Fracture and Fragmentation of Simplicial Finite Elements Meshes using Graphs

Energy Technology Data Exchange (ETDEWEB)

Mota, A; Knap, J; Ortiz, M

2006-10-18

An approach for the topological representation of simplicial finite element meshes as graphs is presented. It is shown that by using a graph, the topological changes induced by fracture reduce to a few, local kernel operations. The performance of the graph representation is demonstrated and analyzed, using as reference the 3D fracture algorithm by Pandolfi and Ortiz [22]. It is shown that the graph representation initializes in O(N{sub E}{sup 1.1}) time and fractures in O(N{sub I}{sup 1.0}) time, while the reference implementation requires O(N{sub E}{sup 2.1}) time to initialize and O(N{sub I}{sup 1.9}) time to fracture, where NE is the number of elements in the mesh and N{sub I} is the number of interfaces to fracture.

Mechanical behaviour of synthetic surgical meshes: finite element simulation of the herniated abdominal wall.

Science.gov (United States)

Hernández-Gascón, B; Peña, E; Melero, H; Pascual, G; Doblaré, M; Ginebra, M P; Bellón, J M; Calvo, B

2011-11-01

The material properties of meshes used in hernia surgery contribute to the overall mechanical behaviour of the repaired abdominal wall. The mechanical response of a surgical mesh has to be defined since the haphazard orientation of an anisotropic mesh can lead to inconsistent surgical outcomes. This study was designed to characterize the mechanical behaviour of three surgical meshes (Surgipro®, Optilene® and Infinit®) and to describe a mechanical constitutive law that accurately reproduces the experimental results. Finally, through finite element simulation, the behaviour of the abdominal wall was modelled before and after surgical mesh implant. Uniaxial loading of mesh samples in two perpendicular directions revealed the isotropic response of Surgipro® and the anisotropic behaviour of Optilene® and Infinit®. A phenomenological constitutive law was used to reproduce the measured experimental curves. To analyze the mechanical effect of the meshes once implanted in the abdomen, finite element simulation of the healthy and partially herniated repaired rabbit abdominal wall served to reproduce wall behaviour before and after mesh implant. In all cases, maximal displacements were lower and maximal principal stresses higher in the implanted abdomen than the intact wall model. Despite the fact that no mesh showed a behaviour that perfectly matched that of abdominal muscle, the Infinit® mesh was able to best comply with the biomechanics of the abdominal wall. Copyright © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Finite element method for solving Kohn-Sham equations based on self-adaptive tetrahedral mesh

International Nuclear Information System (INIS)

Zhang Dier; Shen Lihua; Zhou Aihui; Gong Xingao

2008-01-01

A finite element (FE) method with self-adaptive mesh-refinement technique is developed for solving the density functional Kohn-Sham equations. The FE method adopts local piecewise polynomials basis functions, which produces sparsely structured matrices of Hamiltonian. The method is well suitable for parallel implementation without using Fourier transform. In addition, the self-adaptive mesh-refinement technique can control the computational accuracy and efficiency with optimal mesh density in different regions

A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

Science.gov (United States)

Heumann, Holger; Rapetti, Francesca

2017-04-01

Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in tokamak engineering, is constrained to nodes of the mesh leading to undesired jumps in transient problems. Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map. In this work we propose a mortar element method that employs two overlapping meshes. One mesh with Cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region. The continuity of the numerical solution in the region of overlap is weakly enforced by a mortar-like mapping.

3D visualization and finite element mesh formation from wood anatomy samples, Part II – Algorithm approach

Directory of Open Access Journals (Sweden)

Petr Koňas

2009-01-01

Full Text Available Paper presents new original application WOOD3D in form of program code assembling. The work extends the previous article “Part I – Theoretical approach” in detail description of implemented C++ classes of utilized projects Visualization Toolkit (VTK, Insight Toolkit (ITK and MIMX. Code is written in CMake style and it is available as multiplatform application. Currently GNU Linux (32/64b and MS Windows (32/64b platforms were released. Article discusses various filter classes for image filtering. Mainly Otsu and Binary threshold filters are classified for anatomy wood samples thresholding. Registration of images series is emphasized for difference of colour spaces compensation is included. Resulted work flow of image analysis is new methodological approach for images processing through the composition, visualization, filtering, registration and finite element mesh formation. Application generates script in ANSYS parametric design language (APDL which is fully compatible with ANSYS finite element solver and designer environment. The script includes the whole definition of unstructured finite element mesh formed by individual elements and nodes. Due to simple notation, the same script can be used for generation of geometrical entities in element positions. Such formed volumetric entities are prepared for further geometry approximation (e.g. by boolean or more advanced methods. Hexahedral and tetrahedral types of mesh elements are formed on user request with specified mesh options. Hexahedral meshes are formed both with uniform element size and with anisotropic character. Modified octree method for hexahedral mesh with anisotropic character was declared in application. Multicore CPUs in the application are supported for fast image analysis realization. Visualization of image series and consequent 3D image are realized in VTK format sufficiently known and public format, visualized in GPL application Paraview. Future work based on mesh

Reactor calculation in coarse mesh by finite element method applied to matrix response method

International Nuclear Information System (INIS)

Nakata, H.

1982-01-01

The finite element method is applied to the solution of the modified formulation of the matrix-response method aiming to do reactor calculations in coarse mesh. Good results are obtained with a short running time. The method is applicable to problems where the heterogeneity is predominant and to problems of evolution in coarse meshes where the burnup is variable in one same coarse mesh, making the cross section vary spatially with the evolution. (E.G.) [pt

Coarse mesh finite element method for boiling water reactor physics analysis

International Nuclear Information System (INIS)

Ellison, P.G.

1983-01-01

A coarse mesh method is formulated for the solution of Boiling Water Reactor physics problems using two group diffusion theory. No fuel assembly cross-section homogenization is required; water gaps, control blades and fuel pins of varying enrichments are treated explicitly. The method combines constrained finite element discretization with infinite lattice super cell trial functions to obtain coarse mesh solutions for which the only approximations are along the boundaries between fuel assemblies. The method is applied to bench mark Boiling Water Reactor problems to obtain both the eigenvalue and detailed flux distributions. The solutions to these problems indicate the method is useful in predicting detailed power distributions and eigenvalues for Boiling Water Reactor physics problems

3D visualization and finite element mesh formation from wood anatomy samples, Part I – Theoretical approach

Directory of Open Access Journals (Sweden)

Petr Koňas

2009-01-01

Full Text Available The work summarizes created algorithms for formation of finite element (FE mesh which is derived from bitmap pattern. Process of registration, segmentation and meshing is described in detail. C++ library of STL from Insight Toolkit (ITK Project together with Visualization Toolkit (VTK were used for base processing of images. Several methods for appropriate mesh output are discussed. Multiplatform application WOOD3D for the task under GNU GPL license was assembled. Several methods of segmentation and mainly different ways of contouring were included. Tetrahedral and rectilinear types of mesh were programmed. Improving of mesh quality in some simple ways is mentioned. Testing and verification of final program on wood anatomy samples of spruce and walnut was realized. Methods of microscopic anatomy samples preparation are depicted. Final utilization of formed mesh in the simple structural analysis was performed.The article discusses main problems in image analysis due to incompatible colour spaces, samples preparation, thresholding and final conversion into finite element mesh. Assembling of mentioned tasks together and evaluation of the application are main original results of the presented work. In presented program two thresholding filters were used. By utilization of ITK two following filters were included. Otsu filter based and binary filter based were used. The most problematic task occurred in a production of wood anatomy samples in the unique light conditions with minimal or zero co­lour space shift and the following appropriate definition of thresholds (corresponding thresholding parameters and connected methods (prefiltering + registration which influence the continuity and mainly separation of wood anatomy structure. Solution in samples staining is suggested with the following quick image analysis realization. Next original result of the work is complex fully automated application which offers three types of finite element mesh

Charged particle tracking through electrostatic wire meshes using the finite element method

Energy Technology Data Exchange (ETDEWEB)

Devlin, L. J.; Karamyshev, O.; Welsch, C. P., E-mail: carsten.welsch@cockcroft.ac.uk [The Cockcroft Institute, Daresbury Laboratory, Warrington (United Kingdom); Department of Physics, University of Liverpool, Liverpool (United Kingdom)

2016-06-15

Wire meshes are used across many disciplines to accelerate and focus charged particles, however, analytical solutions are non-exact and few codes exist which simulate the exact fields around a mesh with physical sizes. A tracking code based in Matlab-Simulink using field maps generated using finite element software has been developed which tracks electrons or ions through electrostatic wire meshes. The fields around such a geometry are presented as an analytical expression using several basic assumptions, however, it is apparent that computational calculations are required to obtain realistic values of electric potential and fields, particularly when multiple wire meshes are deployed. The tracking code is flexible in that any quantitatively describable particle distribution can be used for both electrons and ions as well as other benefits such as ease of export to other programs for analysis. The code is made freely available and physical examples are highlighted where this code could be beneficial for different applications.

Some efficient Lagrangian mesh finite elements encoded in ZEPHYR for two dimensional transport calculations

International Nuclear Information System (INIS)

Mordant, Maurice.

1981-04-01

To solve a multigroup stationary neutron transport equation in two-dimensional geometries (X-Y), (R-O) or (R-Z) generally on uses discrete ordinates and rectangular meshes. The way to do it is then well known, well documented and somewhat obvious. If one needs to treat awkward geometries or distorted meshes, things are not so easy and the way to do it is no longer straightforward. We have studied this problem at Limeil Nuclear Center and as an alternative to Monte Carlo methods and code we have implemented in ZEPHYR code at least two efficient finite element solutions for Lagrangian meshes involving any kind of triangles and quadrilaterals

Automatic mesh generation for finite element calculations in the case of thermal loads

International Nuclear Information System (INIS)

Cords, H.; Zimmermann, R.

1975-01-01

The presentation describes a method to generate finite element nodal point networks on the basis of isothermals and flux lines. Such a mesh provides a relatively fine partitioning at regions where pronounced temperature variations exist. In case of entirely thermal loads a net of this kind is advantageous since the refinement is provided at exactly those locations where high stress levels are expected. In the present contribution the method was employed to analyze the structural behavior of a nuclear fuel element under operating conditions. The graphite block fuel elements for high temperature reactors are of prismatic shape with a large number of parallel bores in the axial direction. Some of these bores are open at both ends and cooling is effected by helium flowing through. Blind holes contain the fuel as compacts or cartridges. The basic temperature distribution in a horizontal section of the block was obtained by the boundary point least squares method which yields analytical expressions for both temperature and thermal flux. The corresponding computer code was presented at an earlier SMiRT conference. The method is particularly useful for regular arrays of heat sources and sinks as encountered in heat exchanger problems. The generated mesh matches the requirements of a subsequent structural analysis with finite elements provided there are no other than thermal loads

Moving mesh finite element method for finite time extinction of distributed parameter systems with positive exponential feedback; Lokakarya Komputasi dalam Sains dan Teknologi Nuklir VI

Energy Technology Data Exchange (ETDEWEB)

Garnadi, A D [Department of Matematics, Bogor Institute of Agriculture, Bogor (Indonesia)

1997-07-01

In the distributed parameter systems with exponential feedback, non-global existence of solution is not always exist. For some positive initial values, there exist finite time T such that the solution goes to infinity, i.e. finite time extinction or blow-up. Here is present a numerical solution using Moving Mesh Finite Element to solve the distributed parameter systems with exponential feedback close to blow-up time. The numerical behavior of the mesh close to the time of extinction is the prime interest in this study.

