linear accelerator systems
International Nuclear Information System (INIS)
Schonberg, R.G.; Deruyter, H.; Fowkes, W.R.; Johnson, W.A.; Miller, R.H.; Potter, J.M.; Weaver, J.N.
1985-01-01
Three light-weight, x-band, electron accelerators have been developed to provide a series of highly portable sources of x-rays and neutrons for non-destructive testing. The 1.5 MeV x-ray unit has a 200 kW magnetron for an RF source and an air-cooled, traveling wave accelerating structure to minimize its weight. The 4 and 6 MeV units share the same drive system which contains a 1.2 MW magnetron. The 4 MeV unit uses a traveling-wave guide to produce x-rays and the 6MeV unit uses a standing-wave guide to produce x-rays or neutrons. The choice of 9.3 GHz was dictated by the availability of a high power coaxial magnetron and by the obvious dimensional and weight advantages of a higher frequency over the more common S-band frequencies around 3 GHz
Linear quadratic Gaussian balancing for discrete-time infinite-dimensional linear systems
Opmeer, MR; Curtain, RF
2004-01-01
In this paper, we study the existence of linear quadratic Gaussian (LQG)-balanced realizations for discrete-time infinite-dimensional systems. LQG-balanced realizations are those for which the smallest nonnegative self-adjoint solutions of the control and filter Riccati equations are equal. We show
Perfect commuting-operator strategies for linear system games
Cleve, Richard; Liu, Li; Slofstra, William
2017-01-01
Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators. We show that perfect strategies in this model correspond to possibly infinite-dimensional operator solutions of the non-commutative equations. The proof is based around a finitely presented group associated with the linear system which arises from the non-commutative equations.
A conceptual design of Final Focus Systems for linear colliders
International Nuclear Information System (INIS)
Brown, K.L.
1987-06-01
Linear colliders are a relatively recent development in the evolution of particle accelerators. This report discusses some of the approaches that have been considered for the design of Final Focus Systems to demagnify the beam exiting from a linac to the small size suitable for collisions at the interaction point. The system receiving the most attention is the one adopted for the SLAC Linear Collider. However, the theory and optical techniques discussed should be applicable to the design efforts for future machines
ON THE STABILIZATION OF THE LINEAR HYBRID SYSTEM STRUCTURE
Directory of Open Access Journals (Sweden)
Kirillov
2014-11-01
Full Text Available The linear control hybrid system, consisting of a fi- nite set of subsystems (modes having different dimensions, is considered. The moments of reset time are determined by some complementary function – evolutionary time. This function satisfies the special complementary ordinary differential equation. The mode stabilization problem is solved for some class of piecewise linear controls. The method of stabilization relies on the set of invariant planes, the existence of which is due to the special form of the hybrid system.
Iterative algorithms for large sparse linear systems on parallel computers
Adams, L. M.
1982-01-01
Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.
Simultaneous Balancing and Model Reduction of Switched Linear Systems
Monshizadeh, Nima; Trentelman, Hendrikus; Camlibel, M.K.
2011-01-01
In this paper, first, balanced truncation of linear systems is revisited. Then, simultaneous balancing of multiple linear systems is investigated. Necessary and sufficient conditions are introduced to identify the case where simultaneous balancing is possible. The validity of these conditions is not limited to a certain type of balancing, and they are applicable for different types of balancing corresponding to different equations, like Lyapunov or Riccati equations. The results obtained are ...
Solar photovoltaic water pumping system using a new linear actuator
Andrada Gascón, Pedro; Castro, Javier
2007-01-01
In this paper a photovoltaic solar pumping system using a new linear actuator is presented. This linear actuator is a double-sided flat two-phase variable-reluctance linear stepper motor that moves a piston-type water pump with the help of a rope, a pulley and a counterweight. The entire actuator pump ensemble is controlled by a simple electronic unit that manages the electric power generated by a photovoltaic array. The proposed system is suitable for rural communities in developing...
Computational aeroelasticity using a pressure-based solver
Kamakoti, Ramji
A computational methodology for performing fluid-structure interaction computations for three-dimensional elastic wing geometries is presented. The flow solver used is based on an unsteady Reynolds-Averaged Navier-Stokes (RANS) model. A well validated k-ε turbulence model with wall function treatment for near wall region was used to perform turbulent flow calculations. Relative merits of alternative flow solvers were investigated. The predictor-corrector-based Pressure Implicit Splitting of Operators (PISO) algorithm was found to be computationally economic for unsteady flow computations. Wing structure was modeled using Bernoulli-Euler beam theory. A fully implicit time-marching scheme (using the Newmark integration method) was used to integrate the equations of motion for structure. Bilinear interpolation and linear extrapolation techniques were used to transfer necessary information between fluid and structure solvers. Geometry deformation was accounted for by using a moving boundary module. The moving grid capability was based on a master/slave concept and transfinite interpolation techniques. Since computations were performed on a moving mesh system, the geometric conservation law must be preserved. This is achieved by appropriately evaluating the Jacobian values associated with each cell. Accurate computation of contravariant velocities for unsteady flows using the momentum interpolation method on collocated, curvilinear grids was also addressed. Flutter computations were performed for the AGARD 445.6 wing at subsonic, transonic and supersonic Mach numbers. Unsteady computations were performed at various dynamic pressures to predict the flutter boundary. Results showed favorable agreement of experiment and previous numerical results. The computational methodology exhibited capabilities to predict both qualitative and quantitative features of aeroelasticity.
Phase and amplitude detection system for the Stanford Linear Accelerator
International Nuclear Information System (INIS)
Fox, J.D.; Schwarz, H.D.
1983-01-01
A computer controlled phase and amplitude detection system to measure and stabilize the rf power sources in the Stanford Linear Accelerator is described. This system measures the instantaneous phase and amplitude of a 1 microsecond 2856 MHz rf pulse and will be used for phase feedback control and for amplitude and phase jitter detection. This paper discusses the measurement system performance requirements for the operation of the Stanford Linear Collider, and the design and implementation of the phase and amplitude detection system. The fundamental software algorithms used in the measurement are described, as is the performance of the prototype phase and amplitude detector system
International Nuclear Information System (INIS)
Chen, H.-H.; Chen, C.-S.; Lee, C.-I
2009-01-01
This paper investigates the synchronization of unidirectional and bidirectional coupled unified chaotic systems. A balanced coupling coefficient control method is presented for global asymptotic synchronization using the Lyapunov stability theorem and a minimum scheme with no constraints/constraints. By using the result of the above analysis, the balanced coupling coefficients are then designed to achieve the chaos synchronization of linearly coupled unified chaotic systems. The feasibility and effectiveness of the proposed chaos synchronization scheme are verified via numerical simulations.
Solution of generalized shifted linear systems with complex symmetric matrices
International Nuclear Information System (INIS)
Sogabe, Tomohiro; Hoshi, Takeo; Zhang, Shao-Liang; Fujiwara, Takeo
2012-01-01
We develop the shifted COCG method [R. Takayama, T. Hoshi, T. Sogabe, S.-L. Zhang, T. Fujiwara, Linear algebraic calculation of Green’s function for large-scale electronic structure theory, Phys. Rev. B 73 (165108) (2006) 1–9] and the shifted WQMR method [T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara, On a weighted quasi-residual minimization strategy of the QMR method for solving complex symmetric shifted linear systems, Electron. Trans. Numer. Anal. 31 (2008) 126–140] for solving generalized shifted linear systems with complex symmetric matrices that arise from the electronic structure theory. The complex symmetric Lanczos process with a suitable bilinear form plays an important role in the development of the methods. The numerical examples indicate that the methods are highly attractive when the inner linear systems can efficiently be solved.
Economic MPC for a linear stochastic system of energy units
DEFF Research Database (Denmark)
Jørgensen, John Bagterp; Sokoler, Leo Emil; Standardi, Laura
2016-01-01
This paper summarizes comprehensively the work in four recent PhD theses from the Technical University of Denmark related to Economic MPC of future power systems. Future power systems will consist of a large number of decentralized power producers and a large number of controllable power consumers...... in addition to stochastic power producers such as wind turbines and solar power plants. Control of such large scale systems requires new control algorithms. In this paper, we formulate the control of such a system as an Economic Model Predictive Control (MPC) problem. When the power producers and controllable...... power consumers have linear dynamics, the Economic MPC may be expressed as a linear program. We provide linear models for a number of energy units in an energy system, formulate an Economic MPC for coordination of such a system. We indicate how advances in computational MPC makes the solutions...
Stability analysis of switched linear systems defined by graphs
Athanasopoulos, N.; Lazar, M.
2014-01-01
We present necessary and sufficient conditions for global exponential stability for switched discrete-time linear systems, under arbitrary switching, which is constrained within a set of admissible transitions. The class of systems studied includes the family of systems under arbitrary switching,
Euclidean null controllability of linear systems with delays in state ...
African Journals Online (AJOL)
Sufficient conditions are developed for the Euclidean controllability of linear systems with delay in state and in control. Namely, if the uncontrolled system is uniformly asymptotically stable and the control equation proper, then the control system is Euclidean null controllable. Journal of the Nigerian Association of ...
Incremental Closed-loop Identification of Linear Parameter Varying Systems
DEFF Research Database (Denmark)
Bendtsen, Jan Dimon; Trangbæk, Klaus
2011-01-01
, closed-loop system identification is more difficult than open-loop identification. In this paper we prove that the so-called Hansen Scheme, a technique known from linear time-invariant systems theory for transforming closed-loop system identification problems into open-loop-like problems, can be extended...
Stability and response bounds of non-conservative linear systems
DEFF Research Database (Denmark)
Pommer, Christian
2003-01-01
For a linear system of second order differential equations the stability is studied by Lyapunov's direct method. The Lyapunov matrix equation is solved and a sufficient condition for stability is expressed by the system matrices. For a system which satisfies the condition for stability the Lyapunov...
Linear Optimization of Frequency Spectrum Assignments Across System
2016-03-01
selection tools, frequency allocation, transmission optimization, electromagnetic maneuver warfare, electronic protection, assignment model 15. NUMBER ...Characteristics Modeled ...............................................................29 Table 10. Antenna Systems Modeled , Number of Systems and...surveillance EW early warning GAMS general algebraic modeling system GHz gigahertz IDE integrated development environment ILP integer linear program
Stability analysis of switched linear systems defined by graphs
Athanasopoulos, Nikolaos; Lazar, Mircea
2015-01-01
We present necessary and sufficient conditions for global exponential stability for switched discrete-time linear systems, under arbitrary switching, which is constrained within a set of admissible transitions. The class of systems studied includes the family of systems under arbitrary switching, periodic systems, and systems with minimum and maximum dwell time specifications. To reach the result, we describe the set of rules that define the admissible transitions with a weighted directed gra...
Modeling and analysis of linear hyperbolic systems of balance laws
Bartecki, Krzysztof
2016-01-01
This monograph focuses on the mathematical modeling of distributed parameter systems in which mass/energy transport or wave propagation phenomena occur and which are described by partial differential equations of hyperbolic type. The case of linear (or linearized) 2 x 2 hyperbolic systems of balance laws is considered, i.e., systems described by two coupled linear partial differential equations with two variables representing physical quantities, depending on both time and one-dimensional spatial variable. Based on practical examples of a double-pipe heat exchanger and a transportation pipeline, two typical configurations of boundary input signals are analyzed: collocated, wherein both signals affect the system at the same spatial point, and anti-collocated, in which the input signals are applied to the two different end points of the system. The results of this book emerge from the practical experience of the author gained during his studies conducted in the experimental installation of a heat exchange cente...
A convex optimization approach for solving large scale linear systems
Directory of Open Access Journals (Sweden)
Debora Cores
2017-01-01
Full Text Available The well-known Conjugate Gradient (CG method minimizes a strictly convex quadratic function for solving large-scale linear system of equations when the coefficient matrix is symmetric and positive definite. In this work we present and analyze a non-quadratic convex function for solving any large-scale linear system of equations regardless of the characteristics of the coefficient matrix. For finding the global minimizers, of this new convex function, any low-cost iterative optimization technique could be applied. In particular, we propose to use the low-cost globally convergent Spectral Projected Gradient (SPG method, which allow us to extend this optimization approach for solving consistent square and rectangular linear system, as well as linear feasibility problem, with and without convex constraints and with and without preconditioning strategies. Our numerical results indicate that the new scheme outperforms state-of-the-art iterative techniques for solving linear systems when the symmetric part of the coefficient matrix is indefinite, and also for solving linear feasibility problems.
A comparison between linear and toroidal Extrap systems
International Nuclear Information System (INIS)
Lehnert, B.
1988-09-01
The Extrap scheme consists of a Z-pinch immersed in an octupole field generated by currents in a set of external conductors. A comparison between linear and toroidal Extrap geometry is made in this paper. As compared to toroidal systems, linear geometry has the advantages of relative simplicity and of a current drive by means of electrodes. Linear devices are convenient for basic studies of Extrap, at moderately high pinch currents and plasma temperatures. Within the parameter ranges of experiments at high pinch currents and plasma temperatures, linear systems have on the other hand some substantial disadvantages, on account of the plasma interaction with the end regions. This results in a limitation of the energy confinement time, and leads in the case of an ohmically heated plasma to excessively high plasma densities and small pinch radii which also complicate the introduction of the external conductors. (author)
Linear local stability of electrostatic drift modes in helical systems
International Nuclear Information System (INIS)
Yamagishi, O.; Nakajima, N.; Sugama, H.; Nakamura, Y.
2003-01-01
We investigate the stability of the drift wave in helical systems. For this purpose, we solve the linear local gyrokinetic-Poisson equation, in the electrostatic regime. As a model of helical plasmas, Large helical Device (LHD) is considered. The equation we apply is rather exact in the framework of linear gyrokinetic theory, where only the approximation is the ballooning representation. In this paper, we consider only collisionless cases. All the frequency regime can be naturally reated without any assumptions, and in such cases, ion temperature gradient modes (ITG), trapped electron modes (TEM), and electron temperature gradient modes (ETG) are expected to become unstable linearly independently. (orig.)
H 2 guaranteed cost control of discrete linear systems
Directory of Open Access Journals (Sweden)
Colmenares W.
2000-01-01
Full Text Available This paper presents necessary and sufficient conditions for the existence of a quadratically stabilizing output feedback controller which also assures H 2 guaranteed cost performance on a discrete linear uncertain system where the uncertainty is of the norm bounded type. The conditions are presented as a collection of linear matrix inequalities.The solution, however requires a search over a scalar parameter space.
Structured Control of Affine Linear Parameter Varying Systems
DEFF Research Database (Denmark)
Adegas, Fabiano Daher; Stoustrup, Jakob
2011-01-01
This paper presents a new procedure to design structured controllers for discrete-time afﬁne linear parametervarying systems (A LPV). The class of control structures includes decentralized of any order, ﬁxed order output feedback, simultaneous plant-control design, among others. A parametervarying...... non-convex condition for an upper bound on the induced L2-norm performance is solved by an iterative linear matrix inequalities (LMI) optimization algorithm. Numerical examples demostrate the effectiveness of the proposed approach....
International Nuclear Information System (INIS)
Anton, Luis; MartI, Jose M; Ibanez, Jose M; Aloy, Miguel A.; Mimica, Petar; Miralles, Juan A.
2010-01-01
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.
On the stability of non-linear systems
International Nuclear Information System (INIS)
Guelman, M.
1968-09-01
A study is made of the absolute stability of nonlinear systems, using Liapounov's second method and taking into account the results obtained from V.M. Popov's work. The results already established are first presented, in particular concerning the frequency domain criterions for absolute stability of automatic control systems containing one single non linearity. The results have been extended to show the existence of a limiting parabola. New use is then made of the methods studied for deriving absolute stability criterions for a system containing a different type of non linearity. Finally, the results obtained are considered from the point of view of Aizerman's conjecture. (author) [fr
Applications of equivalent linearization approaches to nonlinear piping systems
International Nuclear Information System (INIS)
Park, Y.; Hofmayer, C.; Chokshi, N.
1997-01-01
The piping systems in nuclear power plants, even with conventional snubber supports, are highly complex nonlinear structures under severe earthquake loadings mainly due to various mechanical gaps in support structures. Some type of nonlinear analysis is necessary to accurately predict the piping responses under earthquake loadings. The application of equivalent linearization approaches (ELA) to seismic analyses of nonlinear piping systems is presented. Two types of ELA's are studied; i.e., one based on the response spectrum method and the other based on the linear random vibration theory. The test results of main steam and feedwater piping systems supported by snubbers and energy absorbers are used to evaluate the numerical accuracy and limitations
Sherlock Holmes, Master Problem Solver.
Ballew, Hunter
1994-01-01
Shows the connections between Sherlock Holmes's investigative methods and mathematical problem solving, including observations, characteristics of the problem solver, importance of data, questioning the obvious, learning from experience, learning from errors, and indirect proof. (MKR)
State space and input-output linear systems
Delchamps, David F
1988-01-01
It is difficult for me to forget the mild sense of betrayal I felt some ten years ago when I discovered, with considerable dismay, that my two favorite books on linear system theory - Desoer's Notes for a Second Course on Linear Systems and Brockett's Finite Dimensional Linear Systems - were both out of print. Since that time, of course, linear system theory has undergone a transformation of the sort which always attends the maturation of a theory whose range of applicability is expanding in a fashion governed by technological developments and by the rate at which such advances become a part of engineering practice. The growth of the field has inspired the publication of some excellent books; the encyclopedic treatises by Kailath and Chen, in particular, come immediately to mind. Nonetheless, I was inspired to write this book primarily by my practical needs as a teacher and researcher in the field. For the past five years, I have taught a one semester first year gradu ate level linear system theory course i...
Unification of three linear models for the transient visual system
Brinker, den A.C.
1989-01-01
Three different linear filters are considered as a model describing the experimentally determined triphasic impulse responses of discs. These impulse responses arc associated with the transient visual system. Each model reveals a different feature of the system. Unification of the models is
Punctuated equilibrium in a non-linear system of action
J.S. Timmermans (Jos)
2008-01-01
textabstractColeman's equilibrium model of social development, the Linear System of Action, is extended to cover the dynamics of societal transitions. The model implemented has the characteristics of a dissipative system. A variation and selection algorithm favoring the retention of relatively
Lag synchronization of chaotic systems with time-delayed linear
Indian Academy of Sciences (India)
In this paper, the lag synchronization of chaotic systems with time-delayed linear terms via impulsive control is investigated. Based on the stability theory of impulsive delayed differential equations, some sufficient conditions are obtained guaranteeing the synchronized behaviours between two delayed chaotic systems.
INPUT-OUTPUT STRUCTURE OF LINEAR-DIFFERENTIAL ALGEBRAIC SYSTEMS
KUIJPER, M; SCHUMACHER, JM
Systems of linear differential and algebraic equations occur in various ways, for instance, as a result of automated modeling procedures and in problems involving algebraic constraints, such as zero dynamics and exact model matching. Differential/algebraic systems may represent an input-output
Frequency Interval Cross Gramians for Linear and Bilinear Systems
DEFF Research Database (Denmark)
Jazlan, Ahmad; Sreeram, Victor; Shaker, Hamid Reza
2017-01-01
In many control engineering problems, it is desired to analyze the systems at particular frequency intervals of interest. This paper focuses on the development of frequency interval cross gramians for both linear and bilinear systems. New generalized Sylvester equations for calculating the freque...
Switching control of linear systems for generating chaos
International Nuclear Information System (INIS)
Liu Xinzhi; Teo, Kok-Lay; Zhang Hongtao; Chen Guanrong
2006-01-01
In this paper, a new switching method is developed, which can be applied to generating different types of chaos or chaos-like dynamics from two or more linear systems. A numerical simulation is given to illustrate the generated chaotic dynamic behavior of the systems with some variable parameters. Finally, a circuit is built to realize various chaotic dynamical behaviors
New approach to solve symmetric fully fuzzy linear systems
Indian Academy of Sciences (India)
In this paper, we present a method to solve fully fuzzy linear systems with symmetric coefﬁcient matrix. The symmetric coefﬁcient matrix is decomposed into two systems of equations by using Cholesky method and then a solution can be obtained. Numerical examples are given to illustrate our method.
Criteria for stability of linear dynamical systems with multiple delays ...
African Journals Online (AJOL)
In this study we considered a linear Dynamical system with multiple delays and find suitable conditions on the systems parameters such that for a given initial function, we can define a mapping in a carefully chosen complete metric space on which the mapping has a unique fixed point. An asymptotic stability theory for the ...
A data-acquisition system for high speed linear CCD
International Nuclear Information System (INIS)
Liu Zhiyan; Chen Xiangcai; Jiang Xiaoshan; Zhang Hongyu; Liang Zhongwang; Xiang Haisheng; Hu Jun
2010-01-01
A data-acquisition system for high speed linear CCD (Charge Coupled device) is mainly introduced. The optical fiber transmission technology is used. The data is sent to PC through USB or PCI interface. The construction of the system, the design of the PCI interface hardware, software design and the design of the control program running on host computer are also introduced. (authors)
Partial Synchronization Manifolds for Linearly Time-Delay Coupled Systems
Steur, Erik; van Leeuwen, Cees; Michiels, Wim
2014-01-01
Sometimes a network of dynamical systems shows a form of incomplete synchronization characterized by synchronization of some but not all of its systems. This type of incomplete synchronization is called partial synchronization. Partial synchronization is associated with the existence of partial synchronization manifolds, which are linear invariant subspaces of C, the state space of the network of systems. We focus on partial synchronization manifolds in networks of system...
The linear sizes tolerances and fits system modernization
Glukhov, V. I.; Grinevich, V. A.; Shalay, V. V.
2018-04-01
The study is carried out on the urgent topic for technical products quality providing in the tolerancing process of the component parts. The aim of the paper is to develop alternatives for improving the system linear sizes tolerances and dimensional fits in the international standard ISO 286-1. The tasks of the work are, firstly, to classify as linear sizes the elements additionally linear coordinating sizes that determine the detail elements location and, secondly, to justify the basic deviation of the tolerance interval for the element's linear size. The geometrical modeling method of real details elements, the analytical and experimental methods are used in the research. It is shown that the linear coordinates are the dimensional basis of the elements linear sizes. To standardize the accuracy of linear coordinating sizes in all accuracy classes, it is sufficient to select in the standardized tolerance system only one tolerance interval with symmetrical deviations: Js for internal dimensional elements (holes) and js for external elements (shafts). The main deviation of this coordinating tolerance is the average zero deviation, which coincides with the nominal value of the coordinating size. Other intervals of the tolerance system are remained for normalizing the accuracy of the elements linear sizes with a fundamental change in the basic deviation of all tolerance intervals is the maximum deviation corresponding to the limit of the element material: EI is the lower tolerance for the of the internal elements (holes) sizes and es is the upper tolerance deviation for the outer elements (shafts) sizes. It is the sizes of the material maximum that are involved in the of the dimensional elements mating of the shafts and holes and determine the fits type.
Damped oscillations of linear systems a mathematical introduction
Veselić, Krešimir
2011-01-01
The theory of linear damped oscillations was originally developed more than hundred years ago and is still of vital research interest to engineers, mathematicians and physicists alike. This theory plays a central role in explaining the stability of mechanical structures in civil engineering, but it also has applications in other fields such as electrical network systems and quantum mechanics. This volume gives an introduction to linear finite dimensional damped systems as they are viewed by an applied mathematician. After a short overview of the physical principles leading to the linear system model, a largely self-contained mathematical theory for this model is presented. This includes the geometry of the underlying indefinite metric space, spectral theory of J-symmetric matrices and the associated quadratic eigenvalue problem. Particular attention is paid to the sensitivity issues which influence numerical computations. Finally, several recent research developments are included, e.g. Lyapunov stability and ...
Ultra-high Frequency Linear Fiber Optic Systems
Lau, Kam
2011-01-01
This book provides an in-depth treatment of both linear fiber-optic systems and their key enabling devices. It presents a concise but rigorous treatment of the theory and practice of analog (linear) fiber-optics links and systems that constitute the foundation of Hybrid Fiber Coax infrastructure in present-day CATV distribution and cable modem Internet access. Emerging applications in remote fiber-optic feed for free-space millimeter wave enterprise campus networks are also described. Issues such as dispersion and interferometric noise are treated quantitatively, and means for mitigating them are explained. This broad but concise text will thus be invaluable not only to students of fiber-optics communication but also to practicing engineers. To the second edition of this book important new aspects of linear fiber-optic transmission technologies are added, such as high level system architectural issues, algorithms for deriving the optimal frequency assignment, directly modulated or externally modulated laser t...
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Dammann, Bernd; Aage, Niels
concerned with developing a proper (COMSOL) model rather than developing efficient linear algebra solvers which motivates this investigation of the efficiency of the coupling COMSOL + SPL. The technicalities of making such a coupling is described in detail along with a measure of the speedup...
A comparison of SuperLU solvers on the intel MIC architecture
Tuncel, Mehmet; Duran, Ahmet; Celebi, M. Serdar; Akaydin, Bora; Topkaya, Figen O.
2016-10-01
In many science and engineering applications, problems may result in solving a sparse linear system AX=B. For example, SuperLU_MCDT, a linear solver, was used for the large penta-diagonal matrices for 2D problems and hepta-diagonal matrices for 3D problems, coming from the incompressible blood flow simulation (see [1]). It is important to test the status and potential improvements of state-of-the-art solvers on new technologies. In this work, sequential, multithreaded and distributed versions of SuperLU solvers (see [2]) are examined on the Intel Xeon Phi coprocessors using offload programming model at the EURORA cluster of CINECA in Italy. We consider a portfolio of test matrices containing patterned matrices from UFMM ([3]) and randomly located matrices. This architecture can benefit from high parallelism and large vectors. We find that the sequential SuperLU benefited up to 45 % performance improvement from the offload programming depending on the sparse matrix type and the size of transferred and processed data.
Zubair, Mohammad; Nielsen, Eric; Luitjens, Justin; Hammond, Dana
2016-01-01
In the field of computational fluid dynamics, the Navier-Stokes equations are often solved using an unstructuredgrid approach to accommodate geometric complexity. Implicit solution methodologies for such spatial discretizations generally require frequent solution of large tightly-coupled systems of block-sparse linear equations. The multicolor point-implicit solver used in the current work typically requires a significant fraction of the overall application run time. In this work, an efficient implementation of the solver for graphics processing units is proposed. Several factors present unique challenges to achieving an efficient implementation in this environment. These include the variable amount of parallelism available in different kernel calls, indirect memory access patterns, low arithmetic intensity, and the requirement to support variable block sizes. In this work, the solver is reformulated to use standard sparse and dense Basic Linear Algebra Subprograms (BLAS) functions. However, numerical experiments show that the performance of the BLAS functions available in existing CUDA libraries is suboptimal for matrices representative of those encountered in actual simulations. Instead, optimized versions of these functions are developed. Depending on block size, the new implementations show performance gains of up to 7x over the existing CUDA library functions.
High-Performance Small-Scale Solvers for Moving Horizon Estimation
DEFF Research Database (Denmark)
Frison, Gianluca; Vukov, Milan; Poulsen, Niels Kjølstad
2015-01-01
implementation techniques focusing on small-scale problems. The proposed MHE solver is implemented using custom linear algebra routines and is compared against implementations using BLAS libraries. Additionally, the MHE solver is interfaced to a code generation tool for nonlinear model predictive control (NMPC...
International Nuclear Information System (INIS)
Na, Y. W.; Park, C. E.; Lee, S. Y.
2009-01-01
main object of this work is not to investigate the whole transient behavior of the models at hand but to focus on the behavior of numerical solutions part of the sparse asymmetric matrix equations in the transient of hydraulic system. It is outside of the scope of this work to improve the diagonal dominance or to pre-condition the matrix in the process of differencing and linearizing the governing equation, even though it is better to do it that way before applying the solver if there is any efficient way available
DEFF Research Database (Denmark)
Bajric, Anela
A single mass Bouc-Wen oscillator with linear static restoring force contribution is approximated by an equivalent linear system. The aim of the linearized model is to emulate the correct force-displacement response of the Bouc-Wenmodel with characteristic hysteretic behaviour. The linearized mod...
Linearly and nonlinearly bidirectionally coupled synchronization of hyperchaotic systems
International Nuclear Information System (INIS)
Zhou Jin; Lu Junan; Wu Xiaoqun
2007-01-01
To date, there have been many results about unidirectionally coupled synchronization of chaotic systems. However, much less work is reported on bidirectionally-coupled synchronization. In this paper, we investigate the synchronization of two bidirectionally coupled Chen hyperchaotic systems, which are coupled linearly and nonlinearly respectively. Firstly, linearly coupled synchronization of two hyperchaotic Chen systems is investigated, and a theorem on how to choose the coupling coefficients are developed to guarantee the global asymptotical synchronization of two coupled hyperchaotic systems. Analysis shows that the choice of the coupling coefficients relies on the bound of the chaotic system. Secondly, the nonlinearly coupled synchronization is studied; a sufficient condition for the locally asymptotical synchronization is derived, which is independent of the bound of the hyperchaotic system. Finally, numerical simulations are included to verify the effectiveness and feasibility of the developed theorems
Linear dynamical quantum systems analysis, synthesis, and control
Nurdin, Hendra I
2017-01-01
This monograph provides an in-depth treatment of the class of linear-dynamical quantum systems. The monograph presents a detailed account of the mathematical modeling of these systems using linear algebra and quantum stochastic calculus as the main tools for a treatment that emphasizes a system-theoretic point of view and the control-theoretic formulations of quantum versions of familiar problems from the classical (non-quantum) setting, including estimation and filtering, realization theory, and feedback control. Both measurement-based feedback control (i.e., feedback control by a classical system involving a continuous-time measurement process) and coherent feedback control (i.e., feedback control by another quantum system without the intervention of any measurements in the feedback loop) are treated. Researchers and graduates studying systems and control theory, quantum probability and stochastics or stochastic control whether from backgrounds in mechanical or electrical engineering or applied mathematics ...
Nonautonomous linear system of the terrestrial carbon cycle
Luo, Y.
2012-12-01
Carbon cycle has been studied by uses of observation through various networks, field and laboratory experiments, and simulation models. Much less has been done on theoretical thinking and analysis to understand fundament properties of carbon cycle and then guide observatory, experimental, and modeling research. This presentation is to explore what would be the theoretical properties of terrestrial carbon cycle and how those properties can be used to make observatory, experimental, and modeling research more effective. Thousands of published data sets from litter decomposition and soil incubation studies almost all indicate that decay processes of litter and soil organic carbon can be well described by first order differential equations with one or more pools. Carbon pool dynamics in plants and soil after disturbances (e.g., wildfire, clear-cut of forests, and plows of soil for cropping) and during natural recovery or ecosystem restoration also exhibit characteristics of first-order linear systems. Thus, numerous lines of empirical evidence indicate that the terrestrial carbon cycle can be adequately described as a nonautonomous linear system. The linearity reflects the nature of the carbon cycle that carbon, once fixed by photosynthesis, is linearly transferred among pools within an ecosystem. The linear carbon transfer, however, is modified by nonlinear functions of external forcing variables. In addition, photosynthetic carbon influx is also nonlinearly influenced by external variables. This nonautonomous linear system can be mathematically expressed by a first-order linear ordinary matrix equation. We have recently used this theoretical property of terrestrial carbon cycle to develop a semi-analytic solution of spinup. The new methods have been applied to five global land models, including NCAR's CLM and CABLE models and can computationally accelerate spinup by two orders of magnitude. We also use this theoretical property to develop an analytic framework to
Refined Fuchs inequalities for systems of linear differential equations
International Nuclear Information System (INIS)
Gontsov, R R
2004-01-01
We refine the Fuchs inequalities obtained by Corel for systems of linear meromorphic differential equations given on the Riemann sphere. Fuchs inequalities enable one to estimate the sum of exponents of the system over all its singular points. We refine these well-known inequalities by considering the Jordan structure of the leading coefficient of the Laurent series for the matrix of the right-hand side of the system in the neighbourhood of a singular point
The graphics software of the Saclay linear accelerator control system
International Nuclear Information System (INIS)
Gournay, J.F.
1987-06-01
The Control system of the Saclay Linear Accelerator is based upon modern technology hardware. In the graphic software, pictures are created in exactly the same manner for all the graphic devices supported by the system. The informations used to draw a picture are stored in an array called a graphic segment. Three output primitives are used to add graphic material in a segment. Three coordinate systems are defined
Stability analysis of linear switching systems with time delays
International Nuclear Information System (INIS)
Li Ping; Zhong Shouming; Cui Jinzhong
2009-01-01
The issue of stability analysis of linear switching system with discrete and distributed time delays is studied in this paper. An appropriate switching rule is applied to guarantee the stability of the whole switching system. Our results use a Riccati-type Lyapunov functional under a condition on the time delay. So, switching systems with mixed delays are developed. A numerical example is given to illustrate the effectiveness of our results.
Chaos synchronization of a unified chaotic system via partial linearization
International Nuclear Information System (INIS)
Yu Yongguang; Li Hanxiong; Duan Jian
2009-01-01
A partial linearization method is proposed for realizing the chaos synchronization of an unified chaotic system. Through synchronizing partial state of the chaotic systems can result in the synchronization of their entire states, and the resulting controller is singularity free. The results can be easily extended to the synchronization of other similar chaotic systems. Simulation results are conducted to show the effectiveness of the method.
SNR Estimation in Linear Systems with Gaussian Matrices
Suliman, Mohamed Abdalla Elhag; Alrashdi, Ayed; Ballal, Tarig; Al-Naffouri, Tareq Y.
2017-01-01
This letter proposes a highly accurate algorithm to estimate the signal-to-noise ratio (SNR) for a linear system from a single realization of the received signal. We assume that the linear system has a Gaussian matrix with one sided left correlation. The unknown entries of the signal and the noise are assumed to be independent and identically distributed with zero mean and can be drawn from any distribution. We use the ridge regression function of this linear model in company with tools and techniques adapted from random matrix theory to achieve, in closed form, accurate estimation of the SNR without prior statistical knowledge on the signal or the noise. Simulation results show that the proposed method is very accurate.
SNR Estimation in Linear Systems with Gaussian Matrices
Suliman, Mohamed Abdalla Elhag
2017-09-27
This letter proposes a highly accurate algorithm to estimate the signal-to-noise ratio (SNR) for a linear system from a single realization of the received signal. We assume that the linear system has a Gaussian matrix with one sided left correlation. The unknown entries of the signal and the noise are assumed to be independent and identically distributed with zero mean and can be drawn from any distribution. We use the ridge regression function of this linear model in company with tools and techniques adapted from random matrix theory to achieve, in closed form, accurate estimation of the SNR without prior statistical knowledge on the signal or the noise. Simulation results show that the proposed method is very accurate.
Experimental quantum computing to solve systems of linear equations.
Cai, X-D; Weedbrook, C; Su, Z-E; Chen, M-C; Gu, Mile; Zhu, M-J; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Pan, Jian-Wei
2013-06-07
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.
Fostering Creative Problem Solvers in Higher Education
DEFF Research Database (Denmark)
Zhou, Chunfang
2016-01-01
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......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...... 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...
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...
Periodic solutions of asymptotically linear Hamiltonian systems without twist conditions
Energy Technology Data Exchange (ETDEWEB)
Cheng Rong [Coll. of Mathematics and Physics, Nanjing Univ. of Information Science and Tech., Nanjing (China); Dept. of Mathematics, Southeast Univ., Nanjing (China); Zhang Dongfeng [Dept. of Mathematics, Southeast Univ., Nanjing (China)
2010-05-15
In dynamical system theory, especially in many fields of applications from mechanics, Hamiltonian systems play an important role, since many related equations in mechanics can be written in an Hamiltonian form. In this paper, we study the existence of periodic solutions for a class of Hamiltonian systems. By applying the Galerkin approximation method together with a result of critical point theory, we establish the existence of periodic solutions of asymptotically linear Hamiltonian systems without twist conditions. Twist conditions play crucial roles in the study of periodic solutions for asymptotically linear Hamiltonian systems. The lack of twist conditions brings some difficulty to the study. To the authors' knowledge, very little is known about the case, where twist conditions do not hold. (orig.)
Theoretical analysis of balanced truncation for linear switched systems
DEFF Research Database (Denmark)
Petreczky, Mihaly; Wisniewski, Rafal; Leth, John-Josef
2012-01-01
In this paper we present theoretical analysis of model reduction of linear switched systems based on balanced truncation, presented in [1,2]. More precisely, (1) we provide a bound on the estimation error using L2 gain, (2) we provide a system theoretic interpretation of grammians and their singu......In this paper we present theoretical analysis of model reduction of linear switched systems based on balanced truncation, presented in [1,2]. More precisely, (1) we provide a bound on the estimation error using L2 gain, (2) we provide a system theoretic interpretation of grammians...... for showing this independence is realization theory of linear switched systems. [1] H. R. Shaker and R. Wisniewski, "Generalized gramian framework for model/controller order reduction of switched systems", International Journal of Systems Science, Vol. 42, Issue 8, 2011, 1277-1291. [2] H. R. Shaker and R....... Wisniewski, "Switched Systems Reduction Framework Based on Convex Combination of Generalized Gramians", Journal of Control Science and Engineering, 2009....
Linear-constraint wavefront control for exoplanet coronagraphic imaging systems
Sun, He; Eldorado Riggs, A. J.; Kasdin, N. Jeremy; Vanderbei, Robert J.; Groff, Tyler Dean
2017-01-01
A coronagraph is a leading technology for achieving high-contrast imaging of exoplanets in a space telescope. It uses a system of several masks to modify the diffraction and achieve extremely high contrast in the image plane around target stars. However, coronagraphic imaging systems are very sensitive to optical aberrations, so wavefront correction using deformable mirrors (DMs) is necessary to avoid contrast degradation in the image plane. Electric field conjugation (EFC) and Stroke minimization (SM) are two primary high-contrast wavefront controllers explored in the past decade. EFC minimizes the average contrast in the search areas while regularizing the strength of the control inputs. Stroke minimization calculates the minimum DM commands under the constraint that a target average contrast is achieved. Recently in the High Contrast Imaging Lab at Princeton University (HCIL), a new linear-constraint wavefront controller based on stroke minimization was developed and demonstrated using numerical simulation. Instead of only constraining the average contrast over the entire search area, the new controller constrains the electric field of each single pixel using linear programming, which could led to significant increases in speed of the wavefront correction and also create more uniform dark holes. As a follow-up of this work, another linear-constraint controller modified from EFC is demonstrated theoretically and numerically and the lab verification of the linear-constraint controllers is reported. Based on the simulation and lab results, the pros and cons of linear-constraint controllers are carefully compared with EFC and stroke minimization.
International Nuclear Information System (INIS)
Murakami, H.; Hirai, T.; Nakata, M.; Kobori, T.; Mizukoshi, K.; Takenaka, Y.; Miyagawa, N.
1989-01-01
Many of the equipment systems of nuclear power plants contain a number of non-linearities, such as gap and friction, due to their mechanical functions. It is desirable to take such non-linearities into account appropriately for the evaluation of the aseismic soundness. However, in usual design works, linear analysis method with rough assumptions is applied from engineering point of view. An equivalent linearization method is considered to be one of the effective analytical techniques to evaluate non-linear responses, provided that errors to a certain extent are tolerated, because it has greater simplicity in analysis and economization in computing time than non-linear analysis. The objective of this paper is to investigate the applicability of the equivalent linearization method to evaluate the maximum earthquake response of equipment systems such as the CANDU Fuelling Machine which has multiple non- linearities
Design techniques for large scale linear measurement systems
International Nuclear Information System (INIS)
Candy, J.V.
1979-03-01
Techniques to design measurement schemes for systems modeled by large scale linear time invariant systems, i.e., physical systems modeled by a large number (> 5) of ordinary differential equations, are described. The techniques are based on transforming the physical system model to a coordinate system facilitating the design and then transforming back to the original coordinates. An example of a three-stage, four-species, extraction column used in the reprocessing of spent nuclear fuel elements is presented. The basic ideas are briefly discussed in the case of noisy measurements. An example using a plutonium nitrate storage vessel (reprocessing) with measurement uncertainty is also presented
Decentralized linear quadratic power system stabilizers for multi ...
Indian Academy of Sciences (India)
Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead–lag power system stabilizers. However, they have not seen much of practical importance as the state variables are generally not measurable; especially the generator rotor angle measurement is not ...
Force analysis of linear induction motor for magnetic levitation system
Kuijpers, A.A.; Nemlioglu, C.; Sahin, F.; Verdel, A.J.D.; Compter, J.C.; Lomonova, E.
2010-01-01
This paper presents the analyses of thrust and normal forces of linear induction motor (LIM) segments which are implemented in a rotating ring system. To obtain magnetic levitation in a cost effective and sustainable way, decoupled control of thrust and normal forces is required. This study includes
Input design for linear dynamic systems using maxmin criteria
DEFF Research Database (Denmark)
Sadegh, Payman; Hansen, Lars H.; Madsen, Henrik
1998-01-01
This paper considers the problem of input design for maximizing the smallest eigenvalue of the information matrix for linear dynamic systems. The optimization of the smallest eigenvalue is of interest in parameter estimation and parameter change detection problems. We describe a simple cutting...