Finite element application to global reactor analysis

International Nuclear Information System (INIS)

Schmidt, F.A.R.

1981-01-01

The Finite Element Method is described as a Coarse Mesh Method with general basis and trial functions. Various consequences concerning programming and application of Finite Element Methods in reactor physics are drawn. One of the conclusions is that the Finite Element Method is a valuable tool in solving global reactor analysis problems. However, problems which can be described by rectangular boxes still can be solved with special coarse mesh programs more efficiently. (orig.) [de

Atlas-Based Automatic Generation of Subject-Specific Finite Element Tongue Meshes.

Science.gov (United States)

Bijar, Ahmad; Rohan, Pierre-Yves; Perrier, Pascal; Payan, Yohan

2016-01-01

Generation of subject-specific 3D finite element (FE) models requires the processing of numerous medical images in order to precisely extract geometrical information about subject-specific anatomy. This processing remains extremely challenging. To overcome this difficulty, we present an automatic atlas-based method that generates subject-specific FE meshes via a 3D registration guided by Magnetic Resonance images. The method extracts a 3D transformation by registering the atlas' volume image to the subject's one, and establishes a one-to-one correspondence between the two volumes. The 3D transformation field deforms the atlas' mesh to generate the subject-specific FE mesh. To preserve the quality of the subject-specific mesh, a diffeomorphic non-rigid registration based on B-spline free-form deformations is used, which guarantees a non-folding and one-to-one transformation. Two evaluations of the method are provided. First, a publicly available CT-database is used to assess the capability to accurately capture the complexity of each subject-specific Lung's geometry. Second, FE tongue meshes are generated for two healthy volunteers and two patients suffering from tongue cancer using MR images. It is shown that the method generates an appropriate representation of the subject-specific geometry while preserving the quality of the FE meshes for subsequent FE analysis. To demonstrate the importance of our method in a clinical context, a subject-specific mesh is used to simulate tongue's biomechanical response to the activation of an important tongue muscle, before and after cancer surgery.

Convergence study of global meshing on enamel-cement-bracket finite element model

Science.gov (United States)

Samshuri, S. F.; Daud, R.; Rojan, M. A.; Basaruddin, K. S.; Abdullah, A. B.; Ariffin, A. K.

2017-09-01

This paper presents on meshing convergence analysis of finite element (FE) model to simulate enamel-cement-bracket fracture. Three different materials used in this study involving interface fracture are concerned. Complex behavior ofinterface fracture due to stress concentration is the reason to have a well-constructed meshing strategy. In FE analysis, meshing size is a critical factor that influenced the accuracy and computational time of analysis. The convergence study meshing scheme involving critical area (CA) and non-critical area (NCA) to ensure an optimum meshing sizes are acquired for this FE model. For NCA meshing, the area of interest are at the back of enamel, bracket ligature groove and bracket wing. For CA meshing, area of interest are enamel area close to cement layer, the cement layer and bracket base. The value of constant NCA meshing tested are meshing size 1 and 0.4. The value constant CA meshing tested are 0.4 and 0.1. Manipulative variables are randomly selected and must abide the rule of NCA must be higher than CA. This study employed first principle stresses due to brittle failure nature of the materials used. Best meshing size are selected according to convergence error analysis. Results show that, constant CA are more stable compare to constant NCA meshing. Then, 0.05 constant CA meshing are tested to test the accuracy of smaller meshing. However, unpromising result obtained as the errors are increasing. Thus, constant CA 0.1 with NCA mesh of 0.15 until 0.3 are the most stable meshing as the error in this region are lowest. Convergence test was conducted on three selected coarse, medium and fine meshes at the range of NCA mesh of 0.15 until 3 and CA mesh area stay constant at 0.1. The result shows that, at coarse mesh 0.3, the error are 0.0003% compare to 3% acceptable error. Hence, the global meshing are converge as the meshing size at CA 0.1 and NCA 0.15 for this model.

A suitable low-order, eight-node tetrahedral finite element for solids

International Nuclear Information System (INIS)

Key, S.W.; Heinstein, M.S.; Stone, C.M.; Mello, F.J.; Blanford, M.L.; Budge, K.G.

1998-03-01

To use the all-tetrahedral mesh generation existing today, the authors have explored the creation of a computationally efficient eight-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four mid-face nodal points). The derivation of the element's gradient operator, studies in obtaining a suitable mass lumping, and the element's performance in applications are presented. In particular they examine the eight-node tetrahedral finite element's behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element samples only constant strain states and, therefore, has 12 hour-glass modes. In this regard it bears similarities to the eight-node, mean-quadrature hexahedral finite element. Comparisons with the results obtained from the mean-quadrature eight-node hexahedral finite element and the four-node tetrahedral finite element are included. Given automatic all-tetrahedral meshing, the eight-node, constant-strain tetrahedral finite element is a suitable replacement for the eight-node hexahedral finite element in those cases where mesh generation requires an inordinate amount of user intervention and direction to obtain acceptable mesh properties

A suitable low-order, eight-node tetrahedral finite element for solids

Energy Technology Data Exchange (ETDEWEB)

Key, S.W.; Heinstein, M.S.; Stone, C.M.; Mello, F.J.; Blanford, M.L.; Budge, K.G.

1998-03-01

To use the all-tetrahedral mesh generation existing today, the authors have explored the creation of a computationally efficient eight-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four mid-face nodal points). The derivation of the element`s gradient operator, studies in obtaining a suitable mass lumping, and the element`s performance in applications are presented. In particular they examine the eight-node tetrahedral finite element`s behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element samples only constant strain states and, therefore, has 12 hour-glass modes. In this regard it bears similarities to the eight-node, mean-quadrature hexahedral finite element. Comparisons with the results obtained from the mean-quadrature eight-node hexahedral finite element and the four-node tetrahedral finite element are included. Given automatic all-tetrahedral meshing, the eight-node, constant-strain tetrahedral finite element is a suitable replacement for the eight-node hexahedral finite element in those cases where mesh generation requires an inordinate amount of user intervention and direction to obtain acceptable mesh properties.

Development of polygon elements based on the scaled boundary finite element method

International Nuclear Information System (INIS)

Chiong, Irene; Song Chongmin

2010-01-01

We aim to extend the scaled boundary finite element method to construct conforming polygon elements. The development of the polygonal finite element is highly anticipated in computational mechanics as greater flexibility and accuracy can be achieved using these elements. The scaled boundary polygonal finite element will enable new developments in mesh generation, better accuracy from a higher order approximation and better transition elements in finite element meshes. Polygon elements of arbitrary number of edges and order have been developed successfully. The edges of an element are discretised with line elements. The displacement solution of the scaled boundary finite element method is used in the development of shape functions. They are shown to be smooth and continuous within the element, and satisfy compatibility and completeness requirements. Furthermore, eigenvalue decomposition has been used to depict element modes and outcomes indicate the ability of the scaled boundary polygonal element to express rigid body and constant strain modes. Numerical tests are presented; the patch test is passed and constant strain modes verified. Accuracy and convergence of the method are also presented and the performance of the scaled boundary polygonal finite element is verified on Cook's swept panel problem. Results show that the scaled boundary polygonal finite element method outperforms a traditional mesh and accuracy and convergence are achieved from fewer nodes. The proposed method is also shown to be truly flexible, and applies to arbitrary n-gons formed of irregular and non-convex polygons.

Mimetic finite difference method for the stokes problem on polygonal meshes

Energy Technology Data Exchange (ETDEWEB)

Lipnikov, K [Los Alamos National Laboratory; Beirao Da Veiga, L [DIPARTIMENTO DI MATE; Gyrya, V [PENNSYLVANIA STATE UNIV; Manzini, G [ISTIUTO DI MATEMATICA

2009-01-01

Various approaches to extend the finite element methods to non-traditional elements (pyramids, polyhedra, etc.) have been developed over the last decade. Building of basis functions for such elements is a challenging task and may require extensive geometry analysis. The mimetic finite difference (MFD) method has many similarities with low-order finite element methods. Both methods try to preserve fundamental properties of physical and mathematical models. The essential difference is that the MFD method uses only the surface representation of discrete unknowns to build stiffness and mass matrices. Since no extension inside the mesh element is required, practical implementation of the MFD method is simple for polygonal meshes that may include degenerate and non-convex elements. In this article, we develop a MFD method for the Stokes problem on arbitrary polygonal meshes. The method is constructed for tensor coefficients, which will allow to apply it to the linear elasticity problem. The numerical experiments show the second-order convergence for the velocity variable and the first-order for the pressure.

On Using Particle Finite Element for Hydrodynamics Problems Solving

Directory of Open Access Journals (Sweden)

E. V. Davidova

2015-01-01

Full Text Available The aim of the present research is to develop software for the Particle Finite Element Method (PFEM and its verification on the model problem of viscous incompressible flow simulation in a square cavity. The Lagrangian description of the medium motion is used: the nodes of the finite element mesh move together with the fluid that allows to consider them as particles of the medium. Mesh cells deform when in time-stepping procedure, so it is necessary to reconstruct the mesh to provide stability of the finite element numerical procedure.Meshing algorithm allows us to obtain the mesh, which satisfies the Delaunay criteria: it is called \\the possible triangles method". This algorithm is based on the well-known Fortune method of Voronoi diagram constructing for a certain set of points in the plane. The graphical representation of the possible triangles method is shown. It is suitable to use generalization of Delaunay triangulation in order to construct meshes with polygonal cells in case of multiple nodes close to be lying on the same circle.The viscous incompressible fluid flow is described by the Navier | Stokes equations and the mass conservation equation with certain initial and boundary conditions. A fractional steps method, which allows us to avoid non-physical oscillations of the pressure, provides the timestepping procedure. Using the finite element discretization and the Bubnov | Galerkin method allows us to carry out spatial discretization.For form functions calculation of finite element mesh with polygonal cells, \

An efficient finite element solution for gear dynamics

International Nuclear Information System (INIS)

Cooley, C G; Parker, R G; Vijayakar, S M

2010-01-01

A finite element formulation for the dynamic response of gear pairs is proposed. Following an established approach in lumped parameter gear dynamic models, the static solution is used as the excitation in a frequency domain solution of the finite element vibration model. The nonlinear finite element/contact mechanics formulation provides accurate calculation of the static solution and average mesh stiffness that are used in the dynamic simulation. The frequency domain finite element calculation of dynamic response compares well with numerically integrated (time domain) finite element dynamic results and previously published experimental results. Simulation time with the proposed formulation is two orders of magnitude lower than numerically integrated dynamic results. This formulation admits system level dynamic gearbox response, which may include multiple gear meshes, flexible shafts, rolling element bearings, housing structures, and other deformable components.