Generating Nice Linear Systems for Matrix Gaussian Elimination
Homewood, L. James
2004-01-01
In this article an augmented matrix that represents a system of linear equations is called nice if a sequence of elementary row operations that reduces the matrix to row-echelon form, through matrix Gaussian elimination, does so by restricting all entries to integers in every step. Many instructors wish to use the example of matrix Gaussian…
Daylighting System Based on Novel Design of Linear Fresnel lens
Directory of Open Access Journals (Sweden)
Thanh Tuan Pham
2017-10-01
Full Text Available In this paper, we present a design and optical simulation of a daylighting system using a novel design of linear Fresnel lens, which is constructed based on the conservation of optical path length and edge ray theorem. The linear Fresnel lens can achieve a high uniformity by using a new idea of design in which each groove of the lens distributes sunlight uniformly over the receiver so that the whole lens also uniformly distributes sunlight over the receiver. In this daylighting system, the novel design of linear Fresnel lens significantly improves the uniformity of collector and distributor. Therefore, it can help to improve the performance of the daylighting system. The structure of the linear Fresnel lenses is designed by using Matlab. Then, the structure of lenses is appreciated by ray tracing in LightToolsTM to find out the optimum lens shape. In addition, the simulation is performed by using LightToolsTM to estimate the efficiency of the daylighting system. The results show that the designed collector can achieve the efficiency of ~80% with the tolerance of ~0.60 and the concentration ratio of 340 times, while the designed distributor can reach a high uniformity of >90%.
Robust self-triggered MPC for constrained linear systems
Brunner, F.D.; Heemels, W.P.M.H.; Allgöwer, F.
2014-01-01
In this paper we propose a robust self-triggered model predictive control algorithm for linear systems with additive bounded disturbances and hard constraints on the inputs and state. In self-triggered control, at every sampling instant the time until the next sampling instant is computed online
Stability Analysis for Multi-Parameter Linear Periodic Systems
DEFF Research Database (Denmark)
Seyranian, A.P.; Solem, Frederik; Pedersen, Pauli
1999-01-01
This paper is devoted to stability analysis of general linear periodic systems depending on real parameters. The Floquet method and perturbation technique are the basis of the development. We start out with the first and higher-order derivatives of the Floquet matrix with respect to problem...
Relative controllability and null controllability of linear delay systems ...
African Journals Online (AJOL)
Necessary and sufficient conditions are established for the relative, absolute controllability and null controllability of the generalized linear delay system and its discrete prototype. The paper presents illuminating examples on previous controllability results by Manitius and Olbrot [7] and carries over the results of Onwuatu [8] ...
Time-optimal feedback control for linear systems
International Nuclear Information System (INIS)
Mirica, S.
1976-01-01
The paper deals with the results of qualitative investigations of the time-optimal feedback control for linear systems with constant coefficients. In the first section, after some definitions and notations, two examples are given and it is shown that even the time-optimal control problem for linear systems with constant coefficients which looked like ''completely solved'' requires a further qualitative investigation of the stability to ''permanent perturbations'' of optimal feedback control. In the second section some basic results of the linear time-optimal control problem are reviewed. The third section deals with the definition of Boltyanskii's ''regular synthesis'' and its connection to Filippov's theory of right-hand side discontinuous differential equations. In the fourth section a theorem is proved concerning the stability to perturbations of time-optimal feedback control for linear systems with scalar control. In the last two sections it is proved that, if the matrix which defines the system has only real eigenvalues or is three-dimensional, the time-optimal feedback control defines a regular synthesis and therefore is stable to perturbations. (author)
Cazzulani, Gabriele; Resta, Ferruccio; Ripamonti, Francesco
2012-04-01
During the last years, more and more mechanical applications saw the introduction of active control strategies. In particular, the need of improving the performances and/or the system health is very often associated to vibration suppression. This goal can be achieved considering both passive and active solutions. In this sense, many active control strategies have been developed, such as the Independent Modal Space Control (IMSC) or the resonant controllers (PPF, IRC, . . .). In all these cases, in order to tune and optimize the control strategy, the knowledge of the system dynamic behaviour is very important and it can be achieved both considering a numerical model of the system or through an experimental identification process. Anyway, dealing with non-linear or time-varying systems, a tool able to online identify the system parameters becomes a key-point for the control logic synthesis. The aim of the present work is the definition of a real-time technique, based on ARMAX models, that estimates the system parameters starting from the measurements of piezoelectric sensors. These parameters are returned to the control logic, that automatically adapts itself to the system dynamics. The problem is numerically investigated considering a carbon-fiber plate model forced through a piezoelectric patch.
System-Solver: una herramienta de código abierto para la modelación de sistemas dinámicos
Directory of Open Access Journals (Sweden)
Efraín Domínguez
2010-09-01
Full Text Available En este artículo se presenta una herramienta de código abierto para la simulación de sistemas dinámicos, representados a través de ecuaciones diferenciales de distinto orden o de sistemas de ecuaciones diferenciales ordinarias (EDO. La idea principal que incentivó el desarrollo de esta herramienta consiste en que muchos procesos físicos, biológicos, ecológicos, económicos, químicos y sociales, y un sinnúmero de problemas ingenieriles, pueden ser expresados de esta forma. Adicionalmente, la solución de ese tipo de problemas exige experticia en métodos numéricos y programación. Este tipo de experticia no es muy común para los expertos de las áreas mencionadas; por ello, se requiere de una herramienta que permita sortear esta falta de experticia e incrementar la productividad en trabajos relacionados con tópicos de modelación. System-Solver es una aplicación que facilita la formulación de problemas de valor inicial en EDO y su solución unmérica, y mediante un programa en Visual Basic la automatiza. El programa obtenido se puede compartir fácilmente con otros investigadores, facilitando la reproducción del ejercicio de modelación incluso en diferentes sistemas operativos. La presentación del software está acompañada con ejercicios de diversas áreas temáticas, incluyendo un ejemplo de modelación estocástica.
Observability of linear control systems on Lie groups
International Nuclear Information System (INIS)
Ayala, V.; Hacibekiroglu, A.K.
1995-01-01
In this paper, we study the observability problem for a linear control system Σ on a Lie group G. The drift vector field of Σ is an infinitesimal automorphism of G and the control vectors are elements in the Lie algebra of G. We establish algebraic conditions to characterize locally and globally observability for Σ. As in the linear case on R n , these conditions are independent of the control vector. We give an algorithm on the co-tangent bundle of G to calculate the equivalence class of the neutral element. (author). 6 refs
Monitoring and control system of the Saclay electron linear accelerator
International Nuclear Information System (INIS)
Lafontaine, Antoine
1974-01-01
A description is given of the automatic monitoring and control system of the 60MeV electron linear accelerator of the Centre d'Etudes Nucleaires de Saclay. The paper is mostly concerned with the programmation of the system. However, in a real time device, there is a very close association between computer and electronics, the latter are therefore described in details and make up most of the paper. [fr
A new timing system for the Stanford Linear Collider
International Nuclear Information System (INIS)
Paffrath, L.; Bernstein, D.; Kang, H.; Koontz, R.; Leger, G.; Pierce, W.; Ross, M.; Wilmunder, A.
1985-01-01
In order to be able to meet the goals of the Stanford Linear Collider, a much more precise timing system had to be implemented. This paper describes the specification and design of this system, and the results obtained from its use on 1/3 of the SLAC linac. The functions of various elements are described, and a programmable delay unit (PDU) is described in detail
Hyperchaotic encryption based on multi-scroll piecewise linear Systems
Czech Academy of Sciences Publication Activity Database
García-Martínez, M.; Ontanon-García, L.J.; Campos-Cantón, E.; Čelikovský, Sergej
2015-01-01
Roč. 270, č. 1 (2015), s. 413-424 ISSN 0096-3003 R&D Projects: GA ČR GA13-20433S Institutional support: RVO:67985556 Keywords : Hyperchaotic encryption * Piecewise linear systems * Stream cipher * Pseudo-random bit generator * Chaos theory * Multi-scrollattractors Subject RIV: BC - Control Systems Theory Impact factor: 1.345, year: 2015 http://library.utia.cas.cz/separaty/2015/TR/celikovsky-0446895.pdf
Global Linear Representations of Nonlinear Systems and the Adjoint Map
Banks, S.P.
1988-01-01
In this paper we shall study the global linearization of nonlinear systems on a manifold by two methods. The first consists of an expansion of the vector field in the space of square integrable vector fields. In the second method we use the adjoint representation of the Lie algebra vector fields to obtain an infinite-dimensional matrix representation of the system. A connection between the two approaches will be developed.
Comments on new iterative methods for solving linear systems
Directory of Open Access Journals (Sweden)
Wang Ke
2017-06-01
Full Text Available Some new iterative methods were presented by Du, Zheng and Wang for solving linear systems in [3], where it is shown that the new methods, comparing to the classical Jacobi or Gauss-Seidel method, can be applied to more systems and have faster convergence. This note shows that their methods are suitable for more matrices than positive matrices which the authors suggested through further analysis and numerical examples.
A representation theorem for linear discrete-space systems
Directory of Open Access Journals (Sweden)
Sandberg Irwin W.
1998-01-01
Full Text Available The cornerstone of the theory of discrete-time single-input single-output linear systems is the idea that every such system has an input–output map H that can be represented by a convolution or the familiar generalization of a convolution. This thinking involves an oversight which is corrected in this note by adding an additional term to the representation.
A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
Czech Academy of Sciences Publication Activity Database
Benzi, M.; Tůma, Miroslav
1998-01-01
Roč. 19, č. 3 (1998), s. 968-994 ISSN 1064-8275 R&D Projects: GA ČR GA201/93/0067; GA AV ČR IAA230401 Keywords : large sparse systems * interative methods * preconditioning * approximate inverse * sparse linear systems * sparse matrices * incomplete factorizations * conjugate gradient -type methods Subject RIV: BA - General Mathematics Impact factor: 1.378, year: 1998
Design and performance of the Stanford Linear Collider Control System
International Nuclear Information System (INIS)
Melen, R.E.
1984-10-01
The success of the Stanford Linear Collider (SLC) will be dependent upon the implementation of a very large advanced computer-based instrumentation and control system. This paper describes the architectural design of this system as well as a critique of its performance. This critique is based on experience obtained from its use in the control and monitoring of 1/3 of the SLAC linac and in support of an expensive experimental machine physics experimental program. 11 references, 3 figures
Universal Linear Precoding for NBI-Proof Widely Linear Equalization in MC Systems
Directory of Open Access Journals (Sweden)
Donatella Darsena
2007-09-01
Full Text Available In multicarrier (MC systems, transmitter redundancy, which is introduced by means of finite-impulse response (FIR linear precoders, allows for perfect or zero-forcing (ZF equalization of FIR channels (in the absence of noise. Recently, it has been shown that the noncircular or improper nature of some symbol constellations offers an intrinsic source of redundancy, which can be exploited to design efficient FIR widely-linear (WL receiving structures for MC systems operating in the presence of narrowband interference (NBI. With regard to both cyclic-prefixed and zero-padded transmission techniques, it is shown in this paper that, with appropriately designed precoders, it is possible to synthesize in both cases WL-ZF universal equalizers, which guarantee perfect symbol recovery for any FIR channel. Furthermore, it is theoretically shown that the intrinsic redundancy of the improper symbol sequence also enables WL-ZF equalization, based on the minimum mean output-energy criterion, with improved NBI suppression capabilities. Finally, results of numerical simulations are presented, which assess the merits of the proposed precoding designs and validate the theoretical analysis carried out.
Self-Tuning Control of Linear Systems Followed by Deadzones
Directory of Open Access Journals (Sweden)
K. Kazlauskas
2014-02-01
Full Text Available The aim of the present paper is to increase the efficiency of self-tuning generalized minimum variance (GMV control of linear time-invariant (LTI systems followed by deadzone nonlinearities. An approach, based on reordering of observations to be processed for the reconstruction of an unknown internal signal that acts between LTI system and a static nonlinear block of the closed-loop Wiener system, has been developed. The results of GMV self-tuning control of the second order LTI system with an ordinary deadzone are given.
Algorithmic Approach to Abstracting Linear Systems by Timed Automata
DEFF Research Database (Denmark)
Sloth, Christoffer; Wisniewski, Rafael
2011-01-01
This paper proposes an LMI-based algorithm for abstracting dynamical systems by timed automata, which enables automatic formal verification of linear systems. The proposed abstraction is based on partitioning the state space of the system using positive invariant sets, generated by Lyapunov...... functions. This partitioning ensures that the vector field of the dynamical system is transversal to all facets of the cells, which induces some desirable properties of the abstraction. The algorithm is based on identifying intersections of level sets of quadratic Lyapunov functions, and determining...
Focal points and principal solutions of linear Hamiltonian systems revisited
Šepitka, Peter; Šimon Hilscher, Roman
2018-05-01
In this paper we present a novel view on the principal (and antiprincipal) solutions of linear Hamiltonian systems, as well as on the focal points of their conjoined bases. We present a new and unified theory of principal (and antiprincipal) solutions at a finite point and at infinity, and apply it to obtain new representation of the multiplicities of right and left proper focal points of conjoined bases. We show that these multiplicities can be characterized by the abnormality of the system in a neighborhood of the given point and by the rank of the associated T-matrix from the theory of principal (and antiprincipal) solutions. We also derive some additional important results concerning the representation of T-matrices and associated normalized conjoined bases. The results in this paper are new even for completely controllable linear Hamiltonian systems. We also discuss other potential applications of our main results, in particular in the singular Sturmian theory.
Fundamentals of linear systems for physical scientists and engineers
Puri, N N
2009-01-01
Thanks to the advent of inexpensive computing, it is possible to analyze, compute, and develop results that were unthinkable in the '60s. Control systems, telecommunications, robotics, speech, vision, and digital signal processing are but a few examples of computing applications. While there are many excellent resources available that focus on one or two topics, few books cover most of the mathematical techniques required for a broader range of applications. Fundamentals of Linear Systems for Physical Scientists and Engineers is such a resource. The book draws from diverse areas of engineering and the physical sciences to cover the fundamentals of linear systems. Assuming no prior knowledge of complex mathematics on the part of the reader, the author uses his nearly 50 years of teaching experience to address all of the necessary mathematical techniques. Original proofs, hundreds of examples, and proven theorems illustrate and clarify the material. An extensive table provides Lyapunov functions for differentia...
Computer Based Dose Control System on Linear Accelerator
International Nuclear Information System (INIS)
Taxwim; Djoko-SP; Widi-Setiawan; Agus-Budi Wiyatna
2000-01-01
The accelerator technology has been used for radio therapy. DokterKaryadi Hospital in Semarang use electron or X-ray linear accelerator (Linac)for cancer therapy. One of the control parameter of linear accelerator isdose rate. It is particle current or amount of photon rate to the target. Thecontrol of dose rate in linac have been done by adjusting repetition rate ofanode pulse train of electron source. Presently the control is stillproportional control. To enhance the quality of the control result (minimalstationer error, velocity and stability), the dose control system has beendesigned by using the PID (Proportional Integral Differential) controlalgorithm and the derivation of transfer function of control object.Implementation of PID algorithm control system is done by giving an input ofdose error (the different between output dose and dose rate set point). Theoutput of control system is used for correction of repetition rate set pointfrom pulse train of electron source anode. (author)
Linear and nonlinear dynamic systems in financial time series prediction
Directory of Open Access Journals (Sweden)
Salim Lahmiri
2012-10-01
Full Text Available Autoregressive moving average (ARMA process and dynamic neural networks namely the nonlinear autoregressive moving average with exogenous inputs (NARX are compared by evaluating their ability to predict financial time series; for instance the S&P500 returns. Two classes of ARMA are considered. The first one is the standard ARMA model which is a linear static system. The second one uses Kalman filter (KF to estimate and predict ARMA coefficients. This model is a linear dynamic system. The forecasting ability of each system is evaluated by means of mean absolute error (MAE and mean absolute deviation (MAD statistics. Simulation results indicate that the ARMA-KF system performs better than the standard ARMA alone. Thus, introducing dynamics into the ARMA process improves the forecasting accuracy. In addition, the ARMA-KF outperformed the NARX. This result may suggest that the linear component found in the S&P500 return series is more dominant than the nonlinear part. In sum, we conclude that introducing dynamics into the ARMA process provides an effective system for S&P500 time series prediction.
Three-Dimensional Inverse Transport Solver Based on Compressive Sensing Technique
Cheng, Yuxiong; Wu, Hongchun; Cao, Liangzhi; Zheng, Youqi
2013-09-01
According to the direct exposure measurements from flash radiographic image, a compressive sensing-based method for three-dimensional inverse transport problem is presented. The linear absorption coefficients and interface locations of objects are reconstructed directly at the same time. It is always very expensive to obtain enough measurements. With limited measurements, compressive sensing sparse reconstruction technique orthogonal matching pursuit is applied to obtain the sparse coefficients by solving an optimization problem. A three-dimensional inverse transport solver is developed based on a compressive sensing-based technique. There are three features in this solver: (1) AutoCAD is employed as a geometry preprocessor due to its powerful capacity in graphic. (2) The forward projection matrix rather than Gauss matrix is constructed by the visualization tool generator. (3) Fourier transform and Daubechies wavelet transform are adopted to convert an underdetermined system to a well-posed system in the algorithm. Simulations are performed and numerical results in pseudo-sine absorption problem, two-cube problem and two-cylinder problem when using compressive sensing-based solver agree well with the reference value.
Directory of Open Access Journals (Sweden)
X. Huang
2016-11-01
Full Text Available In the Community Earth System Model (CESM, the ocean model is computationally expensive for high-resolution grids and is often the least scalable component for high-resolution production experiments. The major bottleneck is that the barotropic solver scales poorly at high core counts. We design a new barotropic solver to accelerate the high-resolution ocean simulation. The novel solver adopts a Chebyshev-type iterative method to reduce the global communication cost in conjunction with an effective block preconditioner to further reduce the iterations. The algorithm and its computational complexity are theoretically analyzed and compared with other existing methods. We confirm the significant reduction of the global communication time with a competitive convergence rate using a series of idealized tests. Numerical experiments using the CESM 0.1° global ocean model show that the proposed approach results in a factor of 1.7 speed-up over the original method with no loss of accuracy, achieving 10.5 simulated years per wall-clock day on 16 875 cores.
Galerkin projection methods for solving multiple related linear systems
Energy Technology Data Exchange (ETDEWEB)
Chan, T.F.; Ng, M.; Wan, W.L.
1996-12-31
We consider using Galerkin projection methods for solving multiple related linear systems A{sup (i)}x{sup (i)} = b{sup (i)} for 1 {le} i {le} s, where A{sup (i)} and b{sup (i)} are different in general. We start with the special case where A{sup (i)} = A and A is symmetric positive definite. The method generates a Krylov subspace from a set of direction vectors obtained by solving one of the systems, called the seed system, by the CG method and then projects the residuals of other systems orthogonally onto the generated Krylov subspace to get the approximate solutions. The whole process is repeated with another unsolved system as a seed until all the systems are solved. We observe in practice a super-convergence behaviour of the CG process of the seed system when compared with the usual CG process. We also observe that only a small number of restarts is required to solve all the systems if the right-hand sides are close to each other. These two features together make the method particularly effective. In this talk, we give theoretical proof to justify these observations. Furthermore, we combine the advantages of this method and the block CG method and propose a block extension of this single seed method. The above procedure can actually be modified for solving multiple linear systems A{sup (i)}x{sup (i)} = b{sup (i)}, where A{sup (i)} are now different. We can also extend the previous analytical results to this more general case. Applications of this method to multiple related linear systems arising from image restoration and recursive least squares computations are considered as examples.
Self-correcting Multigrid Solver
International Nuclear Information System (INIS)
Lewandowski, Jerome L.V.
2004-01-01
A new multigrid algorithm based on the method of self-correction for the solution of elliptic problems is described. The method exploits information contained in the residual to dynamically modify the source term (right-hand side) of the elliptic problem. It is shown that the self-correcting solver is more efficient at damping the short wavelength modes of the algebraic error than its standard equivalent. When used in conjunction with a multigrid method, the resulting solver displays an improved convergence rate with no additional computational work
GPU-Accelerated Sparse Matrix Solvers for Large-Scale Simulations, Phase II
National Aeronautics and Space Administration — At the heart of scientific computing and numerical analysis are linear algebra solvers. In scientific computing, the focus is on the partial differential equations...
An extended GS method for dense linear systems
Niki, Hiroshi; Kohno, Toshiyuki; Abe, Kuniyoshi
2009-09-01
Davey and Rosindale [K. Davey, I. Rosindale, An iterative solution scheme for systems of boundary element equations, Internat. J. Numer. Methods Engrg. 37 (1994) 1399-1411] derived the GSOR method, which uses an upper triangular matrix [Omega] in order to solve dense linear systems. By applying functional analysis, the authors presented an expression for the optimum [Omega]. Moreover, Davey and Bounds [K. Davey, S. Bounds, A generalized SOR method for dense linear systems of boundary element equations, SIAM J. Comput. 19 (1998) 953-967] also introduced further interesting results. In this note, we employ a matrix analysis approach to investigate these schemes, and derive theorems that compare these schemes with existing preconditioners for dense linear systems. We show that the convergence rate of the Gauss-Seidel method with preconditioner PG is superior to that of the GSOR method. Moreover, we define some splittings associated with the iterative schemes. Some numerical examples are reported to confirm the theoretical analysis. We show that the EGS method with preconditioner produces an extremely small spectral radius in comparison with the other schemes considered.
Essential uncontrollability of discrete linear, time-invariant, dynamical systems
Cliff, E. M.
1975-01-01
The concept of a 'best approximating m-dimensional subspace' for a given set of vectors in n-dimensional whole space is introduced. Such a subspace is easily described in terms of the eigenvectors of an associated Gram matrix. This technique is used to approximate an achievable set for a discrete linear time-invariant dynamical system. This approximation characterizes the part of the state space that may be reached using modest levels of control. If the achievable set can be closely approximated by a proper subspace of the whole space then the system is 'essentially uncontrollable'. The notion finds application in studies of failure-tolerant systems, and in decoupling.
The new control system of the Saclay linear accelerator
International Nuclear Information System (INIS)
Gournay, J.F.; Gourcy, G.; Garreau, F.; Giraud, A.; Rouault, J.
1985-05-01
A new control system for the Safety Linear Accelerator is now being designed. The computer control architecture is based on 3 dedicated VME crates with MC68000 micro-processors: one crate with a disk-based operating system will run the high level application programs and the data base management facilities, another one will manage the man-machine communications and the third one will interface the system to the linac equipments. Communications between the VME microcomputers will be done through 16 bit parallel links. The software is modular and organized in specific layers, the data base is fully distributed. About 90% of the code is written in Fortran
Kalman filtering for time-delayed linear systems
Institute of Scientific and Technical Information of China (English)
LU Xiao; WANG Wei
2006-01-01
This paper is to study the linear minimum variance estimation for discrete- time systems. A simple approach to the problem is presented by developing re-organized innovation analysis for the systems with instantaneous and double time-delayed measurements. It is shown that the derived estimator involves solving three different standard Kalman filtering with the same dimension as the original system. The obtained results form the basis for solving some complicated problems such as H∞ fixed-lag smoothing, preview control, H∞ filtering and control with time delays.
Fundamental Matrix for a Class of Point Delay Linear Systems
International Nuclear Information System (INIS)
Sen, M. de la; Alastruey, C. F.
1998-01-01
It is difficult to establish explicit analytic forms for fundamental matrices of delayed linear systems. In this paper, an explicit form of exponential type is given for such a matrix in the case of punctual delays. The existence of real and complex fundamental matrices, for the case of real parameterizations of the differential system, is studied and discussed. Some additional commutativity properties involving the matrices parameters and the fundamental matrices as well as explicit expressions for the solution of the delayed differential system are also given. (Author)
Control of Non-linear Marine Cooling System
DEFF Research Database (Denmark)
Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon
2011-01-01
We consider the problem of designing control laws for a marine cooling system used for cooling the main engine and auxiliary components aboard several classes of container vessels. We focus on achieving simple set point control for the system and do not consider compensation of the non-linearitie......-linearities, closed circuit flow dynamics or transport delays that are present in the system. Control laws are therefore designed using classical control theory and the performance of the design is illustrated through two simulation examples....
Coherent versus Measurement Feedback: Linear Systems Theory for Quantum Information
Directory of Open Access Journals (Sweden)
Naoki Yamamoto
2014-11-01
Full Text Available To control a quantum system via feedback, we generally have two options in choosing a control scheme. One is the coherent feedback, which feeds the output field of the system, through a fully quantum device, back to manipulate the system without involving any measurement process. The other one is measurement-based feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages and disadvantages, depending on the system and the control goal; hence, their comparison in several situations is important. This paper considers a general open linear quantum system with the following specific control goals: backaction evasion, generation of a quantum nondemolished variable, and generation of a decoherence-free subsystem, all of which have important roles in quantum information science. Some no-go theorems are proven, clarifying that those goals cannot be achieved by any measurement-based feedback control. On the other hand, it is shown that, for each control goal there exists a coherent feedback controller accomplishing the task. The key idea to obtain all the results is system theoretic characterizations of the above three notions in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.
Optimal linear precoding for indoor visible light communication system
Sifaou, Houssem
2017-07-31
Visible light communication (VLC) is an emerging technique that uses light-emitting diodes (LED) to combine communication and illumination. It is considered as a promising scheme for indoor wireless communication that can be deployed at reduced costs while offering high data rate performance. In this paper, we focus on the design of the downlink of a multi-user VLC system. Inherent to multi-user systems is the interference caused by the broadcast nature of the medium. Linear precoding based schemes are among the most popular solutions that have recently been proposed to mitigate inter-user interference. This paper focuses on the design of the optimal linear precoding scheme that solves the max-min signal-to-interference-plus-noise ratio (SINR) problem. The performance of the proposed precoding scheme is studied under different working conditions and compared with the classical zero-forcing precoding. Simulations have been provided to illustrate the high gain of the proposed scheme.
Solution of the fully fuzzy linear systems using iterative techniques
International Nuclear Information System (INIS)
Dehghan, Mehdi; Hashemi, Behnam; Ghatee, Mehdi
2007-01-01
This paper mainly intends to discuss the iterative solution of fully fuzzy linear systems which we call FFLS. We employ Dubois and Prade's approximate arithmetic operators on LR fuzzy numbers for finding a positive fuzzy vector x-tilde which satisfies A-tildex-tilde=b, where A-tilde and b-tilde are a fuzzy matrix and a fuzzy vector, respectively. Please note that the positivity assumption is not so restrictive in applied problems. We transform FFLS and propose iterative techniques such as Richardson, Jacobi, Jacobi overrelaxation (JOR), Gauss-Seidel, successive overrelaxation (SOR), accelerated overrelaxation (AOR), symmetric and unsymmetric SOR (SSOR and USSOR) and extrapolated modified Aitken (EMA) for solving FFLS. In addition, the methods of Newton, quasi-Newton and conjugate gradient are proposed from nonlinear programming for solving a fully fuzzy linear system. Various numerical examples are also given to show the efficiency of the proposed schemes
Solution methods for large systems of linear equations in BACCHUS
International Nuclear Information System (INIS)
Homann, C.; Dorr, B.
1993-05-01
The computer programme BACCHUS is used to describe steady state and transient thermal-hydraulic behaviour of a coolant in a fuel element with intact geometry in a fast breeder reactor. In such computer programmes generally large systems of linear equations with sparse matrices of coefficients, resulting from discretization of coolant conservation equations, must be solved thousands of times giving rise to large demands of main storage and CPU time. Direct and iterative solution methods of the systems of linear equations, available in BACCHUS, are described, giving theoretical details and experience with their use in the programme. Besides use of a method of lines, a Runge-Kutta-method, for solution of the partial differential equation is outlined. (orig.) [de
Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control
Johnson, Russell; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta
2016-01-01
This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hami...
Optimal approximation of linear systems by artificial immune response
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper puts forward a novel artificial immune response algorithm for optimal approximation of linear systems. A quaternion model of artificial immune response is proposed for engineering computing. The model abstracts four elements, namely, antigen, antibody, reaction rules among antibodies, and driving algorithm describing how the rules are applied to antibodies, to simulate the process of immune response. Some reaction rules including clonal selection rules, immunological memory rules and immune regulation rules are introduced. Using the theorem of Markov chain, it is proofed that the new model is convergent. The experimental study on the optimal approximation of a stable linear system and an unstable one show that the approximate models searched by the new model have better performance indices than those obtained by some existing algorithms including the differential evolution algorithm and the multi-agent genetic algorithm.
Large linear magnetoresistivity in strongly inhomogeneous planar and layered systems
International Nuclear Information System (INIS)
Bulgadaev, S.A.; Kusmartsev, F.V.
2005-01-01
Explicit expressions for magnetoresistance R of planar and layered strongly inhomogeneous two-phase systems are obtained, using exact dual transformation, connecting effective conductivities of in-plane isotropic two-phase systems with and without magnetic field. These expressions allow to describe the magnetoresistance of various inhomogeneous media at arbitrary concentrations x and magnetic fields H. All expressions show large linear magnetoresistance effect with different dependencies on the phase concentrations. The corresponding plots of the x- and H-dependencies of R(x,H) are represented for various values, respectively, of magnetic field and concentrations at some values of inhomogeneity parameter. The obtained results show a remarkable similarity with the existing experimental data on linear magnetoresistance in silver chalcogenides Ag 2+δ Se. A possible physical explanation of this similarity is proposed. It is shown that the random, stripe type, structures of inhomogeneities are the most suitable for a fabrication of magnetic sensors and a storage of information at room temperatures
Maximization of energy in the output of a linear system
International Nuclear Information System (INIS)
Dudley, D.G.
1976-01-01
A time-limited signal which, when passed through a linear system, maximizes the total output energy is considered. Previous work has shown that the solution is given by the eigenfunction associated with the maximum eigenvalue in a Hilbert-Schmidt integral equation. Analytical results are available for the case where the transfer function is a low-pass filter. This work is extended by obtaining a numerical solution to the integral equation which allows results for reasonably general transfer functions
Linear Quantum Systems: Non-Classical States and Robust Stability
2016-06-29
modulation and entanglement in a compound gradient echo memory, Physical Review A 93(2) 023809 2016. We present a theoretical model for a Kerr...Carvalho, M. Hedges and M R James, Analysis of the operation of gradient echo memories using a quantum input-output model, New Journal of Physics , 15...new structured uncertainty methods that ensure robust stability of quantum systems based on nominal linear models, and (v) physical realizability
Dynamic logic architecture based on piecewise-linear systems
International Nuclear Information System (INIS)
Peng Haipeng; Liu Fei; Li Lixiang; Yang Yixian; Wang Xue
2010-01-01
This Letter explores piecewise-linear systems to construct dynamic logic architecture. The proposed schemes can discriminate the two input signals and obtain 16 kinds of logic operations by different combinations of parameters and conditions for determining the output. Each logic cell performs more flexibly, that makes it possible to achieve complex logic operations more simply and construct computing architecture with less logic cells. We also analyze the various performances of our schemes under different conditions and the characteristics of these schemes.
CHEBYSHEV ACCELERATION TECHNIQUE FOR SOLVING FUZZY LINEAR SYSTEM
Directory of Open Access Journals (Sweden)
S.H. Nasseri
2011-07-01
Full Text Available In this paper, Chebyshev acceleration technique is used to solve the fuzzy linear system (FLS. This method is discussed in details and followed by summary of some other acceleration techniques. Moreover, we show that in some situations that the methods such as Jacobi, Gauss-Sidel, SOR and conjugate gradient is divergent, our proposed method is applicable and the acquired results are illustrated by some numerical examples.
CHEBYSHEV ACCELERATION TECHNIQUE FOR SOLVING FUZZY LINEAR SYSTEM
Directory of Open Access Journals (Sweden)
S.H. Nasseri
2009-10-01
Full Text Available In this paper, Chebyshev acceleration technique is used to solve the fuzzy linear system (FLS. This method is discussed in details and followed by summary of some other acceleration techniques. Moreover, we show that in some situations that the methods such as Jacobi, Gauss-Sidel, SOR and conjugate gradient is divergent, our proposed method is applicable and the acquired results are illustrated by some numerical examples.
Efficient Preconditioning of Sequences of Nonsymmetric Linear Systems
Czech Academy of Sciences Publication Activity Database
Duintjer Tebbens, Jurjen; Tůma, Miroslav
2007-01-01
Roč. 29, č. 5 (2007), s. 1918-1941 ISSN 1064-8275 R&D Projects: GA AV ČR 1ET400300415; GA AV ČR KJB100300703 Institutional research plan: CEZ:AV0Z10300504 Keywords : preconditioned iterative methods * sparse matrices * sequences of linear algebraic systems * incomplete factorizations * factorization updates * Gauss–Jordan transformations * minimum spanning tree Subject RIV: BA - General Mathematics Impact factor: 1.784, year: 2007
AZTEC: A parallel iterative package for the solving linear systems
Energy Technology Data Exchange (ETDEWEB)
Hutchinson, S.A.; Shadid, J.N.; Tuminaro, R.S. [Sandia National Labs., Albuquerque, NM (United States)
1996-12-31
We describe a parallel linear system package, AZTEC. The package incorporates a number of parallel iterative methods (e.g. GMRES, biCGSTAB, CGS, TFQMR) and preconditioners (e.g. Jacobi, Gauss-Seidel, polynomial, domain decomposition with LU or ILU within subdomains). Additionally, AZTEC allows for the reuse of previous preconditioning factorizations within Newton schemes for nonlinear methods. Currently, a number of different users are using this package to solve a variety of PDE applications.
Feedback Linearization Controller for a Wind Energy Power System
Directory of Open Access Journals (Sweden)
Muthana Alrifai
2016-09-01
Full Text Available This paper deals with the control of a doubly-fed induction generator (DFIG-based variable speed wind turbine power system. A system of eight ordinary differential equations is used to model the wind energy conversion system. The generator has a wound rotor type with back-to-back three-phase power converter bridges between its rotor and the grid; it is modeled using the direct-quadrature rotating reference frame with aligned stator flux. An input-state feedback linearization controller is proposed for the wind energy power system. The controller guarantees that the states of the system track the desired states. Simulation results are presented to validate the proposed control scheme. Moreover, further simulation results are shown to investigate the robustness of the proposed control scheme to changes in some of the parameters of the system.
Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory
Richtarik, Peter; Taká č, Martin
2017-01-01
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.
Linear circuits, systems and signal processing: theory and application
International Nuclear Information System (INIS)
Byrnes, C.I.; Saeks, R.E.; Martin, C.F.
1988-01-01
In part because of its universal role as a first approximation of more complicated behaviour and in part because of the depth and breadth of its principle paradigms, the study of linear systems continues to play a central role in control theory and its applications. Enhancing more traditional applications to aerospace and electronics, application areas such as econometrics, finance, and speech and signal processing have contributed to a renaissance in areas such as realization theory and classical automatic feedback control. Thus, the last few years have witnessed a remarkable research effort expended in understanding both new algorithms and new paradigms for modeling and realization of linear processes and in the analysis and design of robust control strategies. The papers in this volume reflect these trends in both the theory and applications of linear systems and were selected from the invited and contributed papers presented at the 8th International Symposium on the Mathematical Theory of Networks and Systems held in Phoenix on June 15-19, 1987
Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory
Richtarik, Peter
2017-06-04
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.
Cao, Jian; Chen, Jing-Bo; Dai, Meng-Xue
2018-01-01
An efficient finite-difference frequency-domain modeling of seismic wave propagation relies on the discrete schemes and appropriate solving methods. The average-derivative optimal scheme for the scalar wave modeling is advantageous in terms of the storage saving for the system of linear equations and the flexibility for arbitrary directional sampling intervals. However, using a LU-decomposition-based direct solver to solve its resulting system of linear equations is very costly for both memory and computational requirements. To address this issue, we consider establishing a multigrid-preconditioned BI-CGSTAB iterative solver fit for the average-derivative optimal scheme. The choice of preconditioning matrix and its corresponding multigrid components is made with the help of Fourier spectral analysis and local mode analysis, respectively, which is important for the convergence. Furthermore, we find that for the computation with unequal directional sampling interval, the anisotropic smoothing in the multigrid precondition may affect the convergence rate of this iterative solver. Successful numerical applications of this iterative solver for the homogenous and heterogeneous models in 2D and 3D are presented where the significant reduction of computer memory and the improvement of computational efficiency are demonstrated by comparison with the direct solver. In the numerical experiments, we also show that the unequal directional sampling interval will weaken the advantage of this multigrid-preconditioned iterative solver in the computing speed or, even worse, could reduce its accuracy in some cases, which implies the need for a reasonable control of directional sampling interval in the discretization.
Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities
Directory of Open Access Journals (Sweden)
Y. N. Pavlov
2015-01-01
Full Text Available The subject of this work is the problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying test signals to the system. The goal is to determinate coefficients of differential equations of systems by experimental frequency hodographs and separate similar, but different, in essence, forces: dissipative forces with the square of the first derivative in the motion equations and dissipative force from the action of dry friction. There was a proposal to use the harmonic linearization method to approximate each of the nonlinearity of "quadratic friction" and "dry friction" by linear friction with the appropriate harmonic linearization coefficient.Assume that a frequency transfer function of the identified system has a known form. Assume as well that there are disturbances while obtaining frequency characteristics of the realworld system. As a result, the points of experimentally obtained hodograph move randomly. Searching for solution of the identification problem was in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified. Minimizing a proximity criterion (measure of the experimentally obtained system hodograph and the system hodograph model for all the experimental points described and previously published by one of the authors allowed searching for the unknown coefficients of the frequenc ransfer function of the system model. The paper shows the possibility to identify a nonlinear dynamic system with multiple nonlinearities, obtained on the experimental samples of the frequency system hodograph. The proposed algorithm allows to select the nonlinearity of the type "quadratic friction" and "dry friction", i.e. also in the case where the nonlinearity is dependent on the same dynamic parameter, in particular, on the derivative of the system output value. For the dynamic
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.
Linear filtering of systems with memory and application to finance
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We study the linear filtering problem for systems driven by continuous Gaussian processes V ( 1 and V ( 2 with memory described by two parameters. The processes V ( j have the virtue that they possess stationary increments and simple semimartingale representations simultaneously. They allow for straightforward parameter estimations. After giving the semimartingale representations of V ( j by innovation theory, we derive Kalman-Bucy-type filtering equations for the systems. We apply the result to the optimal portfolio problem for an investor with partial observations. We illustrate the tractability of the filtering algorithm by numerical implementations.
Parametric Linear Hybrid Automata for Complex Environmental Systems Modeling
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Samar Hayat Khan Tareen
2015-07-01
Full Text Available Environmental systems, whether they be weather patterns or predator-prey relationships, are dependent on a number of different variables, each directly or indirectly affecting the system at large. Since not all of these factors are known, these systems take on non-linear dynamics, making it difficult to accurately predict meaningful behavioral trends far into the future. However, such dynamics do not warrant complete ignorance of different efforts to understand and model close approximations of these systems. Towards this end, we have applied a logical modeling approach to model and analyze the behavioral trends and systematic trajectories that these systems exhibit without delving into their quantification. This approach, formalized by René Thomas for discrete logical modeling of Biological Regulatory Networks (BRNs and further extended in our previous studies as parametric biological linear hybrid automata (Bio-LHA, has been previously employed for the analyses of different molecular regulatory interactions occurring across various cells and microbial species. As relationships between different interacting components of a system can be simplified as positive or negative influences, we can employ the Bio-LHA framework to represent different components of the environmental system as positive or negative feedbacks. In the present study, we highlight the benefits of hybrid (discrete/continuous modeling which lead to refinements among the fore-casted behaviors in order to find out which ones are actually possible. We have taken two case studies: an interaction of three microbial species in a freshwater pond, and a more complex atmospheric system, to show the applications of the Bio-LHA methodology for the timed hybrid modeling of environmental systems. Results show that the approach using the Bio-LHA is a viable method for behavioral modeling of complex environmental systems by finding timing constraints while keeping the complexity of the model
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
This report documents research to develop robust and efficient solution techniques for solving large-scale systems of nonlinear equations. The most widely used method for solving systems of nonlinear equations is Newton's method. While much research has been devoted to augmenting Newton-based solvers (usually with globalization techniques), little has been devoted to exploring the application of different models. Our research has been directed at evaluating techniques using different models than Newton's method: a lower order model, Broyden's method, and a higher order model, the tensor method. We have developed large-scale versions of each of these models and have demonstrated their use in important applications at Sandia. Broyden's method replaces the Jacobian with an approximation, allowing codes that cannot evaluate a Jacobian or have an inaccurate Jacobian to converge to a solution. Limited-memory methods, which have been successful in optimization, allow us to extend this approach to large-scale problems. We compare the robustness and efficiency of Newton's method, modified Newton's method, Jacobian-free Newton-Krylov method, and our limited-memory Broyden method. Comparisons are carried out for large-scale applications of fluid flow simulations and electronic circuit simulations. Results show that, in cases where the Jacobian was inaccurate or could not be computed, Broyden's method converged in some cases where Newton's method failed to converge. We identify conditions where Broyden's method can be more efficient than Newton's method. We also present modifications to a large-scale tensor method, originally proposed by Bouaricha, for greater efficiency, better robustness, and wider applicability. Tensor methods are an alternative to Newton-based methods and are based on computing a step based on a local quadratic model rather than a linear model. The advantage of Bouaricha's method is that it can use any
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
Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.