A finite element formulation of the Darwin electromagnetic PIC model for unstructured meshes of triangles

International Nuclear Information System (INIS)

Sonnendrucker, E.; Ambrosiano, J.; Brandon, S.

1993-01-01

The Darwin model for electromagnetic simulation is a reduced form of the Maxwell-Vlasov system that retains all essential physical processes except the propagation of light waves. It is useful in modeling systems for which the light-transit timescales are less important than Alfven wave propagation, or quasistatic effects. The Darwin model is elliptic rather than hyperbolic as are the full set of Maxwell's equations. Appropriate boundary conditions must be chosen for the problems to be well-posed. Using finite element techniques to apply this method for unstructured triangular meshes, a mesh made up of unstructured triangles allows realistic device geometries to be modeled without the necessity of using a large number of mesh points. Analyzing the dispersion relation allows us to validate the code as well as the Darwin approximation

QMESH RENUM QPLOT, Mesh Generator on 2-D Bodies for Finite Element Method Analysis, with Plot Utility

International Nuclear Information System (INIS)

Jones, R.E.; Schkade, A.F.; Eyberger, L.R.

1991-01-01

1 - Description of problem or function: A set of five programs which make up a self-organising mesh generation package. QMESH generates meshes having quadrilateral elements on arbitrarily-shaped, two-dimensional (planar or axisymmetric) bodies. It is designed for use with two-dimensional finite element analysis applications. A flexible hierarchical input scheme is used to describe bodies to QMESH as collections of regions. A mesh for each region is developed independently, with the final assembly and bandwidth minimization performed by the independent program, RENUM or RENUM8. RENUM is applied when four-node elements are desired. Eight-node elements (with mid-side nodes) may be obtained with RENUM8., QPLOT and QPLOT8 are plot programs for meshes generated by the QMESH/RENUM and QMESH/RENUM8 program pairs, respectively. QPLOT and QPLOT8 automatically section the mesh into appropriately-sized sections for legible display of node and element numbers. An overall plot showing the position of the selected plot areas is produced. 2 - Method of solution: The mesh generating process for each individual region begins with the installation of an initial mesh which is a transformation of a regular grid on the unit square. The dimensions and orientation of the initial mesh may be defined by the user or, optionally, may be chosen by QMESH. Various smoothing algorithms may be applied to the initial mesh. Then, the mesh may be 'restructured' using an iterative scheme involving 'element pair restructuring', 'acute element deletion', and smoothing. In element pair restructuring, the interface side between two elements is removed and placed between two different nodes belonging to the pair of elements, provided that the change produces an overall improvement in the shapes of the two elements. In acute element deletion, an element having one diagonal much shorter than the other is deleted by collapsing the short diagonal to zero length The exact order in which restructuring, element

Minimizing EIT image artefacts from mesh variability in finite element models.

Science.gov (United States)

Adler, Andy; Lionheart, William R B

2011-07-01

Electrical impedance tomography (EIT) solves an inverse problem to estimate the conductivity distribution within a body from electrical simulation and measurements at the body surface, where the inverse problem is based on a solution of Laplace's equation in the body. Most commonly, a finite element model (FEM) is used, largely because of its ability to describe irregular body shapes. In this paper, we show that simulated variations in the positions of internal nodes within a FEM can result in serious image artefacts in the reconstructed images. Such variations occur when designing FEM meshes to conform to conductivity targets, but the effects may also be seen in other applications of absolute and difference EIT. We explore the hypothesis that these artefacts result from changes in the projection of the anisotropic conductivity tensor onto the FEM system matrix, which introduces anisotropic components into the simulated voltages, which cannot be reconstructed onto an isotropic image, and appear as artefacts. The magnitude of the anisotropic effect is analysed for a small regular FEM, and shown to be proportional to the relative node movement as a fraction of element size. In order to address this problem, we show that it is possible to incorporate a FEM node movement component into the formulation of the inverse problem. These results suggest that it is important to consider artefacts due to FEM mesh geometry in EIT image reconstruction.

MESHREF, Finite Elements Mesh Combination with Renumbering

International Nuclear Information System (INIS)

1973-01-01

1 - Nature of physical problem solved: The program can assemble different meshes stored on tape or cards. Renumbering is performed in order to keep band width low. Voids and/ or local refinement are possible. 2 - Method of solution: Topology and geometry are read according to input specifications. Abundant nodes and elements are eliminated. The new topology and geometry are stored on tape. 3 - Restrictions on the complexity of the problem: Maximum number of nodes = 2000. Maximum number of elements = 1500

A coarse-mesh nodal method-diffusive-mesh finite difference method

International Nuclear Information System (INIS)

Joo, H.; Nichols, W.R.

1994-01-01

Modern nodal methods have been successfully used for conventional light water reactor core analyses where the homogenized, node average cross sections (XSs) and the flux discontinuity factors (DFs) based on equivalence theory can reliably predict core behavior. For other types of cores and other geometries characterized by tightly-coupled, heterogeneous core configurations, the intranodal flux shapes obtained from a homogenized nodal problem may not accurately portray steep flux gradients near fuel assembly interfaces or various reactivity control elements. This may require extreme values of DFs (either very large, very small, or even negative) to achieve a desired solution accuracy. Extreme values of DFs, however, can disrupt the convergence of the iterative methods used to solve for the node average fluxes, and can lead to a difficulty in interpolating adjacent DF values. Several attempts to remedy the problem have been made, but nothing has been satisfactory. A new coarse-mesh nodal scheme called the Diffusive-Mesh Finite Difference (DMFD) technique, as contrasted with the coarse-mesh finite difference (CMFD) technique, has been developed to resolve this problem. This new technique and the development of a few-group, multidimensional kinetics computer program are described in this paper

Unstructured Finite Elements and Dynamic Meshing for Explicit Phase Tracking in Multiphase Problems

Science.gov (United States)

Chandra, Anirban; Yang, Fan; Zhang, Yu; Shams, Ehsan; Sahni, Onkar; Oberai, Assad; Shephard, Mark

2017-11-01

Multi-phase processes involving phase change at interfaces, such as evaporation of a liquid or combustion of a solid, represent an interesting class of problems with varied applications. Large density ratio across phases, discontinuous fields at the interface and rapidly evolving geometries are some of the inherent challenges which influence the numerical modeling of multi-phase phase change problems. In this work, a mathematically consistent and robust computational approach to address these issues is presented. We use stabilized finite element methods on mixed topology unstructured grids for solving the compressible Navier-Stokes equations. Appropriate jump conditions derived from conservations laws across the interface are handled by using discontinuous interpolations, while the continuity of temperature and tangential velocity is enforced using a penalty parameter. The arbitrary Lagrangian-Eulerian (ALE) technique is utilized to explicitly track the interface motion. Mesh at the interface is constrained to move with the interface while elsewhere it is moved using the linear elasticity analogy. Repositioning is applied to the layered mesh that maintains its structure and normal resolution. In addition, mesh modification is used to preserve the quality of the volumetric mesh. This work is supported by the U.S. Army Grants W911NF1410301 and W911NF16C0117.

Massively Parallel Finite Element Programming

KAUST Repository

Heister, Timo; Kronbichler, Martin; Bangerth, Wolfgang

2010-01-01

Today's large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.

Massively Parallel Finite Element Programming

KAUST Repository

Heister, Timo

2010-01-01

Today\\'s large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.

Discontinuous finite element solution of the radiation diffusion equation on arbitrary polygonal meshes and locally adapted quadrilateral grids

International Nuclear Information System (INIS)

Ragusa, Jean C.

2015-01-01

In this paper, we propose a piece-wise linear discontinuous (PWLD) finite element discretization of the diffusion equation for arbitrary polygonal meshes. It is based on the standard diffusion form and uses the symmetric interior penalty technique, which yields a symmetric positive definite linear system matrix. A preconditioned conjugate gradient algorithm is employed to solve the linear system. Piece-wise linear approximations also allow a straightforward implementation of local mesh adaptation by allowing unrefined cells to be interpreted as polygons with an increased number of vertices. Several test cases, taken from the literature on the discretization of the radiation diffusion equation, are presented: random, sinusoidal, Shestakov, and Z meshes are used. The last numerical example demonstrates the application of the PWLD discretization to adaptive mesh refinement

A weak Galerkin least-squares finite element method for div-curl systems

Science.gov (United States)

Li, Jichun; Ye, Xiu; Zhang, Shangyou

2018-06-01

In this paper, we introduce a weak Galerkin least-squares method for solving div-curl problem. This finite element method leads to a symmetric positive definite system and has the flexibility to work with general meshes such as hybrid mesh, polytopal mesh and mesh with hanging nodes. Error estimates of the finite element solution are derived. The numerical examples demonstrate the robustness and flexibility of the proposed method.

On symmetric pyramidal finite elements

Czech Academy of Sciences Publication Activity Database

Liu, L.; Davies, K. B.; Yuan, K.; Křížek, Michal

2004-01-01

Roč. 11, 1-2 (2004), s. 213-227 ISSN 1492-8760 R&D Projects: GA AV ČR IAA1019201 Institutional research plan: CEZ:AV0Z1019905 Keywords : mesh generation * finite element method * composite elements Subject RIV: BA - General Mathematics Impact factor: 0.108, year: 2004

A finite element conjugate gradient FFT method for scattering

Science.gov (United States)

Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.

1991-01-01

Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.

Construction of hexahedral elements mesh capturing realistic geometries of Bayou Choctaw SPR site

Energy Technology Data Exchange (ETDEWEB)

Park, Byoung Yoon [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Roberts, Barry L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2015-09-01

The three-dimensional finite element mesh capturing realistic geometries of Bayou Choctaw site has been constructed using the sonar and seismic survey data obtained from the field. The mesh is consisting of hexahedral elements because the salt constitutive model is coded using hexahedral elements. Various ideas and techniques to construct finite element mesh capturing artificially and naturally formed geometries are provided. The techniques to reduce the number of elements as much as possible to save on computer run time with maintaining the computational accuracy is also introduced. The steps and methodologies could be applied to construct the meshes of Big Hill, Bryan Mound, and West Hackberry strategic petroleum reserve sites. The methodology could be applied to the complicated shape masses for not only various civil and geological structures but also biological applications such as artificial limbs.