Qi, Ruxi; Botello-Smith, Wesley M; Luo, Ray
2017-07-11
Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.
Development of a linear induction motor based artificial muscle system.
Gruber, A; Arguello, E; Silva, R
2013-01-01
We present the design of a linear induction motor based on electromagnetic interactions. The engine is capable of producing a linear movement from electricity. The design consists of stators arranged in parallel, which produce a magnetic field sufficient to displace a plunger along its axial axis. Furthermore, the winding has a shell and cap of ferromagnetic material that amplifies the magnetic field. This produces a force along the length of the motor that is similar to that of skeletal muscle. In principle, the objective is to use the engine in the development of an artificial muscle system for prosthetic applications, but it could have multiple applications, not only in the medical field, but in other industries.
Synchronization and Control of Linearly Coupled Singular Systems
Directory of Open Access Journals (Sweden)
Fang Qingxiang
2013-01-01
Full Text Available The synchronization and control problem of linearly coupled singular systems is investigated. The uncoupled dynamical behavior at each node is general and can be chaotic or, otherwise the coupling matrix is not assumed to be symmetrical. Some sufficient conditions for globally exponential synchronization are derived based on Lyapunov stability theory. These criteria, which are in terms of linear matrix inequality (LMI, indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold. The controllers are designed for state feedback control and pinning control, respectively. Finally, a numerical example is provided to illustrate the effectiveness of the proposed conditions.
Demultiplexing of photonic temporal modes by a linear system
Xu, Shuang; Shen, H. Z.; Yi, X. X.
2018-03-01
Temporally and spatially overlapping but field-orthogonal photonic temporal modes (TMs) that intrinsically span a high-dimensional Hilbert space are recently suggested as a promising means of encoding information on photons. Presently, the realization of photonic TM technology, particularly to retrieve the information it carries, i.e., demultiplexing of photonic TMs, is mostly dependent on nonlinear medium and frequency conversion. Meanwhile, its miniaturization, simplification, and optimization remain the focus of research. In this paper, we propose a scheme of TM demultiplexing using linear systems consisting of resonators with linear couplings. Specifically, we examine a unidirectional array of identical resonators with short environment correlations. For both situations with and without tunable couplers, propagation formulas are derived to demonstrate photonic TM demultiplexing capabilities. The proposed scheme, being entirely feasible with current technologies, might find potential applications in quantum information processing.
Linear and Non-Linear Dielectric Response of Periodic Systems from Quantum Monte Carlo
Umari, Paolo
2006-03-01
We present a novel approach that allows to calculate the dielectric response of periodic systems in the quantum Monte Carlo formalism. We employ a many-body generalization for the electric enthalpy functional, where the coupling with the field is expressed via the Berry-phase formulation for the macroscopic polarization. A self-consistent local Hamiltonian then determines the ground-state wavefunction, allowing for accurate diffusion quantum Monte Carlo calculations where the polarization's fixed point is estimated from the average on an iterative sequence. The polarization is sampled through forward-walking. This approach has been validated for the case of the polarizability of an isolated hydrogen atom, and then applied to a periodic system. We then calculate the linear susceptibility and second-order hyper-susceptibility of molecular-hydrogen chains whith different bond-length alternations, and assess the quality of nodal surfaces derived from density-functional theory or from Hartree-Fock. The results found are in excellent agreement with the best estimates obtained from the extrapolation of quantum-chemistry calculations.P. Umari, A.J. Williamson, G. Galli, and N. MarzariPhys. Rev. Lett. 95, 207602 (2005).
Linearization Technologies for Broadband Radio-Over-Fiber Transmission Systems
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Xiupu Zhang
2014-11-01
Full Text Available Linearization technologies that can be used for linearizing RoF transmission are reviewed. Three main linearization methods, i.e. electrical analog linearization, optical linearization, and electrical digital linearization are presented and compared. Analog linearization can be achieved using analog predistortion circuits, and can be used for suppression of odd order nonlinear distortion components, such as third and fifth order. Optical linearization includes mixed-polarization, dual-wavelength, optical channelization and the others, implemented in optical domain, to suppress both even and odd order nonlinear distortion components, such as second and third order. Digital predistortion has been a widely used linearization method for RF power amplifiers. However, digital linearization that requires analog to digital converter is severely limited to hundreds of MHz bandwidth. Instead, analog and optical linearization provide broadband linearization with up to tens of GHz. Therefore, for broadband radio over fiber transmission that can be used for future broadband cloud radio access networks, analog and optical linearization are more appropriate than digital linearization. Generally speaking, both analog and optical linearization are able to improve spur-free dynamic range greater than 10 dB over tens of GHz. In order for current digital linearization to be used for broadband radio over fiber transmission, the reduced linearization complexity and increased linearization bandwidth are required. Moreover, some digital linearization methods in which the complexity can be reduced, such as Hammerstein type, may be more promising and require further investigation.
Control of Linear Parameter Varying Systems with Applications
Mohammadpour, Javad
2012-01-01
Control of Linear Parameter Varying Systems with Applications compiles state-of-the-art contributions on novel analytical and computational methods to address system modeling and identification, complexity reduction, performance analysis and control design for time-varying and nonlinear systems in the LPV framework. The book has an interdisciplinary character by emphasizing techniques that can be commonly applied in various engineering fields. It also includes a rich collection of illustrative applications in diverse domains to substantiate the effectiveness of the design methodologies and provide pointers to open research directions. The book is divided into three parts. The first part collects chapters of a more tutorial character on the background of LPV systems modeling and control. The second part gathers chapters devoted to the theoretical advancement of LPV analysis and synthesis methods to cope with the design constraints such as uncertainties and time delay. The third part of the volume showcases con...
The new control system of the Saclay linear accelerator
International Nuclear Information System (INIS)
Gournay, J.F.
1985-10-01
A new control system for the Saclay Linear Accelerator designed during the two past years is now in operation. The computer control architecture is based on 3 dedicated VME crates: one crate with a disk-based operating system runs the high level application programs and the database management facilities, another one manages the man-machine communications and the third one interfaces the system to the linac equipments. At the present time, communications between the VME micro-computers are done through 16 bit parallel links. The software is modular and organized in specific layers, the database is fully distributed. About 90% of the code is written in Fortran. The present status of the system is discussed and the hardware and software developments are described
Core reset system design for linear induction accelerator
International Nuclear Information System (INIS)
Durga Praveen Kumar, D.; Mitra, S.; Sharma, Archana; Nagesh, K.V.; Chakravarthy, D.P.
2006-01-01
A repetitive pulsed power system based Linear Induction Accelerator (LIA-200) is being developed at BARC to get an electron beam of 200keV, 5kA, 50ns, 10-100 Hz. Amorphous core is the heart of these accelerators. It serves various functions in different subsystems viz. pulse power modulator, pulse transformer, magnetic switches and induction cavities. One of the factors that make the magnetic components compact is utilization of the total flux swing available in the core. In the present system, magnetic switches, pulse transformers, and induction cavity are designed to avail the full flux swing available in the core. For achieving this objective, flux density in the core has to be kept at the reverse saturation, before the main pulse is applied. The electrical circuit which makes it possible is called the core reset system. In this paper the details of core reset system designed for LIA-200 are described. (author)
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...
Practical application of equivalent linearization approaches to nonlinear piping systems
International Nuclear Information System (INIS)
Park, Y.J.; Hofmayer, C.H.
1995-01-01
The use of mechanical energy absorbers as an alternative to conventional hydraulic and mechanical snubbers for piping supports has attracted a wide interest among researchers and practitioners in the nuclear industry. The basic design concept of energy absorbers (EA) is to dissipate the vibration energy of piping systems through nonlinear hysteretic actions of EA exclamation point s under design seismic loads. Therefore, some type of nonlinear analysis needs to be performed in the seismic design of piping systems with EA supports. The equivalent linearization approach (ELA) can be a practical analysis tool for this purpose, particularly when the response approach (RSA) is also incorporated in the analysis formulations. In this paper, the following ELA/RSA methods are presented and compared to each other regarding their practice and numerical accuracy: Response approach using the square root of sum of squares (SRSS) approximation (denoted RS in this paper). Classical ELA based on modal combinations and linear random vibration theory (denoted CELA in this paper). Stochastic ELA based on direct solution of response covariance matrix (denoted SELA in this paper). New algorithms to convert response spectra to the equivalent power spectral density (PSD) functions are presented for both the above CELA and SELA methods. The numerical accuracy of the three EL are studied through a parametric error analysis. Finally, the practicality of the presented analysis is demonstrated in two application examples for piping systems with EA supports
A RECIPE FOR LINEAR COLLIDER FINAL FOCUS SYSTEM DESIGN
International Nuclear Information System (INIS)
Seryi, Andrei
2003-01-01
The design of Final Focus systems for linear colliders is challenging because of the large demagnifications needed to produce nanometer-sized beams at the interaction point. Simple first- and second-order matrix matching have proven insufficient for this task, and minimization of third- and higher-order aberrations is essential. An appropriate strategy is required for the latter to be successful. A recipe for Final Focus design, and a set of computational tools used to implement this approach, are described herein. An example of the use of this procedure is given
Periodic orbits from Δ-modulation of stable linear systems
Xia, X.; Zinober, A.
2004-01-01
The Î�-modulated control of a single input, discrete time, linear stable system is investigated. The modulation direction is given by cTx where c â��Rn/{0} is a given, otherwise arbitrary, vector. We obtain necessary and sufficient conditions for the existence of periodic points of a finite order. Some concrete results about the existence of a certain order of periodic points are also derived. We also study the relationship between certain polyhedra and the periodicity of the Î�-modulated orb...
Probing LINEAR Collider Final Focus Systems in SuperKEKB
Thrane, Paul Conrad Vaagen
2017-01-01
A challenge for future linear collider final focus systems is the large chromaticity produced by the final quadrupoles. SuperKEKB will be correcting high levels of chromaticity using the traditional scheme which has been also proposed for the CLIC FFS. We present early simulation results indicating that lowering β*у in the SuperKEKB Low Energy Ring might be possible given on-axis injection and low bunch current, opening the possibility of testing chromaticity correction beyond FFTB level, similar to ILC and approaching that of CLIC. CLIC – Note – 1077
Optimal Robust Fault Detection for Linear Discrete Time Systems
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Nike Liu
2008-01-01
Full Text Available This paper considers robust fault-detection problems for linear discrete time systems. It is shown that the optimal robust detection filters for several well-recognized robust fault-detection problems, such as ℋ−/ℋ∞, ℋ2/ℋ∞, and ℋ∞/ℋ∞ problems, are the same and can be obtained by solving a standard algebraic Riccati equation. Optimal filters are also derived for many other optimization criteria and it is shown that some well-studied and seeming-sensible optimization criteria for fault-detection filter design could lead to (optimal but useless fault-detection filters.
A novel linear switched reluctance motor for railway transportation systems
International Nuclear Information System (INIS)
Daldaban, Ferhat; Ustkoyuncu, Nurettin
2010-01-01
This paper presents the design and realization of a new linear switched reluctance motor (LSRM) structure, especially suitable for high-speed railway systems. The new model has a double active stator configuration and provides high force for many applications with low cost. The characteristics of the LSRM are obtained by using finite element analysis (FEA) and analytical calculations. The results of the FEA and analytical calculations are presented, and compared with experimental results. In addition, a classical double-sided LSRM (DSLSRM) is modeled with the same specifications of the new motor structure and the results are compared.
Novel Approach to Linear Accelerator Superconducting Magnet System
International Nuclear Information System (INIS)
Kashikhin, Vladimir
2011-01-01
Superconducting Linear Accelerators include a superconducting magnet system for particle beam transportation that provides the beam focusing and steering. This system consists of a large number of quadrupole magnets and dipole correctors mounted inside or between cryomodules with SCRF cavities. Each magnet has current leads and powered from its own power supply. The paper proposes a novel approach to magnet powering based on using superconducting persistent current switches. A group of magnets is powered from the same power supply through the common, for the group of cryomodules, electrical bus and pair of current leads. Superconducting switches direct the current to the chosen magnet and close the circuit providing the magnet operation in a persistent current mode. Two persistent current switches were fabricated and tested. In the paper also presented the results of magnetic field simulations, decay time constants analysis, and a way of improving quadrupole magnetic center stability. Such approach substantially reduces the magnet system cost and increases the reliability.
Considering system non-linearity in transmission pricing
International Nuclear Information System (INIS)
Oloomi-Buygi, M.; Salehizadeh, M. Reza
2008-01-01
In this paper a new approach for transmission pricing is presented. The contribution of a contract on power flow of a transmission line is used as extent-of-use criterion for transmission pricing. In order to determine the contribution of each contract on power flow of each transmission line, first the contribution of each contract on each voltage angle is determined, which is called voltage angle decomposition. To this end, DC power flow is used to compute a primary solution for voltage angle decomposition. To consider the impacts of system non-linearity on voltage angle decomposition, a method is presented to determine the share of different terms of sine argument in sine value. Then the primary solution is corrected in different iterations of decoupled Newton-Raphson power flow using the presented sharing method. The presented approach is applied to a 4-bus test system and IEEE 30-bus test system and the results are analyzed. (author)
Data acquisition system for linear PSD based neutron diffractometer
International Nuclear Information System (INIS)
Pande, S.S.; Borkar, S.P.; Behere, Anita; Ghodgaonkar, M.D.
2001-01-01
Single or multi-PSD configurations are used in different neutron diffractometer setups. A data acquisition system is developed to serve the gross requirements of all the diffractometer setups. It is also customized to specific requirements of different setups. The hardware is developed as a Transputer based add-on card. Most of the hardware functionality is handled in the Transputer program thus improving throughput of the system. The card can handle 16 RDCs, a few motor controls and on/off controls. The software comprises of a front-end Windows98 application, a Transputer program and a device driver. The data acquisition system performs data acquisition, analysis, display and storage. Analysis includes converting raw data of linear PSD to equiangular format, merging and clubbing the data to make a continuous equiangular spectrum. Calibration of individual PSD is a crucial activity in correctly merging the data coming from PSDs. (author)
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)
A generalized gyrokinetic Poisson solver
International Nuclear Information System (INIS)
Lin, Z.; Lee, W.W.
1995-03-01
A generalized gyrokinetic Poisson solver has been developed, which employs local operations in the configuration space to compute the polarization density response. The new technique is based on the actual physical process of gyrophase-averaging. It is useful for nonlocal simulations using general geometry equilibrium. Since it utilizes local operations rather than the global ones such as FFT, the new method is most amenable to massively parallel algorithms
Final focus system tuning studies towards Compact Linear Collider feasibility
Marin, E.; Latina, A.; Tomás, R.; Schulte, D.
2018-01-01
In this paper we present the latest results regarding the tuning study of the baseline design of the final focus system of the Compact Linear Collider (CLIC-FFS). CLIC aims to provide collisions to the experiments at a luminosity above 1034 c m-2 s-1 . In order to deliver such luminosity in a single pass machine, the vertical beam size at the interaction point (IP) is reduced to about 1 nm, which imposes unprecedented tuning difficulties to the system. In previous studies, 90% of the machines reached 90% of the nominal luminosity at the expense of 18 000 luminosity measurements, when considering beam position monitor errors and transverse misalignments of magnets for a single beam case. In the present study, additional static imperfections as, roll misalignments, strength v2.epss are included. Moreover both e- and e+ beamlines are properly simulated. A new tuning procedure based on linear and nonlinear knobs is implemented to effectively cure the most relevant beam size aberrations at the IP. The obtained results for single and double beam studies under solely static imperfections are presented.
Efficient Feedforward Linearization Technique Using Genetic Algorithms for OFDM Systems
Directory of Open Access Journals (Sweden)
García Paloma
2010-01-01
Full Text Available Feedforward is a linearization method that simultaneously offers wide bandwidth and good intermodulation distortion suppression; so it is a good choice for Orthogonal Frequency Division Multiplexing (OFDM systems. Feedforward structure consists of two loops, being necessary an accurate adjustment between them along the time, and when temperature, environmental, or operating changes are produced. Amplitude and phase imbalances of the circuit elements in both loops produce mismatched effects that lead to degrade its performance. A method is proposed to compensate these mismatches, introducing two complex coefficients calculated by means of a genetic algorithm. A full study is carried out to choose the optimal parameters of the genetic algorithm applied to wideband systems based on OFDM technologies, which are very sensitive to nonlinear distortions. The method functionality has been verified by means of simulation.
On modulated complex non-linear dynamical systems
International Nuclear Information System (INIS)
Mahmoud, G.M.; Mohamed, A.A.; Rauh, A.
1999-01-01
This paper is concerned with the development of an approximate analytical method to investigate periodic solutions and their stability in the case of modulated non-linear dynamical systems whose equation of motion is describe. Such differential equations appear, for example, in problems of colliding particle beams in high-energy accelerators or one-mass systems with two or more degrees of freedom, e.g. rotors. The significance of periodic solutions lies on the fact that all non-periodic responses, if convergent, would approach to periodic solutions at the steady-state conditions. The example shows a good agreement between numerical and analytical results for small values of ε. The effect of the periodic modulation on the stability of the 2π-periodic solutions is discussed
Thermodynamic Optimality criteria for biological systems in linear irreversible thermodynamics
International Nuclear Information System (INIS)
Chimal, J C; Sánchez, N; Ramírez, PR
2017-01-01
In this paper the methodology of the so-called Linear Irreversible Thermodynamics (LIT) is applied; although traditionally used locally to study general systems in non-equilibrium states in which it is consider both internal and external contributions to the entropy increments in order to analyze the efficiency of two coupled processes with generalized fluxes J 1 , J 2 and their corresponding forces X 1 , X 2 . We extend the former analysis to takes into account two different operating regimes namely: Omega Function and Efficient Power criterion, respectively. Results show analogies in the optimal performance between and we can say that there exist a criteria of optimization which can be used specially for biological systems where a good design of the biological parameters made by nature at maximum efficient power conditions lead to more efficient engines than those at the maximum power conditions or ecological conditions. (paper)
Linear system identification via backward-time observer models
Juang, Jer-Nan; Phan, Minh
1993-01-01
This paper presents an algorithm to identify a state-space model of a linear system using a backward-time approach. The procedure consists of three basic steps. First, the Markov parameters of a backward-time observer are computed from experimental input-output data. Second, the backward-time observer Markov parameters are decomposed to obtain the backward-time system Markov parameters (backward-time pulse response samples) from which a backward-time state-space model is realized using the Eigensystem Realization Algorithm. Third, the obtained backward-time state space model is converted to the usual forward-time representation. Stochastic properties of this approach will be discussed. Experimental results are given to illustrate when and to what extent this concept works.
Ultra-high Frequency Linear Fiber Optic Systems
Lau, Kam Y
2009-01-01
Designed for a one-semester course on fiber-optics systems and communication links, this book provides a concise but rigorous treatment of the theory and practice of analog (linear) fiber-optics links and systems that constitute the foundation of Hybrid Fiber Coax infrastructure in present-day CATV distribution and cable modem Internet access. Emerging applications in remote fiber-optic feed for free-space millimeter wave enterprise campus networks are also described. Issues such as dispersion and interferometric noise are treated quantitatively, and means for mitigating them are explained. This broad but concise text will thus be invaluable not only to students of fiber-optics communication but also to practicing engineers.
Linear theory for filtering nonlinear multiscale systems with model error.
Berry, Tyrus; Harlim, John
2014-07-08
In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online , as part of a filtering
Scalable multi-grid preconditioning techniques for the even-parity S_N solver in UNIC
International Nuclear Information System (INIS)
Mahadevan, Vijay S.; Smith, Michael A.
2011-01-01
The Even-parity neutron transport equation with FE-S_N discretization is solved traditionally using SOR preconditioned CG method at the lowest level of iterations in order to compute the criticality in reactor analysis problems. The use of high order isoparametric finite elements prohibits the formation of the discrete operator explicitly due to memory constraints in peta scale architectures. Hence, a h-p multi-grid preconditioner based on linear tessellation of the higher order mesh is introduced here for the space-angle system and compared against SOR and Algebraic MG black-box solvers. The performance and scalability of the multi-grid scheme was determined for two test problems and found to be competitive in terms of both computational time and memory requirements. The implementation of this preconditioner in an even-parity solver like UNIC from ANL can further enable high fidelity calculations in a scalable manner on peta flop machines. (author)
Linear analysis of rotationally invariant, radially variant tomographic imaging systems
International Nuclear Information System (INIS)
Huesmann, R.H.
1990-01-01
This paper describes a method to analyze the linear imaging characteristics of rotationally invariant, radially variant tomographic imaging systems using singular value decomposition (SVD). When the projection measurements from such a system are assumed to be samples from independent and identically distributed multi-normal random variables, the best estimate of the emission intensity is given by the unweighted least squares estimator. The noise amplification of this estimator is inversely proportional to the singular values of the normal matrix used to model projection and backprojection. After choosing an acceptable noise amplification, the new method can determine the number of parameters and hence the number of pixels that should be estimated from data acquired from an existing system with a fixed number of angles and projection bins. Conversely, for the design of a new system, the number of angles and projection bins necessary for a given number of pixels and noise amplification can be determined. In general, computing the SVD of the projection normal matrix has cubic computational complexity. However, the projection normal matrix for this class of rotationally invariant, radially variant systems has a block circulant form. A fast parallel algorithm to compute the SVD of this block circulant matrix makes the singular value analysis practical by asymptotically reducing the computation complexity of the method by a multiplicative factor equal to the number of angles squared
Linear homotopy solution of nonlinear systems of equations in geodesy
Paláncz, Béla; Awange, Joseph L.; Zaletnyik, Piroska; Lewis, Robert H.
2010-01-01
A fundamental task in geodesy is solving systems of equations. Many geodetic problems are represented as systems of multivariate polynomials. A common problem in solving such systems is improper initial starting values for iterative methods, leading to convergence to solutions with no physical meaning, or to convergence that requires global methods. Though symbolic methods such as Groebner bases or resultants have been shown to be very efficient, i.e., providing solutions for determined systems such as 3-point problem of 3D affine transformation, the symbolic algebra can be very time consuming, even with special Computer Algebra Systems (CAS). This study proposes the Linear Homotopy method that can be implemented easily in high-level computer languages like C++ and Fortran that are faster than CAS by at least two orders of magnitude. Using Mathematica, the power of Homotopy is demonstrated in solving three nonlinear geodetic problems: resection, GPS positioning, and affine transformation. The method enlarging the domain of convergence is found to be efficient, less sensitive to rounding of numbers, and has lower complexity compared to other local methods like Newton-Raphson.
Boltzmann Solver with Adaptive Mesh in Velocity Space
International Nuclear Information System (INIS)
Kolobov, Vladimir I.; Arslanbekov, Robert R.; Frolova, Anna A.
2011-01-01
We describe the implementation of direct Boltzmann solver with Adaptive Mesh in Velocity Space (AMVS) using quad/octree data structure. The benefits of the AMVS technique are demonstrated for the charged particle transport in weakly ionized plasmas where the collision integral is linear. We also describe the implementation of AMVS for the nonlinear Boltzmann collision integral. Test computations demonstrate both advantages and deficiencies of the current method for calculations of narrow-kernel distributions.
Energy consumption optimization of the total-FETI solver by changing the CPU frequency
Horak, David; Riha, Lubomir; Sojka, Radim; Kruzik, Jakub; Beseda, Martin; Cermak, Martin; Schuchart, Joseph
2017-07-01
The energy consumption of supercomputers is one of the critical problems for the upcoming Exascale supercomputing era. The awareness of power and energy consumption is required on both software and hardware side. This paper deals with the energy consumption evaluation of the Finite Element Tearing and Interconnect (FETI) based solvers of linear systems, which is an established method for solving real-world engineering problems. We have evaluated the effect of the CPU frequency on the energy consumption of the FETI solver using a linear elasticity 3D cube synthetic benchmark. In this problem, we have evaluated the effect of frequency tuning on the energy consumption of the essential processing kernels of the FETI method. The paper provides results for two types of frequency tuning: (1) static tuning and (2) dynamic tuning. For static tuning experiments, the frequency is set before execution and kept constant during the runtime. For dynamic tuning, the frequency is changed during the program execution to adapt the system to the actual needs of the application. The paper shows that static tuning brings up 12% energy savings when compared to default CPU settings (the highest clock rate). The dynamic tuning improves this further by up to 3%.
The theory of a general quantum system interacting with a linear dissipative system
International Nuclear Information System (INIS)
Feynman, R.P.; Vernon, F.L.
2000-01-01
A formalism has been developed, using Feynman's space-time formulation of nonrelativistic quantum mechanics whereby the behavior of a system of interest, which is coupled to other external quantum systems, may be calculated in terms of its own variables only. It is shown that the effect of the external systems in such a formalism can always be included in a general class of functionals (influence functionals) of the coordinates of the system only. The properties of influence functionals for general systems are examined. Then, specific forms of influence functionals representing the effect of definite and random classical forces, linear dissipative systems at finite temperatures, and combinations of these are analyzed in detail. The linear system analysis is first done for perfectly linear systems composed of combinations of harmonic oscillators, loss being introduced by continuous distributions of oscillators. Then approximately linear systems and restrictions necessary for the linear behavior are considered. Influence functionals for all linear systems are shown to have the same form in terms of their classical response functions. In addition, a fluctuation-dissipation theorem is derived relating temperature and dissipation of the linear system to a fluctuating classical potential acting on the system of interest which reduces to the Nyquist-Johnson relation for noise in the case of electric circuits. Sample calculations of transition probabilities for the spontaneous emission of an atom in free space and in a cavity are made. Finally, a theorem is proved showing that within the requirements of linearity all sources of noise or quantum fluctuation introduced by maser-type amplification devices are accounted for by a classical calculation of the characteristics of the maser
Radii of Solvability and Unsolvability of Linear Systems
Czech Academy of Sciences Publication Activity Database
Hladík, M.; Rohn, Jiří
2016-01-01
Roč. 503, 15 August (2016), s. 120-134 ISSN 0024-3795 Institutional support: RVO:67985807 Keywords : interval matrix * linear equations * linear inequalities * matrix norm Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016
Numerical Study of Concentration Characteristics of Linear Fresnel Reflector System
International Nuclear Information System (INIS)
Lee, Hyun Jin; Kim, Jong Kyu; Lee, Sang Nam
2015-01-01
In this study, we numerically investigated the concentration characteristics of a linear Fresnel reflector system that can drive a solar thermal absorption refrigeration system to be installed in Saudi Arabia. Using an optical modeling program based on the Monte Carlo ray-tracing method, we simulated the concentrated solar flux, concentration efficiency, and concentrated solar energy on four representative days of the year - the vernal equinox, summer solstice, autumnal equinox, and winter solstice. Except the winter solstice, the concentrations were approximately steady from 9 AM to 15 PM, and the concentration efficiencies exceed 70%. Moreover, the maximum solar flux around the solar receiver center changes only within the range of 13.0 - 14.6 kW/m 2 . When we investigated the effects of the receiver installation height, reflector width, and reflector gap, the optimal receiver installation height was found to be 5 m. A smaller reflector width had a greater concentration efficiency. However, the design of the reflector width should be based on the capacity of the refrigeration system because it dominantly affects the concentrated solar energy. The present study was an essential prerequisite for thermal analyses of the solar receiver. Thus, an optical-thermal integration study in the future will assist with the performance prediction and design of the entire system
Numerical Study of Concentration Characteristics of Linear Fresnel Reflector System
Energy Technology Data Exchange (ETDEWEB)
Lee, Hyun Jin [Kookmin Univ., Seoul (Korea, Republic of); Kim, Jong Kyu; Lee, Sang Nam [Korea Institute of Energy Research, Daejeon (Korea, Republic of)
2015-12-15
In this study, we numerically investigated the concentration characteristics of a linear Fresnel reflector system that can drive a solar thermal absorption refrigeration system to be installed in Saudi Arabia. Using an optical modeling program based on the Monte Carlo ray-tracing method, we simulated the concentrated solar flux, concentration efficiency, and concentrated solar energy on four representative days of the year - the vernal equinox, summer solstice, autumnal equinox, and winter solstice. Except the winter solstice, the concentrations were approximately steady from 9 AM to 15 PM, and the concentration efficiencies exceed 70%. Moreover, the maximum solar flux around the solar receiver center changes only within the range of 13.0 - 14.6 kW/m{sup 2}. When we investigated the effects of the receiver installation height, reflector width, and reflector gap, the optimal receiver installation height was found to be 5 m. A smaller reflector width had a greater concentration efficiency. However, the design of the reflector width should be based on the capacity of the refrigeration system because it dominantly affects the concentrated solar energy. The present study was an essential prerequisite for thermal analyses of the solar receiver. Thus, an optical-thermal integration study in the future will assist with the performance prediction and design of the entire system.
Periodic inventory system in cafeteria using linear programming
Usop, Mohd Fais; Ishak, Ruzana; Hamdan, Ahmad Ridhuan
2017-11-01
Inventory management is an important factor in running a business. It plays a big role of managing the stock in cafeteria. If the inventories are failed to be managed wisely, it will affect the profit of the cafeteria. Therefore, the purpose of this study is to find the solution of the inventory management in cafeteria. Most of the cafeteria in Malaysia did not manage their stock well. Therefore, this study is to propose a database system of inventory management and to develop the inventory model in cafeteria management. In this study, new database system to improve the management of the stock in a weekly basis will be provided using Linear Programming Model to get the optimal range of the inventory needed for selected categories. Data that were collected by using the Periodic Inventory System at the end of the week within three months period being analyzed by using the Food Stock-take Database. The inventory model was developed from the collected data according to the category of the inventory in the cafeteria. Results showed the effectiveness of using the Periodic Inventory System and will be very helpful to the cafeteria management in organizing the inventory. Moreover, the findings in this study can reduce the cost of operation and increased the profit.
Incomplete factorization technique for positive definite linear systems
International Nuclear Information System (INIS)
Manteuffel, T.A.
1980-01-01
This paper describes a technique for solving the large sparse symmetric linear systems that arise from the application of finite element methods. The technique combines an incomplete factorization method called the shifted incomplete Cholesky factorization with the method of generalized conjugate gradients. The shifted incomplete Cholesky factorization produces a splitting of the matrix A that is dependent upon a parameter α. It is shown that if A is positive definite, then there is some α for which this splitting is possible and that this splitting is at least as good as the Jacobi splitting. The method is shown to be more efficient on a set of test problems than either direct methods or explicit iteration schemes
Stability and complexity of small random linear systems
Hastings, Harold
2010-03-01
We explore the stability of the small random linear systems, typically involving 10-20 variables, motivated by dynamics of the world trade network and the US and Canadian power grid. This report was prepared as an account of work sponsored by an agency of the US Government. Neither the US Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the US Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the US Government or any agency thereof.
Compressive System Identification in the Linear Time-Invariant framework
Toth, Roland
2011-12-01
Selection of an efficient model parametrization (model order, delay, etc.) has crucial importance in parametric system identification. It navigates a trade-off between representation capabilities of the model (structural bias) and effects of over-parametrization (variance increase of the estimates). There exists many approaches to this widely studied problem in terms of statistical regularization methods and information criteria. In this paper, an alternative ℓ 1 regularization scheme is proposed for estimation of sparse linear-regression models based on recent results in compressive sensing. It is shown that the proposed scheme provides consistent estimation of sparse models in terms of the so-called oracle property, it is computationally attractive for large-scale over-parameterized models and it is applicable in case of small data sets, i.e., underdetermined estimation problems. The performance of the approach w.r.t. other regularization schemes is demonstrated in an extensive Monte Carlo study. © 2011 IEEE.
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.
Preisach hysteresis model for non-linear 2D heat diffusion
International Nuclear Information System (INIS)
Jancskar, Ildiko; Ivanyi, Amalia
2006-01-01
This paper analyzes a non-linear heat diffusion process when the thermal diffusivity behaviour is a hysteretic function of the temperature. Modelling this temperature dependence, the discrete Preisach algorithm as general hysteresis model has been integrated into a non-linear multigrid solver. The hysteretic diffusion shows a heating-cooling asymmetry in character. The presented type of hysteresis speeds up the thermal processes in the modelled systems by a very interesting non-linear way
Yihaa Roodhiyah, Lisa’; Tjong, Tiffany; Nurhasan; Sutarno, D.
2018-04-01
The late research, linear matrices of vector finite element in two dimensional(2-D) magnetotelluric (MT) responses modeling was solved by non-sparse direct solver in TE mode. Nevertheless, there is some weakness which have to be improved especially accuracy in the low frequency (10-3 Hz-10-5 Hz) which is not achieved yet and high cost computation in dense mesh. In this work, the solver which is used is sparse direct solver instead of non-sparse direct solverto overcome the weaknesses of solving linear matrices of vector finite element metod using non-sparse direct solver. Sparse direct solver will be advantageous in solving linear matrices of vector finite element method because of the matrix properties which is symmetrical and sparse. The validation of sparse direct solver in solving linear matrices of vector finite element has been done for a homogen half-space model and vertical contact model by analytical solution. Thevalidation result of sparse direct solver in solving linear matrices of vector finite element shows that sparse direct solver is more stable than non-sparse direct solver in computing linear problem of vector finite element method especially in low frequency. In the end, the accuracy of 2D MT responses modelling in low frequency (10-3 Hz-10-5 Hz) has been reached out under the efficient allocation memory of array and less computational time consuming.
Sampled-data models for linear and nonlinear systems
Yuz, Juan I
2014-01-01
Sampled-data Models for Linear and Nonlinear Systems provides a fresh new look at a subject with which many researchers may think themselves familiar. Rather than emphasising the differences between sampled-data and continuous-time systems, the authors proceed from the premise that, with modern sampling rates being as high as they are, it is becoming more appropriate to emphasise connections and similarities. The text is driven by three motives: · the ubiquity of computers in modern control and signal-processing equipment means that sampling of systems that really evolve continuously is unavoidable; · although superficially straightforward, sampling can easily produce erroneous results when not treated properly; and · the need for a thorough understanding of many aspects of sampling among researchers and engineers dealing with applications to which they are central. The authors tackle many misconceptions which, although appearing reasonable at first sight, are in fact either p...
Linear program differentiation for single-channel speech separation
DEFF Research Database (Denmark)
Pearlmutter, Barak A.; Olsson, Rasmus Kongsgaard
2006-01-01
Many apparently difficult problems can be solved by reduction to linear programming. Such problems are often subproblems within larger systems. When gradient optimisation of the entire larger system is desired, it is necessary to propagate gradients through the internally-invoked LP solver....... For instance, when an intermediate quantity z is the solution to a linear program involving constraint matrix A, a vector of sensitivities dE/dz will induce sensitivities dE/dA. Here we show how these can be efficiently calculated, when they exist. This allows algorithmic differentiation to be applied...... to algorithms that invoke linear programming solvers as subroutines, as is common when using sparse representations in signal processing. Here we apply it to gradient optimisation of over complete dictionaries for maximally sparse representations of a speech corpus. The dictionaries are employed in a single...
DEFF Research Database (Denmark)
Ommen, Torben Schmidt; Markussen, Wiebke Brix; Elmegaard, Brian
2014-01-01
In the paper, three frequently used operation optimisation methods are examined with respect to their impact on operation management of the combined utility technologies for electric power and DH (district heating) of eastern Denmark. The investigation focusses on individual plant operation...... differences and differences between the solution found by each optimisation method. One of the investigated approaches utilises LP (linear programming) for optimisation, one uses LP with binary operation constraints, while the third approach uses NLP (non-linear programming). The LP model is used...... as a benchmark, as this type is frequently used, and has the lowest amount of constraints of the three. A comparison of the optimised operation of a number of units shows significant differences between the three methods. Compared to the reference, the use of binary integer variables, increases operation...
2-D linear motion system. Innovative technology summary report
International Nuclear Information System (INIS)
1998-11-01
The US Department of Energy's (DOE's) nuclear facility decontamination and decommissioning (D and D) program requires buildings to be decontaminated, decommissioned, and surveyed for radiological contamination in an expeditious and cost-effective manner. Simultaneously, the health and safety of personnel involved in the D and D activities is of primary concern. D and D workers must perform duties high off the ground, requiring the use of manlifts or scaffolding, often, in radiologically or chemically contaminated areas or in areas with limited access. Survey and decontamination instruments that are used are sometimes heavy or awkward to use, particularly when the worker is operating from a manlift or scaffolding. Finding alternative methods of performing such work on manlifts or scaffolding is important. The 2-D Linear Motion System (2-D LMS), also known as the Wall Walker trademark, is designed to remotely position tools and instruments on walls for use in such activities as radiation surveys, decontamination, and painting. Traditional (baseline) methods for operating equipment for these tasks require workers to perform duties on elevated platforms, sometimes several meters above the ground surface and near potential sources of contamination. The Wall Walker 2-D LMS significantly improves health and safety conditions by facilitating remote operation of equipment. The Wall Walker 2-D LMS performed well in a demonstration of its precision, accuracy, maneuverability, payload capacity, and ease of use. Thus, this innovative technology is demonstrated to be a viable alternative to standard methods of performing work on large, high walls, especially those that have potential contamination concerns. The Wall Walker was used to perform a final release radiological survey on over 167 m 2 of walls. In this application, surveying using a traditional (baseline) method that employs an aerial lift for manual access was 64% of the total cost of the improved technology. However
Low-Rank Linear Dynamical Systems for Motor Imagery EEG.
Zhang, Wenchang; Sun, Fuchun; Tan, Chuanqi; Liu, Shaobo
2016-01-01
The common spatial pattern (CSP) and other spatiospectral feature extraction methods have become the most effective and successful approaches to solve the problem of motor imagery electroencephalography (MI-EEG) pattern recognition from multichannel neural activity in recent years. However, these methods need a lot of preprocessing and postprocessing such as filtering, demean, and spatiospectral feature fusion, which influence the classification accuracy easily. In this paper, we utilize linear dynamical systems (LDSs) for EEG signals feature extraction and classification. LDSs model has lots of advantages such as simultaneous spatial and temporal feature matrix generation, free of preprocessing or postprocessing, and low cost. Furthermore, a low-rank matrix decomposition approach is introduced to get rid of noise and resting state component in order to improve the robustness of the system. Then, we propose a low-rank LDSs algorithm to decompose feature subspace of LDSs on finite Grassmannian and obtain a better performance. Extensive experiments are carried out on public dataset from "BCI Competition III Dataset IVa" and "BCI Competition IV Database 2a." The results show that our proposed three methods yield higher accuracies compared with prevailing approaches such as CSP and CSSP.