A local level set method based on a finite element method for unstructured meshes

International Nuclear Information System (INIS)

Ngo, Long Cu; Choi, Hyoung Gwon

2016-01-01

A local level set method for unstructured meshes has been implemented by using a finite element method. A least-square weighted residual method was employed for implicit discretization to solve the level set advection equation. By contrast, a direct re-initialization method, which is directly applicable to the local level set method for unstructured meshes, was adopted to re-correct the level set function to become a signed distance function after advection. The proposed algorithm was constructed such that the advection and direct reinitialization steps were conducted only for nodes inside the narrow band around the interface. Therefore, in the advection step, the Gauss–Seidel method was used to update the level set function using a node-by-node solution method. Some benchmark problems were solved by using the present local level set method. Numerical results have shown that the proposed algorithm is accurate and efficient in terms of computational time

A local level set method based on a finite element method for unstructured meshes

Energy Technology Data Exchange (ETDEWEB)

Ngo, Long Cu; Choi, Hyoung Gwon [School of Mechanical Engineering, Seoul National University of Science and Technology, Seoul (Korea, Republic of)

2016-12-15

A local level set method for unstructured meshes has been implemented by using a finite element method. A least-square weighted residual method was employed for implicit discretization to solve the level set advection equation. By contrast, a direct re-initialization method, which is directly applicable to the local level set method for unstructured meshes, was adopted to re-correct the level set function to become a signed distance function after advection. The proposed algorithm was constructed such that the advection and direct reinitialization steps were conducted only for nodes inside the narrow band around the interface. Therefore, in the advection step, the Gauss–Seidel method was used to update the level set function using a node-by-node solution method. Some benchmark problems were solved by using the present local level set method. Numerical results have shown that the proposed algorithm is accurate and efficient in terms of computational time.

A geometric toolbox for tetrahedral finite element partitions

NARCIS (Netherlands)

Brandts, J.; Korotov, S.; Křížek, M.; Axelsson, O.; Karátson, J.

2011-01-01

In this work we present a survey of some geometric results on tetrahedral partitions and their refinements in a unified manner. They can be used for mesh generation and adaptivity in practical calculations by the finite element method (FEM), and also in theoretical finite element (FE) analysis.

Node-based finite element method for large-scale adaptive fluid analysis in parallel environments

International Nuclear Information System (INIS)

Toshimitsu, Fujisawa; Genki, Yagawa

2003-01-01

In this paper, a FEM-based (finite element method) mesh free method with a probabilistic node generation technique is presented. In the proposed method, all computational procedures, from the mesh generation to the solution of a system of equations, can be performed fluently in parallel in terms of nodes. Local finite element mesh is generated robustly around each node, even for harsh boundary shapes such as cracks. The algorithm and the data structure of finite element calculation are based on nodes, and parallel computing is realized by dividing a system of equations by the row of the global coefficient matrix. In addition, the node-based finite element method is accompanied by a probabilistic node generation technique, which generates good-natured points for nodes of finite element mesh. Furthermore, the probabilistic node generation technique can be performed in parallel environments. As a numerical example of the proposed method, we perform a compressible flow simulation containing strong shocks. Numerical simulations with frequent mesh refinement, which are required for such kind of analysis, can effectively be performed on parallel processors by using the proposed method. (authors)

Node-based finite element method for large-scale adaptive fluid analysis in parallel environments

Energy Technology Data Exchange (ETDEWEB)

Toshimitsu, Fujisawa [Tokyo Univ., Collaborative Research Center of Frontier Simulation Software for Industrial Science, Institute of Industrial Science (Japan); Genki, Yagawa [Tokyo Univ., Department of Quantum Engineering and Systems Science (Japan)

2003-07-01

In this paper, a FEM-based (finite element method) mesh free method with a probabilistic node generation technique is presented. In the proposed method, all computational procedures, from the mesh generation to the solution of a system of equations, can be performed fluently in parallel in terms of nodes. Local finite element mesh is generated robustly around each node, even for harsh boundary shapes such as cracks. The algorithm and the data structure of finite element calculation are based on nodes, and parallel computing is realized by dividing a system of equations by the row of the global coefficient matrix. In addition, the node-based finite element method is accompanied by a probabilistic node generation technique, which generates good-natured points for nodes of finite element mesh. Furthermore, the probabilistic node generation technique can be performed in parallel environments. As a numerical example of the proposed method, we perform a compressible flow simulation containing strong shocks. Numerical simulations with frequent mesh refinement, which are required for such kind of analysis, can effectively be performed on parallel processors by using the proposed method. (authors)

Three dimensional stress analysis of nozzle-to-shell intersections by the finite element method and a auto-mesh generation program

International Nuclear Information System (INIS)

Fujihara, Hirohiko; Ueda, Masahiro

1975-01-01

In the design of chemical reactors or nuclear pressure vessels it is often important to evaluate the stress distribution in nozzle-to-shell intersections. The finite element method is a powerful tool for stress analysis, but it has a defects to require troublesome work in preparing input data. Specially, the mesh data of oblique nozzles and tangential nozzles, in which stress concentration is very high, are very difficult to be prepared. The authors made a mesh generation program which can be used to any nozzle-to-shell intersections, and combining this program with a three dimensional stress analysis program by the finite element method they made the stress analysis of nozzle-to-shell intersections under internal pressure. Consequently, stresses, strains and deformations of nozzles nonsymmetrical to spherical shells and nozzles tangential to cylindrical shells were made clear and it was shown that the curvature of the inner surface of the nozzle corner was a controlling factor in reducing stress concentration. (auth.)

Finite Element Residual Stress Analysis of Planetary Gear Tooth

Directory of Open Access Journals (Sweden)

Jungang Wang

2013-01-01

Full Text Available A method to simulate residual stress field of planetary gear is proposed. In this method, the finite element model of planetary gear is established and divided to tooth zone and profile zone, whose different temperature field is set. The gear's residual stress simulation is realized by the thermal compression stress generated by the temperature difference. Based on the simulation, the finite element model of planetary gear train is established, the dynamic meshing process is simulated, and influence of residual stress on equivalent stress of addendum, pitch circle, and dedendum of internal and external meshing planetary gear tooth profile is analyzed, according to non-linear contact theory, thermodynamic theory, and finite element theory. The results show that the equivalent stresses of planetary gear at both meshing and nonmeshing surface are significantly and differently reduced by residual stress. The study benefits fatigue cracking analysis and dynamic optimization design of planetary gear train.

Extended finite element method and its application in heterogeneous materials with inclusions

International Nuclear Information System (INIS)

Du Chengbin; Jiang Shouyan; Ying Zongquan

2010-01-01

To simplify the technology of finite element mesh generation for particle reinforced material, enrichment techniques is used to account for the material interfaces in the framework of extended finite element method (XFEM). The geometry of material distribution is described by level set function, which allows one to model the internal boundaries of the microstructure without the adaptation of the mesh. The enrichment function is used to improve the shape function of classical finite element method (FEM) for the nodes supporting the elements cut by the interface. The key issue of XFEM including constructing displacement pattern, establishment of the governing equation and scheme of numerical integration is also presented. It is not necessarily matching the internal features of the inclusions using XFEM, so the generation of finite element mesh can be performed easily. Finally, a plate with multi-circular inclusions under uniaxial tension is simulated by XFEM and FEM, respectively. The results show that XFEM is highly effective and efficient.

Finite element methods a practical guide

CERN Document Server

Whiteley, Jonathan

2017-01-01

This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.

A combined finite volume-nonconforming finite element scheme for compressible two phase flow in porous media

KAUST Repository

Saad, Bilal Mohammed; Saad, Mazen Naufal B M

2014-01-01

We propose and analyze a combined finite volume-nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh, where the dual volumes are constructed around the sides of the original mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. This technique also ensures the validity of the discrete maximum principle for the saturation under a non restrictive shape regularity of the space mesh and the positiveness of all transmissibilities. Next, a priori estimates on the pressures and a function of the saturation that denote capillary terms are established. These stabilities results lead to some compactness arguments based on the use of the Kolmogorov compactness theorem, and allow us to derive the convergence of a subsequence of the sequence of approximate solutions to a weak solution of the continuous equations, provided the mesh size tends to zero. The proof is given for the complete system when the density of the each phase depends on its own pressure. © 2014 Springer-Verlag Berlin Heidelberg.

A combined finite volume-nonconforming finite element scheme for compressible two phase flow in porous media

KAUST Repository

Saad, Bilal Mohammed

2014-06-28

We propose and analyze a combined finite volume-nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh, where the dual volumes are constructed around the sides of the original mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. This technique also ensures the validity of the discrete maximum principle for the saturation under a non restrictive shape regularity of the space mesh and the positiveness of all transmissibilities. Next, a priori estimates on the pressures and a function of the saturation that denote capillary terms are established. These stabilities results lead to some compactness arguments based on the use of the Kolmogorov compactness theorem, and allow us to derive the convergence of a subsequence of the sequence of approximate solutions to a weak solution of the continuous equations, provided the mesh size tends to zero. The proof is given for the complete system when the density of the each phase depends on its own pressure. © 2014 Springer-Verlag Berlin Heidelberg.

Algorithms and data structures for massively parallel generic adaptive finite element codes

KAUST Repository

Bangerth, Wolfgang

2011-12-01

Today\\'s largest supercomputers have 100,000s of processor cores and offer the potential to solve partial differential equations discretized by billions of unknowns. However, the complexity of scaling to such large machines and problem sizes has so far prevented the emergence of generic software libraries that support such computations, although these would lower the threshold of entry and enable many more applications to benefit from large-scale computing. We are concerned with providing this functionality for mesh-adaptive finite element computations. We assume the existence of an "oracle" that implements the generation and modification of an adaptive mesh distributed across many processors, and that responds to queries about its structure. Based on querying the oracle, we develop scalable algorithms and data structures for generic finite element methods. Specifically, we consider the parallel distribution of mesh data, global enumeration of degrees of freedom, constraints, and postprocessing. Our algorithms remove the bottlenecks that typically limit large-scale adaptive finite element analyses. We demonstrate scalability of complete finite element workflows on up to 16,384 processors. An implementation of the proposed algorithms, based on the open source software p4est as mesh oracle, is provided under an open source license through the widely used deal.II finite element software library. © 2011 ACM 0098-3500/2011/12-ART10 $10.00.

Finite element analysis of human joints

Energy Technology Data Exchange (ETDEWEB)

Bossart, P.L.; Hollerbach, K.

1996-09-01

Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiring data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described.

Finite element analysis of human joints

International Nuclear Information System (INIS)

Bossart, P.L.; Hollerbach, K.

1996-09-01

Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiring data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described

LOOM-P: a finite element mesh generation program with on-line graphic display

International Nuclear Information System (INIS)

Ise, Takeharu; Yamazaki, Toshio.

1977-06-01

A description of the two-dimensional mesh generation program, LOOM-P, is given in detail. The program is developed newly to produce a mesh network for a reactor core geometry with the help of an automatic mesh generation routine built in it, under the control of the refresh-type graphic display. It is therefore similar to the edit program of the self-organizing mesh generator, QMESH-RENUM. Additional techniques are incorporated to improve the pattern of mesh elements by means of on-line conversational mode. The obtained mesh network is edited out as input data to the three-dimensional neutron diffusion theory code, FEM-BABEL. (auth.)

On using moving windows in finite element time domain simulation for long accelerator structures

International Nuclear Information System (INIS)

Lee, L.-Q.; Candel, Arno; Ng, Cho; Ko, Kwok

2010-01-01

A finite element moving window technique is developed to simulate the propagation of electromagnetic waves induced by the transit of a charged particle beam inside large and long structures. The window moving along with the beam in the computational domain adopts high-order finite element basis functions through p refinement and/or a high-resolution mesh through h refinement so that a sufficient accuracy is attained with substantially reduced computational costs. Algorithms to transfer discretized fields from one mesh to another, which are the keys to implementing a moving window in a finite element unstructured mesh, are presented. Numerical experiments are carried out using the moving window technique to compute short-range wakefields in long accelerator structures. The results are compared with those obtained from the normal finite element time domain (FETD) method and the advantages of using the moving window technique are discussed.