A virtual linear accelerator for verification of treatment planning systems
International Nuclear Information System (INIS)
Wieslander, Elinore
2000-01-01
A virtual linear accelerator is implemented into a commercial pencil-beam-based treatment planning system (TPS) with the purpose of investigating the possibility of verifying the system using a Monte Carlo method. The characterization set for the TPS includes depth doses, profiles and output factors, which is generated by Monte Carlo simulations. The advantage of this method over conventional measurements is that variations in accelerator output are eliminated and more complicated geometries can be used to study the performance of a TPS. The difference between Monte Carlo simulated and TPS calculated profiles and depth doses in the characterization geometry is less than ±2% except for the build-up region. This is of the same order as previously reported results based on measurements. In an inhomogeneous, mediastinum-like case, the deviations between TPS and simulations are small in the unit-density regions. In low-density regions, the TPS overestimates the dose, and the overestimation increases with increasing energy from 3.5% for 6 MV to 9.5% for 18 MV. This result points out the widely known fact that the pencil beam concept does not handle changes in lateral electron transport, nor changes in scatter due to lateral inhomogeneities. It is concluded that verification of a pencil-beam-based TPS with a Monte Carlo based virtual accelerator is possible, which facilitates the verification procedure. (author)
Stochastic linear hybrid systems: Modeling, estimation, and application
Seah, Chze Eng
Hybrid systems are dynamical systems which have interacting continuous state and discrete state (or mode). Accurate modeling and state estimation of hybrid systems are important in many applications. We propose a hybrid system model, known as the Stochastic Linear Hybrid System (SLHS), to describe hybrid systems with stochastic linear system dynamics in each mode and stochastic continuous-state-dependent mode transitions. We then develop a hybrid estimation algorithm, called the State-Dependent-Transition Hybrid Estimation (SDTHE) algorithm, to estimate the continuous state and discrete state of the SLHS from noisy measurements. It is shown that the SDTHE algorithm is more accurate or more computationally efficient than existing hybrid estimation algorithms. Next, we develop a performance analysis algorithm to evaluate the performance of the SDTHE algorithm in a given operating scenario. We also investigate sufficient conditions for the stability of the SDTHE algorithm. The proposed SLHS model and SDTHE algorithm are illustrated to be useful in several applications. In Air Traffic Control (ATC), to facilitate implementations of new efficient operational concepts, accurate modeling and estimation of aircraft trajectories are needed. In ATC, an aircraft's trajectory can be divided into a number of flight modes. Furthermore, as the aircraft is required to follow a given flight plan or clearance, its flight mode transitions are dependent of its continuous state. However, the flight mode transitions are also stochastic due to navigation uncertainties or unknown pilot intents. Thus, we develop an aircraft dynamics model in ATC based on the SLHS. The SDTHE algorithm is then used in aircraft tracking applications to estimate the positions/velocities of aircraft and their flight modes accurately. Next, we develop an aircraft conformance monitoring algorithm to detect any deviations of aircraft trajectories in ATC that might compromise safety. In this application, the SLHS
Popov–Belevitch–Hautus type tests for the controllability of linear complementarity systems
Camlibel, M. Kanat
2007-01-01
It is well-known that checking certain controllability properties of very simple piecewise linear systems are undecidable problems. This paper deals with the controllability problem of a class of piecewise linear systems, known as linear complementarity systems. By exploiting the underlying
A General Symbolic PDE Solver Generator: Explicit Schemes
Directory of Open Access Journals (Sweden)
K. Sheshadri
2003-01-01
Full Text Available A symbolic solver generator to deal with a system of partial differential equations (PDEs in functions of an arbitrary number of variables is presented; it can also handle arbitrary domains (geometries of the independent variables. Given a system of PDEs, the solver generates a set of explicit finite-difference methods to any specified order, and a Fourier stability criterion for each method. For a method that is stable, an iteration function is generated symbolically using the PDE and its initial and boundary conditions. This iteration function is dynamically generated for every PDE problem, and its evaluation provides a solution to the PDE problem. A C++/Fortran 90 code for the iteration function is generated using the MathCode system, which results in a performance gain of the order of a thousand over Mathematica, the language that has been used to code the solver generator. Examples of stability criteria are presented that agree with known criteria; examples that demonstrate the generality of the solver and the speed enhancement of the generated C++ and Fortran 90 codes are also presented.
On computation of Groebner bases for linear difference systems
Energy Technology Data Exchange (ETDEWEB)
Gerdt, Vladimir P. [Laboratory of Information Technologies, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation)]. E-mail: gerdt@jinr.ru
2006-04-01
In this paper, we present an algorithm for computing Groebner bases of linear ideals in a difference polynomial ring over a ground difference field. The input difference polynomials generating the ideal are also assumed to be linear. The algorithm is an adaptation to difference ideals of our polynomial algorithm based on Janet-like reductions.
On computation of Groebner bases for linear difference systems
International Nuclear Information System (INIS)
Gerdt, Vladimir P.
2006-01-01
In this paper, we present an algorithm for computing Groebner bases of linear ideals in a difference polynomial ring over a ground difference field. The input difference polynomials generating the ideal are also assumed to be linear. The algorithm is an adaptation to difference ideals of our polynomial algorithm based on Janet-like reductions
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).
Directory of Open Access Journals (Sweden)
Huiying Sun
2014-01-01
Full Text Available We mainly consider the stability of discrete-time Markovian jump linear systems with state-dependent noise as well as its linear quadratic (LQ differential games. A necessary and sufficient condition involved with the connection between stochastic Tn-stability of Markovian jump linear systems with state-dependent noise and Lyapunov equation is proposed. And using the theory of stochastic Tn-stability, we give the optimal strategies and the optimal cost values for infinite horizon LQ stochastic differential games. It is demonstrated that the solutions of infinite horizon LQ stochastic differential games are concerned with four coupled generalized algebraic Riccati equations (GAREs. Finally, an iterative algorithm is presented to solve the four coupled GAREs and a simulation example is given to illustrate the effectiveness of it.
Evaluation of beach cleanup effects using linear system analysis.
Kataoka, Tomoya; Hinata, Hirofumi
2015-02-15
We established a method for evaluating beach cleanup effects (BCEs) based on a linear system analysis, and investigated factors determining BCEs. Here we focus on two BCEs: decreasing the total mass of toxic metals that could leach into a beach from marine plastics and preventing the fragmentation of marine plastics on the beach. Both BCEs depend strongly on the average residence time of marine plastics on the beach (τ(r)) and the period of temporal variability of the input flux of marine plastics (T). Cleanups on the beach where τ(r) is longer than T are more effective than those where τ(r) is shorter than T. In addition, both BCEs are the highest near the time when the remnants of plastics reach the local maximum (peak time). Therefore, it is crucial to understand the following three factors for effective cleanups: the average residence time, the plastic input period and the peak time. Copyright © 2014 Elsevier Ltd. All rights reserved.
Kuźnik, Krzysztof; Paszyński, Maciej; Calo, Victor M.
2013-01-01
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
On differential operators generating iterative systems of linear ODEs of maximal symmetry algebra
Ndogmo, J. C.
2017-06-01
Although every iterative scalar linear ordinary differential equation is of maximal symmetry algebra, the situation is different and far more complex for systems of linear ordinary differential equations, and an iterative system of linear equations need not be of maximal symmetry algebra. We illustrate these facts by examples and derive families of vector differential operators whose iterations are all linear systems of equations of maximal symmetry algebra. Some consequences of these results are also discussed.
A Nonlinear Modal Aeroelastic Solver for FUN3D
Goldman, Benjamin D.; Bartels, Robert E.; Biedron, Robert T.; Scott, Robert C.
2016-01-01
A nonlinear structural solver has been implemented internally within the NASA FUN3D computational fluid dynamics code, allowing for some new aeroelastic capabilities. Using a modal representation of the structure, a set of differential or differential-algebraic equations are derived for general thin structures with geometric nonlinearities. ODEPACK and LAPACK routines are linked with FUN3D, and the nonlinear equations are solved at each CFD time step. The existing predictor-corrector method is retained, whereby the structural solution is updated after mesh deformation. The nonlinear solver is validated using a test case for a flexible aeroshell at transonic, supersonic, and hypersonic flow conditions. Agreement with linear theory is seen for the static aeroelastic solutions at relatively low dynamic pressures, but structural nonlinearities limit deformation amplitudes at high dynamic pressures. No flutter was found at any of the tested trajectory points, though LCO may be possible in the transonic regime.
Nonlinear Multigrid solver exploiting AMGe Coarse Spaces with Approximation Properties
DEFF Research Database (Denmark)
Christensen, Max la Cour; Villa, Umberto; Engsig-Karup, Allan Peter
The 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 main motivation to use FAS for unstructured problems is the guaranteed approximation property of the AMGe coarse...... 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...
Design of a Modular Monolithic Implicit Solver for Multi-Physics Applications
Carton De Wiart, Corentin; Diosady, Laslo T.; Garai, Anirban; Burgess, Nicholas; Blonigan, Patrick; Ekelschot, Dirk; Murman, Scott M.
2018-01-01
The design of a modular multi-physics high-order space-time finite-element framework is presented together with its extension to allow monolithic coupling of different physics. One of the main objectives of the framework is to perform efficient high- fidelity simulations of capsule/parachute systems. This problem requires simulating multiple physics including, but not limited to, the compressible Navier-Stokes equations, the dynamics of a moving body with mesh deformations and adaptation, the linear shell equations, non-re effective boundary conditions and wall modeling. The solver is based on high-order space-time - finite element methods. Continuous, discontinuous and C1-discontinuous Galerkin methods are implemented, allowing one to discretize various physical models. Tangent and adjoint sensitivity analysis are also targeted in order to conduct gradient-based optimization, error estimation, mesh adaptation, and flow control, adding another layer of complexity to the framework. The decisions made to tackle these challenges are presented. The discussion focuses first on the "single-physics" solver and later on its extension to the monolithic coupling of different physics. The implementation of different physics modules, relevant to the capsule/parachute system, are also presented. Finally, examples of coupled computations are presented, paving the way to the simulation of the full capsule/parachute system.
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
Electron linear accelerator system for natural rubber vulcanization
Rimjaem, S.; Kongmon, E.; Rhodes, M. W.; Saisut, J.; Thongbai, C.
2017-09-01
Development of an electron accelerator system, beam diagnostic instruments, an irradiation apparatus and electron beam processing methodology for natural rubber vulcanization is underway at the Plasma and Beam Physics Research Facility, Chiang Mai University, Thailand. The project is carried out with the aims to improve the qualities of natural rubber products. The system consists of a DC thermionic electron gun, 5-cell standing-wave radio-frequency (RF) linear accelerator (linac) with side-coupling cavities and an electron beam irradiation apparatus. This system is used to produce electron beams with an adjustable energy between 0.5 and 4 MeV and a pulse current of 10-100 mA at a pulse repetition rate of 20-400 Hz. An average absorbed dose between 160 and 640 Gy is expected to be archived for 4 MeV electron beam when the accelerator is operated at 400 Hz. The research activities focus firstly on assembling of the accelerator system, study on accelerator properties and electron beam dynamic simulations. The resonant frequency of the RF linac in π/2 operating mode is 2996.82 MHz for the operating temperature of 35 °C. The beam dynamic simulations were conducted by using the code ASTRA. Simulation results suggest that electron beams with an average energy of 4.002 MeV can be obtained when the linac accelerating gradient is 41.7 MV/m. The rms transverse beam size and normalized rms transverse emittance at the linac exit are 0.91 mm and 10.48 π mm·mrad, respectively. This information can then be used as the input data for Monte Carlo simulations to estimate the electron beam penetration depth and dose distribution in the natural rubber latex. The study results from this research will be used to define optimal conditions for natural rubber vulcanization with different electron beam energies and doses. This is very useful for development of future practical industrial accelerator units.
Direct linear driving systems; Les entrainements lineaires directs
Energy Technology Data Exchange (ETDEWEB)
Favre, E.; Brunner, C.; Piaget, D. [ETEL SA (France)
1999-11-01
The linear motor is one of the most important developments in electrical drive technology. However, it only, began to be adopted on a large scale at the beginning of the 1990's and will not be considered a mature technology until well into the next millennium. Actuators based on linear motor technology have a number of technical advantages including high speed, high positional accuracy and fine resolution. They also require fewer component parts. Some precautions are necessary when using linear motors. Care must be taken to avoid overheating and excessive vibration, and the magnetic components must be protected.
Directory of Open Access Journals (Sweden)
Heinz Toparkus
2014-04-01
Full Text Available In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classification of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial value problems in appropriate basic areas, and you can try to achieve a solution of these problems by means of transform methods.
Badly approximable systems of linear forms in absolute value
DEFF Research Database (Denmark)
Hussain, M.; Kristensen, Simon
In this paper we show that the set of mixed type badly approximable simultaneously small linear forms is of maximal dimension. As a consequence of this theorem we settle the conjecture stated in [9]....
The graphics software of the Saclay Linear Accelerator control system
International Nuclear Information System (INIS)
Gournay, J.F.
1988-01-01
The graphics software used for the control of the Saclay Linear Accelerator is described. The specific requirements that such a software must have in this environment are outlined and some typical applications are presented. (orig.)
Lag synchronization of chaotic systems with time-delayed linear ...
Indian Academy of Sciences (India)
delayed linear terms via impulsive control is investigated. Based on the stability theory of impulsive delayed differen- tial equations, some sufficient conditions are obtained guaranteeing the synchronized behaviours between two delayed chaotic ...
Metrical theorems on systems of small inhomogeneous linear forms
DEFF Research Database (Denmark)
Hussain, Mumtaz; Kristensen, Simon
In this paper we establish complete Khintchine-Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed.......In this paper we establish complete Khintchine-Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed....
Metrical results on systems of small linear forms
DEFF Research Database (Denmark)
Hussain, M.; Kristensen, Simon
In this paper the metric theory of Diophantine approximation associated with the small linear forms is investigated. Khintchine--Groshev theorems are established along with Hausdorff measure generalization without the monotonic assumption on the approximating function.......In this paper the metric theory of Diophantine approximation associated with the small linear forms is investigated. Khintchine--Groshev theorems are established along with Hausdorff measure generalization without the monotonic assumption on the approximating function....
Robustness of Linear Systems towards Multi-Dissipative Pertubations
DEFF Research Database (Denmark)
Thygesen, Uffe Høgsbro; Poulsen, Niels Kjølstad
1997-01-01
We consider the question of robust stability of a linear time invariant plant subject to dynamic perturbations, which are dissipative in the sense of Willems with respect to several quadratic supply rates. For instance, parasitic dynamics are often both small gain and passive. We reduce several...... robustness analysis questions to linear matrix inequalities: robust stability, robust H2 performance and robust performance in presence of disturbances with finite signal-to-noise ratios...
Hybrid direct and iterative solvers for h refined grids with singularities
Paszyński, Maciej R.
2015-04-27
This paper describes a hybrid direct and iterative solver for two and three dimensional h adaptive grids with point singularities. The point singularities are eliminated by using a sequential linear computational cost solver O(N) on CPU [1]. The remaining Schur complements are submitted to incomplete LU preconditioned conjugated gradient (ILUPCG) iterative solver. The approach is compared to the standard algorithm performing static condensation over the entire mesh and executing the ILUPCG algorithm on top of it. The hybrid solver is applied for two or three dimensional grids automatically h refined towards point or edge singularities. The automatic refinement is based on the relative error estimations between the coarse and fine mesh solutions [2], and the optimal refinements are selected using the projection based interpolation. The computational mesh is partitioned into sub-meshes with local point and edge singularities separated. This is done by using the following greedy algorithm.
User's Manual for PCSMS (Parallel Complex Sparse Matrix Solver). Version 1.
Reddy, C. J.
2000-01-01
PCSMS (Parallel Complex Sparse Matrix Solver) is a computer code written to make use of the existing real sparse direct solvers to solve complex, sparse matrix linear equations. PCSMS converts complex matrices into real matrices and use real, sparse direct matrix solvers to factor and solve the real matrices. The solution vector is reconverted to complex numbers. Though, this utility is written for Silicon Graphics (SGI) real sparse matrix solution routines, it is general in nature and can be easily modified to work with any real sparse matrix solver. The User's Manual is written to make the user acquainted with the installation and operation of the code. Driver routines are given to aid the users to integrate PCSMS routines in their own codes.
Reimer, Ashton S.; Cheviakov, Alexei F.
2013-03-01
A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.
Linear Matrix Inequalities for Analysis and Control of Linear Vector Second-Order Systems
DEFF Research Database (Denmark)
Adegas, Fabiano Daher; Stoustrup, Jakob
2015-01-01
the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter-dependent Lyapunov functions as certificates of stability of uncertain and time-varying vector second-order systems......SUMMARY Many dynamical systems are modeled as vector second-order differential equations. This paper presents analysis and synthesis conditions in terms of LMI with explicit dependence in the coefficient matrices of vector second-order systems. These conditions benefit from the separation between....... The conditions introduced in this work have the potential to increase the practice of analyzing and controlling systems directly in vector second-order form. Copyright © 2014 John Wiley & Sons, Ltd....
A note on the time decay of solutions for the linearized Wigner-Poisson system
Gamba, Irene; Gualdani, Maria; Sparber, Christof
2009-01-01
We consider the one-dimensional Wigner-Poisson system of plasma physics, linearized around a (spatially homogeneous) Lorentzian distribution and prove that the solution of the corresponding linearized problem decays to zero in time. We also give
New approach to solve fully fuzzy system of linear equations using ...
Indian Academy of Sciences (India)
Known example problems are solved to illustrate the efficacy and ... The concept of fuzzy set and fuzzy number were first introduced by Zadeh .... (iii) Fully fuzzy linear systems can be solved by linear programming approach, Gauss elim-.
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.
Decision Engines for Software Analysis Using Satisfiability Modulo Theories Solvers
Bjorner, Nikolaj
2010-01-01
The area of software analysis, testing and verification is now undergoing a revolution thanks to the use of automated and scalable support for logical methods. A well-recognized premise is that at the core of software analysis engines is invariably a component using logical formulas for describing states and transformations between system states. The process of using this information for discovering and checking program properties (including such important properties as safety and security) amounts to automatic theorem proving. In particular, theorem provers that directly support common software constructs offer a compelling basis. Such provers are commonly called satisfiability modulo theories (SMT) solvers. Z3 is a state-of-the-art SMT solver. It is developed at Microsoft Research. It can be used to check the satisfiability of logical formulas over one or more theories such as arithmetic, bit-vectors, lists, records and arrays. The talk describes some of the technology behind modern SMT solvers, including the solver Z3. Z3 is currently mainly targeted at solving problems that arise in software analysis and verification. It has been applied to various contexts, such as systems for dynamic symbolic simulation (Pex, SAGE, Vigilante), for program verification and extended static checking (Spec#/Boggie, VCC, HAVOC), for software model checking (Yogi, SLAM), model-based design (FORMULA), security protocol code (F7), program run-time analysis and invariant generation (VS3). We will describe how it integrates support for a variety of theories that arise naturally in the context of the applications. There are several new promising avenues and the talk will touch on some of these and the challenges related to SMT solvers. Proceedings
Jamison, J. W.
1994-01-01
CFORM was developed by the Kennedy Space Center Robotics Lab to assist in linear control system design and analysis using closed form and transient response mechanisms. The program computes the closed form solution and transient response of a linear (constant coefficient) differential equation. CFORM allows a choice of three input functions: the Unit Step (a unit change in displacement); the Ramp function (step velocity); and the Parabolic function (step acceleration). It is only accurate in cases where the differential equation has distinct roots, and does not handle the case for roots at the origin (s=0). Initial conditions must be zero. Differential equations may be input to CFORM in two forms - polynomial and product of factors. In some linear control analyses, it may be more appropriate to use a related program, Linear Control System Design and Analysis (KSC-11376), which uses root locus and frequency response methods. CFORM was written in VAX FORTRAN for a VAX 11/780 under VAX VMS 4.7. It has a central memory requirement of 30K. CFORM was developed in 1987.
Evaluation of Linear and Non-Linear Control Schemes Applied to a Hydraulic Servo System
DEFF Research Database (Denmark)
Andersen, Torben Ole; Hansen, Michael Rygaard; Pedersen, Henrik Clemmensen
2005-01-01
Due to the innovation of low-cost electronics such as sensors, microcontrollers etc., the focus on highperformance motion control is increasing. This work focuses on position control of single-input single-output hydraulic servo-systems in general. A hydraulically actuated robotic manipulator...
Practical Implementations of Advanced Process Control for Linear Systems
DEFF Research Database (Denmark)
Knudsen, Jørgen K . H.; Huusom, Jakob Kjøbsted; Jørgensen, John Bagterp
2013-01-01
This paper describes some practical problems encountered, when implementing Advanced Process Control, APC, schemes on linear processes. The implemented APC controllers discussed will be LQR, Riccati MPC and Condensed MPC controllers illustrated by simulation of the Four Tank Process and a lineari......This paper describes some practical problems encountered, when implementing Advanced Process Control, APC, schemes on linear processes. The implemented APC controllers discussed will be LQR, Riccati MPC and Condensed MPC controllers illustrated by simulation of the Four Tank Process...... on pilot plant equipment on the department of Chemical Engineering DTU Lyngby....
Smoothing identification of systems with small non-linearities
Czech Academy of Sciences Publication Activity Database
Kozánek, Jan; Piranda, J.
2003-01-01
Roč. 38, č. 1 (2003), s. 71-84 ISSN 0025-6455 R&D Projects: GA ČR GA101/00/1471 Institutional research plan: CEZ:AV0Z2076919 Keywords : identification * small non-linearities * smoothing methods Subject RIV: BI - Acoustics Impact factor: 0.237, year: 2003
Estimation of Physical Parameters in Linear and Nonlinear Dynamic Systems
DEFF Research Database (Denmark)
Knudsen, Morten
variance and confidence ellipsoid is demonstrated. The relation is based on a new theorem on maxima of an ellipsoid. The procedure for input signal design and physical parameter estimation is tested on a number of examples, linear as well as nonlinear and simulated as well as real processes, and it appears...
Estimation of failure probabilities of linear dynamic systems by ...
Indian Academy of Sciences (India)
An iterative method for estimating the failure probability for certain time-variant reliability problems has been developed. In the paper, the focus is on the displacement response of a linear oscillator driven by white noise. Failure is then assumed to occur when the displacement response exceeds a critical threshold.
Linear wave systems on n-D spatial domains
Kurula, Mikael; Zwart, Heiko J.
2015-01-01
In this paper, we study the linear wave equation on an n-dimensional spatial domain.We show that there is a boundary triplet associated to the undamped wave equation. This enables us to characterise all boundary conditions for which the undamped wave equation possesses a unique solution
Riccati transformations and principal solutions of discrete linear systems
International Nuclear Information System (INIS)
Ahlbrandt, C.D.; Hooker, J.W.
1984-01-01
Consider a second-order linear matrix difference equation. A definition of principal and anti-principal, or recessive and dominant, solutions of the equation are given and the existence of principal and anti-principal solutions and the essential uniqueness of principal solutions is proven
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.
The duality in the topological vector spaces and the linear physical system theory
International Nuclear Information System (INIS)
Oliveira Castro, F.M. de.
1980-01-01
The excitation-response relation in a linear, passive, and causal physical system who has the property of this relation be invariant for a time translation is univocally determined by the general form of the linear and continuous functionals defined on the linear topological space chosen for the representation of the excitations. (L.C.) [pt
Approximate Riemann solvers and flux vector splitting schemes for two-phase flow
International Nuclear Information System (INIS)
Toumi, I.; Kumbaro, A.; Paillere, H.
1999-01-01
These course notes, presented at the 30. Von Karman Institute Lecture Series in Computational Fluid Dynamics, give a detailed and through review of upwind differencing methods for two-phase flow models. After recalling some fundamental aspects of two-phase flow modelling, from mixture model to two-fluid models, the mathematical properties of the general 6-equation model are analysed by examining the Eigen-structure of the system, and deriving conditions under which the model can be made hyperbolic. The following chapters are devoted to extensions of state-of-the-art upwind differencing schemes such as Roe's Approximate Riemann Solver or the Characteristic Flux Splitting method to two-phase flow. Non-trivial steps in the construction of such solvers include the linearization, the treatment of non-conservative terms and the construction of a Roe-type matrix on which the numerical dissipation of the schemes is based. Extension of the 1-D models to multi-dimensions in an unstructured finite volume formulation is also described; Finally, numerical results for a variety of test-cases are shown to illustrate the accuracy and robustness of the methods. (authors)
Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices
Freund, Roland
1989-01-01
We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.
FATCOP: A Fault Tolerant Condor-PVM Mixed Integer Program Solver
National Research Council Canada - National Science Library
Chen, Qun
1999-01-01
We describe FATCOP, a new parallel mixed integer program solver written in PVM. The implementation uses the Condor resource management system to provide a virtual machine composed of otherwise idle computers...
Solution of systems of linear algebraic equations by the method of summation of divergent series
International Nuclear Information System (INIS)
Kirichenko, G.A.; Korovin, Ya.S.; Khisamutdinov, M.V.; Shmojlov, V.I.
2015-01-01
A method for solving systems of linear algebraic equations has been proposed on the basis on the summation of the corresponding continued fractions. The proposed algorithm for solving systems of linear algebraic equations is classified as direct algorithms providing an exact solution in a finite number of operations. Examples of solving systems of linear algebraic equations have been presented and the effectiveness of the algorithm has been estimated [ru
A final focus system for the Next Linear Collider
International Nuclear Information System (INIS)
Zimmermann, F.; Brown, K.; Emma, P.; Helm, R.; Irwin, J.; Tenenbaum, P.; Wilson, P.
1995-06-01
The final focus of the Next Linear Collider (NLC) demagnifies electron and positron beams of 250--750 GeV energy down to a transverse size of about 2.5 x 350 nm 2 at the interaction point (IP). The basic layout, momentum bandwidth, vibration tolerances, wakefield effects, and the tunability of the proposed final focus design are discussed. Also a perspective is given on the crab cavity and on effects of the solenoid field in the interaction region
Algebraic coarsening methods for linear and nonlinear PDE and systems
International Nuclear Information System (INIS)
McWilliams, J C
2000-01-01
In [l] Brandt describes a general approach for algebraic coarsening. Given fine-grid equations and a prescribed relaxation method, an approach is presented for defining both the coarse-grid variables and the coarse-grid equations corresponding to these variables. Although, these two tasks are not necessarily related (and, indeed, are often performed independently and with distinct techniques) in the approaches of [1] both revolve around the same underlying observation. To determine whether a given set of coarse-grid variables is appropriate it is suggested that one should employ compatible relaxation. This is a generalization of so-called F-relaxation (e.g., [2]). Suppose that the coarse-grid variables are defined as a subset of the fine-grid variables. Then, F-relaxation simply means relaxing only the F-variables (i.e., fine-grid variables that do not correspond to coarse-grid variables), while leaving the remaining fine-grid variables (C-variables) unchanged. The generalization of compatible relaxation is in allowing the coarse-grid variables to be defined differently, say as linear combinations of fine-grid variables, or even nondeterministically (see examples in [1]). For the present summary it suffices to consider the simple case. The central observation regarding the set of coarse-grid variables is the following [1]: Observation 1--A general measure for the quality of the set of coarse-grid variables is the convergence rate of compatible relaxation. The conclusion is that a necessary condition for efficient multigrid solution (e.g., with convergence rates independent of problem size) is that the compatible-relaxation convergence be bounded away from 1, independently of the number of variables. This is often a sufficient condition, provided that the coarse-grid equations are sufficiently accurate. Therefore, it is suggested in [1] that the convergence rate of compatible relaxation should be used as a criterion for choosing and evaluating the set of coarse
On stabilization of linear systems with stochastic disturbances and input saturation
Stoorvogel, A.A.; Weiland, S.; Saberi, A.
2004-01-01
It is well-known that for linear systems internal asymptotic stability implies external stability in the sense that when the external input is in Lp then also the state will be in Lp. However, for the control of linear systems with saturation where the controlled system is nonlinear this implication
New approach to solve fully fuzzy system of linear equations using ...
Indian Academy of Sciences (India)
This paper proposes two new methods to solve fully fuzzy system of linear equations. The fuzzy system has been converted to a crisp system of linear equations by using single and double parametric form of fuzzy numbers to obtain the non-negative solution. Double parametric form of fuzzy numbers is defined and applied ...
Design of offline measuring system for radiation damage effects on linear CCD
International Nuclear Information System (INIS)
Zhang Yong; Tang Benqi; Xiao Zhigang; Wang Zujun; Huang Fang; Huang Shaoyan
2004-01-01
The paper discusses the hardware design of offline measuring system for radiation damage effects on linear CCD. Some credible results were achieved by using this system. The test results indicate that the system is available for the study of the radiation damage effects on linear CCD. (authors)
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
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...
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.
On the convergence of linear passive complementarity systems
Camlibel, M. Kanat; Wouw, Nathan van de
2007-01-01
The notion of convergent systems is a powerful tool both in the analysis and synthesis of nonlinear systems. Sufficient conditions for convergence have been under investigation for smooth systems and for classes of non-smooth switching systems in the literature. In this paper, we look at a very
Dissipative open systems theory as a foundation for the thermodynamics of linear systems.
Delvenne, Jean-Charles; Sandberg, Henrik
2017-03-06
In this paper, we advocate the use of open dynamical systems, i.e. systems sharing input and output variables with their environment, and the dissipativity theory initiated by Jan Willems as models of thermodynamical systems, at the microscopic and macroscopic level alike. We take linear systems as a study case, where we show how to derive a global Lyapunov function to analyse networks of interconnected systems. We define a suitable notion of dynamic non-equilibrium temperature that allows us to derive a discrete Fourier law ruling the exchange of heat between lumped, discrete-space systems, enriched with the Maxwell-Cattaneo correction. We complete these results by a brief recall of the steps that allow complete derivation of the dissipation and fluctuation in macroscopic systems (i.e. at the level of probability distributions) from lossless and deterministic systems.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).
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 new linearized equation for servo valve in hydraulic control systems
International Nuclear Information System (INIS)
Kim, Tae Hyung; Lee, Ill Yeong
2002-01-01
In the procedure of the hydraulic control system analysis, a linearized approximate equation described by the first order term of Taylor's series has been widely used. Such a linearized equation is effective just near the operating point. And, as of now, there are no general standards on how to determine the operating point of a servo valve in the process of applying the linearized equation. So, in this study, a new linearized equation for valve characteristics is proposed as a modified form of the existing linearized equation. And, a method for selecting an optimal operating point is proposed for the new linearized equation. The effectiveness of the new linearized equation is confirmed through numerical simulations and experiments for a model hydraulic control system
Storage functions for dissipative linear systems are quadratic state functions
Trentelman, Harry L.; Willems, Jan C.
1997-01-01
This paper deals with dissipative dynamical systems. Dissipative dynamical systems can be used as models for physical phenomena in which energy exchange with their environment plays a role. In a dissipative dynamical system, the book-keeping of energy is done via the supply rate and a storage
Attractor reconstruction for non-linear systems: a methodological note
Nichols, J.M.; Nichols, J.D.
2001-01-01
Attractor reconstruction is an important step in the process of making predictions for non-linear time-series and in the computation of certain invariant quantities used to characterize the dynamics of such series. The utility of computed predictions and invariant quantities is dependent on the accuracy of attractor reconstruction, which in turn is determined by the methods used in the reconstruction process. This paper suggests methods by which the delay and embedding dimension may be selected for a typical delay coordinate reconstruction. A comparison is drawn between the use of the autocorrelation function and mutual information in quantifying the delay. In addition, a false nearest neighbor (FNN) approach is used in minimizing the number of delay vectors needed. Results highlight the need for an accurate reconstruction in the computation of the Lyapunov spectrum and in prediction algorithms.
Linear and/or curvilinear rail mount system
Thomas, Jackie D. (Inventor); Harris, Lawanna L. (Inventor)
2012-01-01
One or more linear and/or curvilinear mounting rails are coupled to a structure. Each mounting rail defines a channel and at least one cartridge assembly is engaged in the channel. Each cartridge assembly includes a housing that slides within the channel. The housing defines a curvilinearly-shaped recess longitudinally aligned with the channel when the housing is in engagement therewith. The cartridge assembly also includes a cleat fitted in the recess for sliding engagement therealong. The cleat can be coupled to a fastener that passes through the mounting rail and the housing when the housing is so-engaged in the channel. The cleat is positioned in the recess by a position of the fastener.
Dynamics and thermodynamics of linear quantum open systems.
Martinez, Esteban A; Paz, Juan Pablo
2013-03-29
We analyze the evolution of the quantum state of networks of quantum oscillators coupled with arbitrary external environments. We show that the reduced density matrix of the network always obeys a local master equation with a simple analytical solution. We use this to study the emergence of thermodynamical laws in the long time regime demonstrating two main results: First, we show that it is impossible to build a quantum absorption refrigerator using linear networks (thus, nonlinearity is an essential resource for such refrigerators recently studied by Levy and Kosloff [Phys. Rev. Lett. 108, 070604 (2012)] and Levy et al. [Phys. Rev. B 85, 061126 (2012)]). Then, we show that the third law imposes constraints on the low frequency behavior of the environmental spectral densities.
Parallel computation for solving the tridiagonal linear system of equations
International Nuclear Information System (INIS)
Ishiguro, Misako; Harada, Hiroo; Fujii, Minoru; Fujimura, Toichiro; Nakamura, Yasuhiro; Nanba, Katsumi.
1981-09-01
Recently, applications of parallel computation for scientific calculations have increased from the need of the high speed calculation of large scale programs. At the JAERI computing center, an array processor FACOM 230-75 APU has installed to study the applicability of parallel computation for nuclear codes. We made some numerical experiments by using the APU on the methods of solution of tridiagonal linear equation which is an important problem in scientific calculations. Referring to the recent papers with parallel methods, we investigate eight ones. These are Gauss elimination method, Parallel Gauss method, Accelerated parallel Gauss method, Jacobi method, Recursive doubling method, Cyclic reduction method, Chebyshev iteration method, and Conjugate gradient method. The computing time and accuracy were compared among the methods on the basis of the numerical experiments. As the result, it is found that the Cyclic reduction method is best both in computing time and accuracy and the Gauss elimination method is the second one. (author)
Weak regularizability and pole assignment for non-square linear systems
Czech Academy of Sciences Publication Activity Database
Korotka, Tetiana; Loiseau, J. J.; Zagalak, Petr
2012-01-01
Roč. 48, č. 6 (2012), s. 1065-1088 ISSN 0023-5954 R&D Projects: GA ČR GAP103/12/2431 Keywords : linear systems * linear state feedback * pole assignment Subject RIV: BC - Control Systems Theory Impact factor: 0.619, year: 2012 http://library.utia.cas.cz/separaty/2013/AS/korotka-0386325.pdf
Iterative solution of linear systems in the 20th century
Saad, Y.; Vorst, H.A. van der
2000-01-01
This paper sketches the main research developments in the area of iterative methods for solving linear systems during the 20th century. Although iterative methods for solving linear systems find their origin in the early nineteenth century (work by Gauss), the field has seen an explosion of
Dynamic Response of Non-Linear Inelsatic Systems to Poisson-Driven Stochastic Excitations
DEFF Research Database (Denmark)
Nielsen, Søren R. K.; Iwankiewicz, R.
of an equivalent linearization techni que and substituting the non-analytical non-linearity in the original system by the cubic form in the pertinent state variables. The response moments are evaluated for the equivalent systems with the help of a generalized Ito's differential rule. The analytical results...
Linear regressive model structures for estimation and prediction of compartmental diffusive systems
Vries, D; Keesman, K.J.; Zwart, Heiko J.
In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its short-comings regarding global optimality and computational effort. Given a LTI system in state space
Linear regressive model structures for estimation and prediction of compartmental diffusive systems
Vries, D.; Keesman, K.J.; Zwart, H.
2006-01-01
Abstract In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its short-comings regarding global optimality and computational effort. Given a LTI system in state
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 canonical form of the equation of motion of linear dynamical systems
Kawano, Daniel T.; Salsa, Rubens Goncalves; Ma, Fai; Morzfeld, Matthias
2018-03-01
The equation of motion of a discrete linear system has the form of a second-order ordinary differential equation with three real and square coefficient matrices. It is shown that, for almost all linear systems, such an equation can always be converted by an invertible transformation into a canonical form specified by two diagonal coefficient matrices associated with the generalized acceleration and displacement. This canonical form of the equation of motion is unique up to an equivalence class for non-defective systems. As an important by-product, a damped linear system that possesses three symmetric and positive definite coefficients can always be recast as an undamped and decoupled system.
Safe Exploration for Identifying Linear Systems via Robust Optimization
Lu, Tyler; Zinkevich, Martin; Boutilier, Craig; Roy, Binz; Schuurmans, Dale
2017-01-01
Safely exploring an unknown dynamical system is critical to the deployment of reinforcement learning (RL) in physical systems where failures may have catastrophic consequences. In scenarios where one knows little about the dynamics, diverse transition data covering relevant regions of state-action space is needed to apply either model-based or model-free RL. Motivated by the cooling of Google's data centers, we study how one can safely identify the parameters of a system model with a desired ...
International Nuclear Information System (INIS)
Duan, Chaowei; Zhan, Yafeng
2016-01-01
The output characteristics of a linear monostable system driven with a periodic signal and an additive white Gaussian noise are studied in this paper. Theoretical analysis shows that the output signal-to-noise ratio (SNR) decreases monotonously with the increasing noise intensity but the output SNR-gain is stable. Inspired by this high SNR-gain phenomenon, this paper applies the linear monostable system in the parameters estimation algorithm for phase shift keying (PSK) signals and improves the estimation performance. - Highlights: • The response of a linear monostable system driven with a periodic signal and an additive white Gaussian noise is analyzed. • The optimal parameter of this linear monostable system to maximum the output SNR-gain is obtained. • Application of this linear monostable system in parameters estimation algorithm for PSK signals obtains performance improvement.
Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces
Jacob, Birgit
2012-01-01
This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the fir
An alternative solver for the nodal expansion method equations - 106
International Nuclear Information System (INIS)
Carvalho da Silva, F.; Carlos Marques Alvim, A.; Senra Martinez, A.
2010-01-01
An automated procedure for nuclear reactor core design is accomplished by using a quick and accurate 3D nodal code, aiming at solving the diffusion equation, which describes the spatial neutron distribution in the reactor. This paper deals with an alternative solver for nodal expansion method (NEM), with only two inner iterations (mesh sweeps) per outer iteration, thus having the potential to reduce the time required to calculate the power distribution in nuclear reactors, but with accuracy similar to the ones found in conventional NEM. The proposed solver was implemented into a computational system which, besides solving the diffusion equation, also solves the burnup equations governing the gradual changes in material compositions of the core due to fuel depletion. Results confirm the effectiveness of the method for practical purposes. (authors)
CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. II. GRAY RADIATION HYDRODYNAMICS
International Nuclear Information System (INIS)
Zhang, W.; Almgren, A.; Bell, J.; Howell, L.; Burrows, A.
2011-01-01
We describe the development of a flux-limited gray radiation solver for the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. The gray radiation solver is based on a mixed-frame formulation of radiation hydrodynamics. In our approach, the system is split into two parts, one part that couples the radiation and fluid in a hyperbolic subsystem, and another parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem is solved explicitly with a high-order Godunov scheme, whereas the parabolic part is solved implicitly with a first-order backward Euler method.
Conservation laws for multidimensional systems and related linear algebra problems
Igonine, Sergei
2002-01-01
We consider multidimensional systems of PDEs of generalized evolution form with t-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order t-derivatives and arbitrary space derivatives. For such systems we find an explicit necessary condition for the
Conservation laws for multidimensional systems and related linear algebra problems
Igonin, S.
2002-01-01
We consider multidimensional systems of PDEs of generalized evolution form with $t$-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order $t$-derivatives and arbitrary space derivatives. For such systems we find an explicit necessary condition for
Linear time heteronymous damping in nonlinear parametric systems
Czech Academy of Sciences Publication Activity Database
Hortel, Milan; Škuderová, Alena; Houfek, Martin
2016-01-01
Roč. 40, 23-24 (2016), s. 10038-10051 ISSN 0307-904X Institutional support: RVO:61388998 Keywords : nonlinear dynamics of systems * parametric systems * time heteronymous damping * gears Subject RIV: JT - Propulsion, Motors ; Fuels Impact factor: 2.350, year: 2016
Experiment design for identification of structured linear systems
Potters, M.G.
2016-01-01
Experiment Design for system identification involves the design of an optimal input signal with the purpose of accurately estimating unknown parameters in a system. Specifically, in the Least-Costly Experiment Design (LCED) framework, the optimal input signal results from an optimisation problem in
Optimal angle reduction - a behavioral approach to linear system appromixation
Roorda, B.; Weiland, S.
2001-01-01
We investigate the problem of optimal state reduction under minimization of the angle between system behaviors. The angle is defined in a worst-case sense, as the largest angle that can occur between a system trajectory and its optimal approximation in the reduced-order model. This problem is
Static linear Fresnel lenses as LCPV system in a greenhouse
Sonneveld, P.J.; Swinkels, G.L.A.M.; Tuijl, van B.A.J.; Janssen, H.J.J.; Zwart, de H.F.
2011-01-01
A low concentrating PV system with water cooling (LCPVT system) will result in electrical and thermal energy output from the solar energy excess entering a building or greenhouse. All the direct radiation could be converted, which corresponds to 75% of the incoming solar energy. This will
Conservation laws for multidimensional systems and related linear algebra problems
International Nuclear Information System (INIS)
Igonin, Sergei
2002-01-01
We consider multidimensional systems of PDEs of generalized evolution form with t-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order t-derivatives and arbitrary space derivatives. For such systems we find an explicit necessary condition for the existence of higher conservation laws in terms of the system's symbol. For systems that violate this condition we give an effective upper bound on the order of conservation laws. Using this result, we completely describe conservation laws for viscous transonic equations, for the Brusselator model and the Belousov-Zhabotinskii system. To achieve this, we solve over an arbitrary field the matrix equations SA=A t S and SA=-A t S for a quadratic matrix A and its transpose A t , which may be of independent interest
Determining the Optimal Values of Exponential Smoothing Constants--Does Solver Really Work?
Ravinder, Handanhal V.
2013-01-01
A key issue in exponential smoothing is the choice of the values of the smoothing constants used. One approach that is becoming increasingly popular in introductory management science and operations management textbooks is the use of Solver, an Excel-based non-linear optimizer, to identify values of the smoothing constants that minimize a measure…