ZONE, Finite Elements Method Quadrilateral and Triangular Mesh Generator for 2-D Axisymmetric Geometry

International Nuclear Information System (INIS)

Burger, M. J.

1981-01-01

1 - Description of problem or function: The ZONE program is a finite element mesh generator which produces the nodes and element description of any two-dimensional geometry. The geometry is divided into a mesh of quadrilateral and triangular zones defined by node points taken in a counter-clockwise sequence. The zones are arranged sequentially in an ordered march through the geometry. The order can be chosen so that the minimum bandwidth is obtained. The mesh that is generated can be used as input to any two-dimensional as well as any axisymmetrical structure program. 2 - Method of solution: The basic concept used is the definition of a two-dimensional structure by the intersection of two sets of lines which describe the geometric and material boundaries. A set of lines called meridians define the geometric and material boundaries and generally run in the same direction. Another set of linear line segments called rays which intersect the meridians are also defined at the material and geometric boundaries. The section of the structure between successive rays is called a region. The ray segment between any two consecutive ray-meridian intersections or void area in the structure is called a layer and is described as passing through, or bounding a material. The boundaries can be directly defined as a sequence of straight line segments or can be computed in terms of elliptic segments or circular arcs. A meridian or ray can also be made to follow a previously-defined meridian or ray at a fixed distance by invoking an offset option. 3 - Restrictions on the complexity of the problem: The following are limited only by a DIMENSION statement. The code currently has a maxima of: 100 coordinate points defining a meridian or ray, 40 meridians, 40 layers. There are no limits on the number of zones or nodes for any problems

Comparison of 3-D finite elements for incompressible fluid flow

International Nuclear Information System (INIS)

Robichaud, M.; Tanguy, P.A.

1985-01-01

In recent years, the finite element method applied to the solution of incompressible fluid flow has been in constant evolution. In the present state-of-the-art, 2-D problems are solved routinely and reliable results are obtained at a reasonable cost. In 3-D the finite element method is still undergoing active research and many methods have been proposed to solve the Navier-Stokes equations at 'low cost'. These methods have in common the choice of the element which has a trilinear velocity and a discontinuous constant pressure (Q1-PO). The prohibitive cost of 3-D finite element method in fluid flow is the reason for this choice: the Q1-PO is the simplest and the cheapest 3-D element. However, as mentioned in (5) and (6), it generates 'spurious' pressure modes phenomenon called checkerboarding. On regular mesh these spurious modes can be filtered but on distorted mesh the pressure solution is meaningless. (author)

The transmission of stress to grafted bone inside a titanium mesh cage used in anterior column reconstruction after total spondylectomy: a finite-element analysis.

Science.gov (United States)

Akamaru, Tomoyuki; Kawahara, Norio; Sakamoto, Jiro; Yoshida, Akira; Murakami, Hideki; Hato, Taizo; Awamori, Serina; Oda, Juhachi; Tomita, Katsuro

2005-12-15

A finite-element study of posterior alone or anterior/posterior combined instrumentation following total spondylectomy and replacement with a titanium mesh cage used as an anterior strut. To compare the effect of posterior instrumentation versus anterior/posterior instrumentation on transmission of the stress to grafted bone inside a titanium mesh cage following total spondylectomy. The most recent reconstruction techniques following total spondylectomy for malignant spinal tumor include a titanium mesh cage filled with autologous bone as an anterior strut. The need for additional anterior instrumentation with posterior pedicle screws and rods is controversial. Transmission of the mechanical stress to grafted bone inside a titanium mesh cage is important for fusion and remodeling. To our knowledge, there are no published reports comparing the load-sharing properties of the different reconstruction methods following total spondylectomy. A 3-dimensional finite-element model of the reconstructed spine (T10-L4) following total spondylectomy at T12 was constructed. A Harms titanium mesh cage (DePuy Spine, Raynham, MA) was positioned as an anterior replacement, and 3 types of the reconstruction methods were compared: (1) multilevel posterior instrumentation (MPI) (i.e., posterior pedicle screws and rods at T10-L2 without anterior instrumentation); (2) MPI with anterior instrumentation (MPAI) (i.e., MPAI [Kaneda SR; DePuy Spine] at T11-L1); and (3) short posterior and anterior instrumentation (SPAI) (i.e., posterior pedicle screws and rods with anterior instrumentation at T11-L1). The mechanical energy stress distribution exerted inside the titanium mesh cage was evaluated and compared by finite-element analysis for the 3 different reconstruction methods. Simulated forces were applied to give axial compression, flexion, extension, and lateral bending. In flexion mode, the energy stress distribution in MPI was higher than 3.0 x 10 MPa in 73.0% of the total volume inside

Fracture Capabilities in Grizzly with the extended Finite Element Method (X-FEM)

Energy Technology Data Exchange (ETDEWEB)

Dolbow, John [Idaho National Lab. (INL), Idaho Falls, ID (United States); Zhang, Ziyu [Idaho National Lab. (INL), Idaho Falls, ID (United States); Spencer, Benjamin [Idaho National Lab. (INL), Idaho Falls, ID (United States); Jiang, Wen [Idaho National Lab. (INL), Idaho Falls, ID (United States)

2015-09-01

Efforts are underway to develop fracture mechanics capabilities in the Grizzly code to enable it to be used to perform deterministic fracture assessments of degraded reactor pressure vessels (RPVs). A capability was previously developed to calculate three-dimensional interaction- integrals to extract mixed-mode stress-intensity factors. This capability requires the use of a finite element mesh that conforms to the crack geometry. The eXtended Finite Element Method (X-FEM) provides a means to represent a crack geometry without explicitly fitting the finite element mesh to it. This is effected by enhancing the element kinematics to represent jump discontinuities at arbitrary locations inside of the element, as well as the incorporation of asymptotic near-tip fields to better capture crack singularities. In this work, use of only the discontinuous enrichment functions was examined to see how accurate stress intensity factors could still be calculated. This report documents the following work to enhance Grizzly’s engineering fracture capabilities by introducing arbitrary jump discontinuities for prescribed crack geometries; X-FEM Mesh Cutting in 3D: to enhance the kinematics of elements that are intersected by arbitrary crack geometries, a mesh cutting algorithm was implemented in Grizzly. The algorithm introduces new virtual nodes and creates partial elements, and then creates a new mesh connectivity; Interaction Integral Modifications: the existing code for evaluating the interaction integral in Grizzly was based on the assumption of a mesh that was fitted to the crack geometry. Modifications were made to allow for the possibility of a crack front that passes arbitrarily through the mesh; and Benchmarking for 3D Fracture: the new capabilities were benchmarked against mixed-mode three-dimensional fracture problems with known analytical solutions.

Finite cover method with mortar elements for elastoplasticity problems

Science.gov (United States)

Kurumatani, M.; Terada, K.

2005-06-01

Finite cover method (FCM) is extended to elastoplasticity problems. The FCM, which was originally developed under the name of manifold method, has recently been recognized as one of the generalized versions of finite element methods (FEM). Since the mesh for the FCM can be regular and squared regardless of the geometry of structures to be analyzed, structural analysts are released from a burdensome task of generating meshes conforming to physical boundaries. Numerical experiments are carried out to assess the performance of the FCM with such discretization in elastoplasticity problems. Particularly to achieve this accurately, the so-called mortar elements are introduced to impose displacement boundary conditions on the essential boundaries, and displacement compatibility conditions on material interfaces of two-phase materials or on joint surfaces between mutually incompatible meshes. The validity of the mortar approximation is also demonstrated in the elastic-plastic FCM.

A unified monolithic approach for multi-fluid flows and fluid-structure interaction using the Particle Finite Element Method with fixed mesh

Science.gov (United States)

Becker, P.; Idelsohn, S. R.; Oñate, E.

2015-06-01

This paper describes a strategy to solve multi-fluid and fluid-structure interaction (FSI) problems using Lagrangian particles combined with a fixed finite element (FE) mesh. Our approach is an extension of the fluid-only PFEM-2 (Idelsohn et al., Eng Comput 30(2):2-2, 2013; Idelsohn et al., J Numer Methods Fluids, 2014) which uses explicit integration over the streamlines to improve accuracy. As a result, the convective term does not appear in the set of equations solved on the fixed mesh. Enrichments in the pressure field are used to improve the description of the interface between phases.

Multisymplectic Structure-Preserving in Simple Finite Element Method in High Dimensional Case

Institute of Scientific and Technical Information of China (English)

BAI Yong-Qiang; LIU Zhen; PEI Ming; ZHENG Zhu-Jun

2003-01-01

In this paper, we study a finite element scheme of some semi-linear elliptic boundary value problems inhigh-dimensional space. With uniform mesh, we find that, the numerical scheme derived from finite element method cankeep a preserved multisymplectic structure.

Multisymplectic Structure－Preserving in Simple Finite Element Method in High Dimensional Case

Institute of Scientific and Technical Information of China (English)

BAIYong-Qiang; LIUZhen; PEIMing; ZHENGZhu-Jun

2003-01-01

In this paper, we study a finite element scheme of some semi-linear elliptic boundary value problems in high-dhnensjonal space. With uniform mesh, we find that, the numerical scheme derived from finite element method can keep a preserved multisymplectic structure.

A Note on Symplectic, Multisymplectic Scheme in Finite Element Method

Institute of Scientific and Technical Information of China (English)

GUO Han-Ying; JI Xiao-Mei; LI Yu-Qi; WU Ke

2001-01-01

We find that with uniform mesh, the numerical schemes derived from finite element method can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimensional case respectively. These results are in fact the intrinsic reason why the numerical experiments show that such finite element algorithms are accurate in practice.``

Assessment of finite element and smoothed particles hydrodynamics methods for modeling serrated chip formation in hardened steel

Directory of Open Access Journals (Sweden)

Usama Umer

2016-05-01

Full Text Available This study aims to perform comparative analyses in modeling serrated chip morphologies using traditional finite element and smoothed particles hydrodynamics methods. Although finite element models are being employed in predicting machining performance variables for the last two decades, many drawbacks and limitations exist with the current finite element models. The problems like excessive mesh distortions, high numerical cost of adaptive meshing techniques, and need of geometric chip separation criteria hinder its practical implementation in metal cutting industries. In this study, a mesh free method, namely, smoothed particles hydrodynamics, is implemented for modeling serrated chip morphology while machining AISI H13 hardened tool steel. The smoothed particles hydrodynamics models are compared with the traditional finite element models, and it has been found that the smoothed particles hydrodynamics models have good capabilities in handling large distortions and do not need any geometric or mesh-based chip separation criterion.

A study on the improvement of shape optimization associated with the modification of a finite element

International Nuclear Information System (INIS)

Sung, Jin Il; Yoo, Jeong Hoon

2002-01-01

In this paper, we investigate the effect and the importance of the accuracy of finite element analysis in the shape optimization based on the finite element method and improve the existing finite element which has inaccuracy in some cases. And then, the shape optimization is performed by using the improved finite element. One of the main stream to improve finite element is the prevention of locking phenomenon. In case of bending dominant problems, finite element solutions cannot be reliable because of shear locking phenomenon. In the process of shape optimization, the mesh distortion is large due to the change of the structure outline. So, we have to raise the accuracy of finite element analysis for the large mesh distortion. We cannot guarantee the accurate result unless the finite element itself is accurate or the finite elements are remeshed. So, we approach to more accurate shape optimization to diminish these inaccuracies by improving the existing finite element. The shape optimization using the modified finite element is applied to a two and three dimensional simple beam. Results show that the modified finite element has improved the optimization results

Finite element formulation of fluctuating hydrodynamics for fluids filled with rigid particles using boundary fitted meshes

Energy Technology Data Exchange (ETDEWEB)

De Corato, M., E-mail: marco.decorato@unina.it [Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli (Italy); Slot, J.J.M., E-mail: j.j.m.slot@tue.nl [Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven (Netherlands); Hütter, M., E-mail: m.huetter@tue.nl [Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven (Netherlands); D' Avino, G., E-mail: gadavino@unina.it [Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli (Italy); Maffettone, P.L., E-mail: pierluca.maffettone@unina.it [Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli (Italy); Hulsen, M.A., E-mail: m.a.hulsen@tue.nl [Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven (Netherlands)

2016-07-01

In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementation fulfills the fluctuation–dissipation theorem exactly at the discrete level. Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements. Brownian motion of arbitrarily shaped particles in complex confinements can be considered within the present formulation. A multi-step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation (SDE) describing the evolution of the positions of the particles. The proposed approach is validated by simulating the Brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity. The time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential.

A multilevel correction adaptive finite element method for Kohn-Sham equation

Science.gov (United States)

Hu, Guanghui; Xie, Hehu; Xu, Fei

2018-02-01

In this paper, an adaptive finite element method is proposed for solving Kohn-Sham equation with the multilevel correction technique. In the method, the Kohn-Sham equation is solved on a fixed and appropriately coarse mesh with the finite element method in which the finite element space is kept improving by solving the derived boundary value problems on a series of adaptively and successively refined meshes. A main feature of the method is that solving large scale Kohn-Sham system is avoided effectively, and solving the derived boundary value problems can be handled efficiently by classical methods such as the multigrid method. Hence, the significant acceleration can be obtained on solving Kohn-Sham equation with the proposed multilevel correction technique. The performance of the method is examined by a variety of numerical experiments.

Adaptive Smoothed Finite Elements (ASFEM) for history dependent material models

International Nuclear Information System (INIS)

Quak, W.; Boogaard, A. H. van den

2011-01-01

A successful simulation of a bulk forming process with finite elements can be difficult due to distortion of the finite elements. Nodal smoothed Finite Elements (NSFEM) are an interesting option for such a process since they show good distortion insensitivity and moreover have locking-free behavior and good computational efficiency. In this paper a method is proposed which takes advantage of the nodally smoothed field. This method, named adaptive smoothed finite elements (ASFEM), revises the mesh for every step of a simulation without mapping the history dependent material parameters. In this paper an updated-Lagrangian implementation is presented. Several examples are given to illustrate the method and to show its properties.

Optical breast shape capture and finite-element mesh generation for electrical impedance tomography

International Nuclear Information System (INIS)

Forsyth, J; Borsic, A; Halter, R J; Hartov, A; Paulsen, K D

2011-01-01

X-ray mammography is the standard for breast cancer screening. The development of alternative imaging modalities is desirable because mammograms expose patients to ionizing radiation. Electrical impedance tomography (EIT) may be used to determine tissue conductivity, a property which is an indicator of cancer presence. EIT is also a low-cost imaging solution and does not involve ionizing radiation. In breast EIT, impedance measurements are made using electrodes placed on the surface of the patient's breast. The complex conductivity of the volume of the breast is estimated by a reconstruction algorithm. EIT reconstruction is a severely ill-posed inverse problem. As a result, noisy instrumentation and incorrect modelling of the electrodes and domain shape produce significant image artefacts. In this paper, we propose a method that has the potential to reduce these errors by accurately modelling the patient breast shape. A 3D hand-held optical scanner is used to acquire the breast geometry and electrode positions. We develop methods for processing the data from the scanner and producing volume meshes accurately matching the breast surface and electrode locations, which can be used for image reconstruction. We demonstrate this method for a plaster breast phantom and a human subject. Using this approach will allow patient-specific finite-element meshes to be generated which has the potential to improve the clinical value of EIT for breast cancer diagnosis

Finite-element solution to multidimensional multisource electromagnetic problems in the frequency domain using non-conforming meshes

Science.gov (United States)

Soloveichik, Yury G.; Persova, Marina G.; Domnikov, Petr A.; Koshkina, Yulia I.; Vagin, Denis V.

2018-03-01

We propose an approach to solving multisource induction logging problems in multidimensional media. According to the type of induction logging tools, the measurements are performed in the frequency range of 10 kHz to 14 MHz, transmitter-receiver offsets vary in the range of 0.5-8 m or more, and the trajectory length is up to 1 km. For calculating the total field, the primary-secondary field approach is used. The secondary field is calculated with the use of the finite-element method (FEM), irregular non-conforming meshes with local refinements and a direct solver. The approach to constructing basis functions with the continuous tangential components (from Hcurl(Ω)) on the non-conforming meshes from the standard shape vector functions is developed. On the basis of this method, the algorithm of generating global matrices and a vector of the finite-element equation system is proposed. We also propose the method of grouping the logging tool positions, which makes it possible to significantly increase the computational effectiveness. This is achieved due to the compromise between the possibility of using the 1-D background medium, which is very similar to the investigated multidimensional medium for a small group, and the decrease in the number of the finite-element matrix factorizations with the increasing number of tool positions in one group. For calculating the primary field, we propose the method based on the use of FEM. This method is highly effective when the 1-D field is required to be calculated at a great number of points. The use of this method significantly increases the effectiveness of the primary-secondary field approach. The proposed approach makes it possible to perform modelling both in the 2.5-D case (i.e. without taking into account a borehole and/or invasion zone effect) and the 3-D case (i.e. for models with a borehole and invasion zone). The accuracy of numerical results obtained with the use of the proposed approach is compared with the one

The application of finite volume methods for modelling three-dimensional incompressible flow on an unstructured mesh

Science.gov (United States)

Lonsdale, R. D.; Webster, R.

This paper demonstrates the application of a simple finite volume approach to a finite element mesh, combining the economy of the former with the geometrical flexibility of the latter. The procedure is used to model a three-dimensional flow on a mesh of linear eight-node brick (hexahedra). Simulations are performed for a wide range of flow problems, some in excess of 94,000 nodes. The resulting computer code ASTEC that incorporates these procedures is described.

A short summary on finite element modelling of fatigue crack closure

Energy Technology Data Exchange (ETDEWEB)

Singh, Konjengbam Darunkumar [Indian Institute of Technology, Guwahati (India); Parry, Matthew Roger [Airbus Operations Ltd, Bristol(United Kingdom); Sinclair, Ian [University of Southampton, Southampton (United Kingdom)

2011-12-15

This paper presents a short summary pertaining to the finite element modelling of fatigue crack closure. Several key issues related to finite element modelling of fatigue crack closure are highlighted: element type, mesh refinement, stabilization of crack closure, crack-tip node release scheme, constitutive model, specimen geometry, stress-states (i.e., plane stress, plane strain), crack closure monitoring. Reviews are presented for both straight and deflected cracks.

A least squares principle unifying finite element, finite difference and nodal methods for diffusion theory

International Nuclear Information System (INIS)

Ackroyd, R.T.

1987-01-01

A least squares principle is described which uses a penalty function treatment of boundary and interface conditions. Appropriate choices of the trial functions and vectors employed in a dual representation of an approximate solution established complementary principles for the diffusion equation. A geometrical interpretation of the principles provides weighted residual methods for diffusion theory, thus establishing a unification of least squares, variational and weighted residual methods. The complementary principles are used with either a trial function for the flux or a trial vector for the current to establish for regular meshes a connection between finite element, finite difference and nodal methods, which can be exact if the mesh pitches are chosen appropriately. Whereas the coefficients in the usual nodal equations have to be determined iteratively, those derived via the complementary principles are given explicitly in terms of the data. For the further development of the connection between finite element, finite difference and nodal methods, some hybrid variational methods are described which employ both a trial function and a trial vector. (author)

The finite element response matrix method

International Nuclear Information System (INIS)

Nakata, H.; Martin, W.R.

1983-02-01

A new technique is developed with an alternative formulation of the response matrix method implemented with the finite element scheme. Two types of response matrices are generated from the Galerkin solution to the weak form of the diffusion equation subject to an arbitrary current and source. The piecewise polynomials are defined in two levels, the first for the local (assembly) calculations and the second for the global (core) response matrix calculations. This finite element response matrix technique was tested in two 2-dimensional test problems, 2D-IAEA benchmark problem and Biblis benchmark problem, with satisfatory results. The computational time, whereas the current code is not extensively optimized, is of the same order of the well estabilished coarse mesh codes. Furthermore, the application of the finite element technique in an alternative formulation of response matrix method permits the method to easily incorporate additional capabilities such as treatment of spatially dependent cross-sections, arbitrary geometrical configurations, and high heterogeneous assemblies. (Author) [pt

A Finite Element Method for Simulation of Compressible Cavitating Flows

Science.gov (United States)

Shams, Ehsan; Yang, Fan; Zhang, Yu; Sahni, Onkar; Shephard, Mark; Oberai, Assad

2016-11-01

This work focuses on a novel approach for finite element simulations of multi-phase flows which involve evolving interface with phase change. Modeling problems, such as cavitation, requires addressing multiple challenges, including compressibility of the vapor phase, interface physics caused by mass, momentum and energy fluxes. We have developed a mathematically consistent and robust computational approach to address these problems. We use stabilized finite element methods on unstructured meshes to solve for the compressible Navier-Stokes equations. Arbitrary Lagrangian-Eulerian formulation is used to handle the interface motions. Our method uses a mesh adaptation strategy to preserve the quality of the volumetric mesh, while the interface mesh moves along with the interface. The interface jump conditions are accurately represented using a discontinuous Galerkin method on the conservation laws. Condensation and evaporation rates at the interface are thermodynamically modeled to determine the interface velocity. We will present initial results on bubble cavitation the behavior of an attached cavitation zone in a separated boundary layer. We acknowledge the support from Army Research Office (ARO) under ARO Grant W911NF-14-1-0301.

Study on the Influence of the Refinement of a 3-D Finite Element Mesh in Springback Evaluation of Plane-Strain Channel Sections

International Nuclear Information System (INIS)

Padmanabhan, R.; Oliveira, M. C.; Baptista, A. J.; Menezes, L. F.; Alves, J. L.

2007-01-01

Springback phenomenon associated with the elastic properties of sheet metals makes the design of forming dies a complex task. Thus, to develop consistent algorithms for springback compensation an accurate prediction of the amount of springback is mandatory. The numerical simulation using the finite element method is consensually the only feasible method to predict springback. However, springback prediction is a very complicated task and highly sensitive to various numerical parameters of finite elements (FE), such as: type, order, integration scheme, shape and size, as well the time integration formulae and the unloading strategy. All these numerical parameters make numerical simulation of springback more sensitive to numerical tolerances than the forming operation. In case of an unconstrained cylindrical bending, the in-plane to thickness FE size ratio is more relevant than the number of FE layers through-thickness, for the numerical prediction of final stress and strain states, variables of paramount importance for an accurate springback prediction. The aim of the present work is to evaluate the influence of the refinement of a 3-D FE mesh, namely the in-plane mesh refinement and the number of through-thickness FE layers, in springback prediction. The selected example corresponds to the first stage of the 'Numisheet'05 Benchmark no. 3', which consists basically in the sheet forming of a channel section in an industrial-scale channel draw die. The physical drawbeads are accurately taken into account in the numerical model in order to accurately reproduce its influence during the forming process simulation. FEM simulations were carried out with the in-house code DD3IMP. Solid finite elements were used. They are recommended for accuracy in FE springback simulation when the ratio between the tool radius and blank thickness is lower than 5-6. In the selected example the drawbead radius is 4.0 mm. The influence of the FE mesh refinement in springback prediction is

Finite element method for neutron diffusion problems in hexagonal geometry

International Nuclear Information System (INIS)

Wei, T.Y.C.; Hansen, K.F.

1975-06-01

The use of the finite element method for solving two-dimensional static neutron diffusion problems in hexagonal reactor configurations is considered. It is investigated as a possible alternative to the low-order finite difference method. Various piecewise polynomial spaces are examined for their use in hexagonal problems. The central questions which arise in the design of these spaces are the degree of incompleteness permissible and the advantages of using a low-order space fine-mesh approach over that of a high-order space coarse-mesh one. There is also the question of the degree of smoothness required. Two schemes for the construction of spaces are described and a number of specific spaces, constructed with the questions outlined above in mind, are presented. They range from a complete non-Lagrangian, non-Hermite quadratic space to an incomplete ninth order space. Results are presented for two-dimensional problems typical of a small high temperature gas-cooled reactor. From the results it is concluded that the space used should at least include the complete linear one. Complete spaces are to be preferred to totally incomplete ones. Once function continuity is imposed any additional degree of smoothness is of secondary importance. For flux shapes typical of the small high temperature gas-cooled reactor the linear space fine-mesh alternative is to be preferred to the perturbation quadratic space coarse-mesh one and the low-order finite difference method is to be preferred over both finite element schemes

Hybrid finite difference/finite element immersed boundary method.

Science.gov (United States)

E Griffith, Boyce; Luo, Xiaoyu

2017-12-01

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International  Journal  for  Numerical  Methods  in  Biomedical  Engineering Published by John Wiley & Sons Ltd.

Coupling of smooth particle hydrodynamics with the finite element method

International Nuclear Information System (INIS)

Attaway, S.W.; Heinstein, M.W.; Swegle, J.W.

1994-01-01

A gridless technique called smooth particle hydrodynamics (SPH) has been coupled with the transient dynamics finite element code ppercase[pronto]. In this paper, a new weighted residual derivation for the SPH method will be presented, and the methods used to embed SPH within ppercase[pronto] will be outlined. Example SPH ppercase[pronto] calculations will also be presented. One major difficulty associated with the Lagrangian finite element method is modeling materials with no shear strength; for example, gases, fluids and explosive biproducts. Typically, these materials can be modeled for only a short time with a Lagrangian finite element code. Large distortions cause tangling of the mesh, which will eventually lead to numerical difficulties, such as negative element area or ''bow tie'' elements. Remeshing will allow the problem to continue for a short while, but the large distortions can prevent a complete analysis. SPH is a gridless Lagrangian technique. Requiring no mesh, SPH has the potential to model material fracture, large shear flows and penetration. SPH computes the strain rate and the stress divergence based on the nearest neighbors of a particle, which are determined using an efficient particle-sorting technique. Embedding the SPH method within ppercase[pronto] allows part of the problem to be modeled with quadrilateral finite elements, while other parts are modeled with the gridless SPH method. SPH elements are coupled to the quadrilateral elements through a contact-like algorithm. ((orig.))

The Finite Element Numerical Modelling of 3D Magnetotelluric

Directory of Open Access Journals (Sweden)

Ligang Cao

2014-01-01

Full Text Available The ideal numerical simulation of 3D magnetotelluric was restricted by the methodology complexity and the time-consuming calculation. Boundary values, the variation of weighted residual equation, and the hexahedral mesh generation method of finite element are three major causes. A finite element method for 3D magnetotelluric numerical modeling is presented in this paper as a solution for the problem mentioned above. In this algorithm, a hexahedral element coefficient matrix for magnetoelluric finite method is developed, which solves large-scale equations using preconditioned conjugate gradient of the first-type boundary conditions. This algorithm is verified using the homogeneous model, and the positive landform model, as well as the low resistance anomaly model.

New mixed finite-element methods

International Nuclear Information System (INIS)

Franca, L.P.

1987-01-01

New finite-element methods are proposed for mixed variational formulations. The methods are constructed by adding to the classical Galerkin method various least-squares like terms. The additional terms involve integrals over element interiors, and include mesh-parameter dependent coefficients. The methods are designed to enhance stability. Consistency is achieved in the sense that exact solutions identically satisfy the variational equations.Applied to several problems, simple finite-element interpolations are rendered convergent, including convenient equal-order interpolations generally unstable within the Galerkin approach. The methods are subdivided into two classes according to the manner in which stability is attained: (1) circumventing Babuska-Brezzi condition methods; (2) satisfying Babuska-Brezzi condition methods. Convergence is established for each class of methods. Applications of the first class of methods to Stokes flow and compressible linear elasticity are presented. The second class of methods is applied to the Poisson, Timoshenko beam and incompressible elasticity problems. Numerical results demonstrate the good stability and accuracy of the methods, and confirm the error estimates

The ACR-program for automatic finite element model generation for part through cracks

International Nuclear Information System (INIS)

Leinonen, M.S.; Mikkola, T.P.J.

1989-01-01

The ACR-program (Automatic Finite Element Model Generation for Part Through Cracks) has been developed at the Technical Research Centre of Finland (VTT) for automatic finite element model generation for surface flaws using three dimensional solid elements. Circumferential or axial cracks can be generated on the inner or outer surface of a cylindrical or toroidal geometry. Several crack forms are available including the standard semi-elliptical surface crack. The program can be used in the development of automated systems for fracture mechanical analyses of structures. The tests for the accuracy of the FE-mesh have been started with two-dimensional models. The results indicate that the accuracy of the standard mesh is sufficient for practical analyses. Refinement of the standard mesh is needed in analyses with high load levels well over the limit load of the structure

Preconditioning for Mixed Finite Element Formulations of Elliptic Problems

KAUST Repository

Wildey, Tim; Xue, Guangri

2013-01-01

In this paper, we discuss a preconditioning technique for mixed finite element discretizations of elliptic equations. The technique is based on a block-diagonal approximation of the mass matrix which maintains the sparsity and positive definiteness of the corresponding Schur complement. This preconditioner arises from the multipoint flux mixed finite element method and is robust with respect to mesh size and is better conditioned for full permeability tensors than a preconditioner based on a diagonal approximation of the mass matrix. © Springer-Verlag Berlin Heidelberg 2013.

A parallel direct solver for the self-adaptive hp Finite Element Method

KAUST Repository

Paszyński, Maciej R.; Pardo, David; Torres-Verdí n, Carlos; Demkowicz, Leszek F.; Calo, Victor M.

2010-01-01

measurement simulations problems. We measure the execution time and memory usage of the solver over a large regular mesh with 1.5 million degrees of freedom as well as on the highly non-regular mesh, generated by the self-adaptive h p-FEM, with finite elements

Generalized multiscale finite element method. Symmetric interior penalty coupling

KAUST Repository

Efendiev, Yalchin R.; Galvis, Juan; Lazarov, Raytcho D.; Moon, M.; Sarkis, Marcus V.

2013-01-01

Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.

Generalized multiscale finite element method. Symmetric interior penalty coupling

KAUST Repository

Efendiev, Yalchin R.

2013-12-01

Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.

Finite element approximation to the even-parity transport equation

International Nuclear Information System (INIS)

Lewis, E.E.

1981-01-01

This paper studies the finite element method, a procedure for reducing partial differential equations to sets of algebraic equations suitable for solution on a digital computer. The differential equation is cast into the form of a variational principle, the resulting domain then subdivided into finite elements. The dependent variable is then approximated by a simple polynomial, and these are linked across inter-element boundaries by continuity conditions. The finite element method is tailored to a variety of transport problems. Angular approximations are formulated, and the extent of ray effect mitigation is examined. Complex trial functions are introduced to enable the inclusion of buckling approximations. The ubiquitous curved interfaces of cell calculations, and coarse mesh methods are also treated. A concluding section discusses limitations of the work to date and suggests possible future directions

Linear finite element method for one-dimensional diffusion problems

Energy Technology Data Exchange (ETDEWEB)

Brandao, Michele A.; Dominguez, Dany S.; Iglesias, Susana M., E-mail: micheleabrandao@gmail.com, E-mail: dany@labbi.uesc.br, E-mail: smiglesias@uesc.br [Universidade Estadual de Santa Cruz (LCC/DCET/UESC), Ilheus, BA (Brazil). Departamento de Ciencias Exatas e Tecnologicas. Laboratorio de Computacao Cientifica

2011-07-01

We describe in this paper the fundamentals of Linear Finite Element Method (LFEM) applied to one-speed diffusion problems in slab geometry. We present the mathematical formulation to solve eigenvalue and fixed source problems. First, we discretized a calculus domain using a finite set of elements. At this point, we obtain the spatial balance equations for zero order and first order spatial moments inside each element. Then, we introduce the linear auxiliary equations to approximate neutron flux and current inside the element and architect a numerical scheme to obtain the solution. We offer numerical results for fixed source typical model problems to illustrate the method's accuracy for coarse-mesh calculations in homogeneous and heterogeneous domains. Also, we compare the accuracy and computational performance of LFEM formulation with conventional Finite Difference Method (FDM). (author)

Goal-Oriented Self-Adaptive hp Finite Element Simulation of 3D DC Borehole Resistivity Simulations

KAUST Repository

Calo, Victor M.

2011-05-14

In this paper we present a goal-oriented self-adaptive hp Finite Element Method (hp-FEM) with shared data structures and a parallel multi-frontal direct solver. The algorithm automatically generates (without any user interaction) a sequence of meshes delivering exponential convergence of a prescribed quantity of interest with respect to the number of degrees of freedom. The sequence of meshes is generated from a given initial mesh, by performing h (breaking elements into smaller elements), p (adjusting polynomial orders of approximation) or hp (both) refinements on the finite elements. The new parallel implementation utilizes a computational mesh shared between multiple processors. All computational algorithms, including automatic hp goal-oriented adaptivity and the solver work fully in parallel. We describe the parallel self-adaptive hp-FEM algorithm with shared computational domain, as well as its efficiency measurements. We apply the methodology described to the three-dimensional simulation of the borehole resistivity measurement of direct current through casing in the presence of invasion.

A finite element modeling method for predicting long term corrosion rates

International Nuclear Information System (INIS)

Fu, J.W.; Chan, S.

1984-01-01

For the analyses of galvanic corrosion, pitting and crevice corrosion, which have been identified as possible corrosion processes for nuclear waste isolation, a finite element method has been developed for the prediction of corrosion rates. The method uses a finite element mesh to model the corrosive environment and the polarization curves of metals are assigned as the boundary conditions to calculate the corrosion cell current distribution. A subroutine is used to calculate the chemical change with time in the crevice or the pit environments. In this paper, the finite element method is described along with experimental confirmation

Domain decomposition based iterative methods for nonlinear elliptic finite element problems

Energy Technology Data Exchange (ETDEWEB)

Cai, X.C. [Univ. of Colorado, Boulder, CO (United States)

1994-12-31

The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.

The sensitivity of biological finite element models to the resolution of surface geometry: a case study of crocodilian crania

Directory of Open Access Journals (Sweden)

Matthew R. McCurry

2015-06-01

Full Text Available The reliability of finite element analysis (FEA in biomechanical investigations depends upon understanding the influence of model assumptions. In producing finite element models, surface mesh resolution is influenced by the resolution of input geometry, and influences the resolution of the ensuing solid mesh used for numerical analysis. Despite a large number of studies incorporating sensitivity studies of the effects of solid mesh resolution there has not yet been any investigation into the effect of surface mesh resolution upon results in a comparative context. Here we use a dataset of crocodile crania to examine the effects of surface resolution on FEA results in a comparative context. Seven high-resolution surface meshes were each down-sampled to varying degrees while keeping the resulting number of solid elements constant. These models were then subjected to bite and shake load cases using finite element analysis. The results show that incremental decreases in surface resolution can result in fluctuations in strain magnitudes, but that it is possible to obtain stable results using lower resolution surface in a comparative FEA study. As surface mesh resolution links input geometry with the resulting solid mesh, the implication of these results is that low resolution input geometry and solid meshes may provide valid results in a comparative context.

A particle finite element method for machining simulations

Science.gov (United States)

Sabel, Matthias; Sator, Christian; Müller, Ralf

2014-07-01

The particle finite element method (PFEM) appears to be a convenient technique for machining simulations, since the geometry and topology of the problem can undergo severe changes. In this work, a short outline of the PFEM-algorithm is given, which is followed by a detailed description of the involved operations. The -shape method, which is used to track the topology, is explained and tested by a simple example. Also the kinematics and a suitable finite element formulation are introduced. To validate the method simple settings without topological changes are considered and compared to the standard finite element method for large deformations. To examine the performance of the method, when dealing with separating material, a tensile loading is applied to a notched plate. This investigation includes a numerical analysis of the different meshing parameters, and the numerical convergence is studied. With regard to the cutting simulation it is found that only a sufficiently large number of particles (and thus a rather fine finite element discretisation) leads to converged results of process parameters, such as the cutting force.

Methods for high-resolution anisotropic finite element modeling of the human head: automatic MR white matter anisotropy-adaptive mesh generation.

Science.gov (United States)

Lee, Won Hee; Kim, Tae-Seong

2012-01-01

This study proposes an advanced finite element (FE) head modeling technique through which high-resolution FE meshes adaptive to the degree of tissue anisotropy can be generated. Our adaptive meshing scheme (called wMesh) uses MRI structural information and fractional anisotropy maps derived from diffusion tensors in the FE mesh generation process, optimally reflecting electrical properties of the human brain. We examined the characteristics of the wMeshes through various qualitative and quantitative comparisons to the conventional FE regular-sized meshes that are non-adaptive to the degree of white matter anisotropy. We investigated numerical differences in the FE forward solutions that include the electrical potential and current density generated by current sources in the brain. The quantitative difference was calculated by two statistical measures of relative difference measure (RDM) and magnification factor (MAG). The results show that the wMeshes are adaptive to the anisotropic density of the WM anisotropy, and they better reflect the density and directionality of tissue conductivity anisotropy. Our comparison results between various anisotropic regular mesh and wMesh models show that there are substantial differences in the EEG forward solutions in the brain (up to RDM=0.48 and MAG=0.63 in the electrical potential, and RDM=0.65 and MAG=0.52 in the current density). Our analysis results indicate that the wMeshes produce different forward solutions that are different from the conventional regular meshes. We present some results that the wMesh head modeling approach enhances the sensitivity and accuracy of the FE solutions at the interfaces or in the regions where the anisotropic conductivities change sharply or their directional changes are complex. The fully automatic wMesh generation technique should be useful for modeling an individual-specific and high-resolution anisotropic FE head model incorporating realistic anisotropic conductivity distributions

Stress distributions in finite element analysis of concrete gravity dam ...

African Journals Online (AJOL)

Gravity dams are solid structures built of mass concrete material; they maintain their stability against the design loads from the geometric shape, the mass, and the strength of the concrete. The model was meshed with an 8-node biquadratic plane strain quadrilateral (CPE8R) elements, using ABAQUS, a finite element ...

Numerical solution of multi group-Two dimensional- Adjoint equation with finite element method

International Nuclear Information System (INIS)

Poursalehi, N.; Khalafi, H.; Shahriari, M.; Minoochehr

2008-01-01

Adjoint equation is used for perturbation theory in nuclear reactor design. For numerical solution of adjoint equation, usually two methods are applied. These are Finite Element and Finite Difference procedures. Usually Finite Element Procedure is chosen for solving of adjoint equation, because it is more use able in variety of geometries. In this article, Galerkin Finite Element method is discussed. This method is applied for numerical solving multi group, multi region and two dimensional (X, Y) adjoint equation. Typical reactor geometry is partitioned with triangular meshes and boundary condition for adjoint flux is considered zero. Finally, for a case of defined parameters, Finite Element Code was applied and results were compared with Citation Code

Accuracy of finite-element models for the stress analysis of multiple-holed moderator blocks

International Nuclear Information System (INIS)

Smith, P.D.; Sullivan, R.M.; Lewis, A.C.; Yu, H.J.

1981-01-01

Two steps have been taken to quantify and improve the accuracy in the analysis. First, the limitations of various approximation techniques have been studied with the aid of smaller benchmark problems containing fewer holes. Second, a new family of computer programs has been developed for handling such large problems. This paper describes the accuracy studies and the benchmark problems. A review is given of some proposed modeling techniques including local mesh refinement, homogenization, a special-purpose finite element, and substructuring. Some limitations of these approaches are discussed. The new finite element programs and the features that contribute to their efficiency are discussed. These include a standard architecture for out-of-core data processing and an equation solver that operates on a peripheral array processor. The central conclusions of the paper are: (1) modeling approximation methods such as local mesh refinement and homogenization tend to be unreliable, and they should be justified by a fine mesh benchmark analysis; and (2) finite element codes are now available that can achieve accurate solutions at a reasonable cost, and there is no longer a need to employ modeling approximations in the two-dimensional analysis of HTGR fuel elements. 10 figures

The finite element response Matrix method

International Nuclear Information System (INIS)

Nakata, H.; Martin, W.R.

1983-01-01

A new method for global reactor core calculations is described. This method is based on a unique formulation of the response matrix method, implemented with a higher order finite element method. The unique aspects of this approach are twofold. First, there are two levels to the overall calculational scheme: the local or assembly level and the global or core level. Second, the response matrix scheme, which is formulated at both levels, consists of two separate response matrices rather than one response matrix as is generally the case. These separate response matrices are seen to be quite beneficial for the criticality eigenvalue calculation, because they are independent of k /SUB eff/. The response matrices are generated from a Galerkin finite element solution to the weak form of the diffusion equation, subject to an arbitrary incoming current and an arbitrary distributed source. Calculational results are reported for two test problems, the two-dimensional International Atomic Energy Agency benchmark problem and a two-dimensional pressurized water reactor test problem (Biblis reactor), and they compare well with standard coarse mesh methods with respect to accuracy and efficiency. Moreover, the accuracy (and capability) is comparable to fine mesh for a fraction of the computational cost. Extension of the method to treat heterogeneous assemblies and spatial depletion effects is discussed

Application of hexagonal element scheme in finite element method to three-dimensional diffusion problem of fast reactors

International Nuclear Information System (INIS)

Ishiguro, Misako; Higuchi, Kenji

1983-01-01

The finite element method is applied in Galerkin-type approximation to three-dimensional neutron diffusion equations of fast reactors. A hexagonal element scheme is adopted for treating the hexagonal lattice which is typical for fast reactors. The validity of the scheme is verified by applying the scheme as well as alternative schemes to the neutron diffusion calculation of a gas-cooled fast reactor of actual scale. The computed results are compared with corresponding values obtained using the currently applied triangular-element and also with conventional finite difference schemes. The hexagonal finite element scheme is found to yield a reasonable solution to the problem taken up here, with some merit in terms of saving in computing time, but the resulting multiplication factor differs by 1% and the flux by 9% compared with the triangular mesh finite difference scheme. The finite element method, even in triangular element scheme, would appear to incur error in inadmissible amount and which could not be easily eliminated by refining the nodes. (author)

Solving the Einstein constraint equations on multi-block triangulations using finite element methods

Energy Technology Data Exchange (ETDEWEB)

Korobkin, Oleg; Pazos, Enrique [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803 (United States); Aksoylu, Burak [Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803 (United States); Holst, Michael [Department of Mathematics, University of California at San Diego 9500 Gilman Drive La Jolla, CA 92093-0112 (United States); Tiglio, Manuel [Department of Physics, University of Maryland, College Park, MD 20742 (United States)

2009-07-21

In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these equations on three-dimensional multi-block domains using finite element methods. We illustrate our approach on a simple example of Brill wave initial data, with the constraints reducing to a single linear elliptic equation for the conformal factor psi. We use quadratic Lagrange elements on semi-structured simplicial meshes, obtained by triangulation of multi-block grids. In the case of uniform refinement the scheme is superconvergent at most mesh vertices, due to local symmetry of the finite element basis with respect to local spatial inversions. We show that in the superconvergent case subsequent unstructured mesh refinements do not improve the quality of our initial data. As proof of concept that this approach is feasible for generating multi-block initial data in three dimensions, after constructing the initial data we evolve them in time using a high-order finite-differencing multi-block approach and extract the gravitational waves from the numerical solution.

Solving the Einstein constraint equations on multi-block triangulations using finite element methods

International Nuclear Information System (INIS)

Korobkin, Oleg; Pazos, Enrique; Aksoylu, Burak; Holst, Michael; Tiglio, Manuel

2009-01-01

In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these equations on three-dimensional multi-block domains using finite element methods. We illustrate our approach on a simple example of Brill wave initial data, with the constraints reducing to a single linear elliptic equation for the conformal factor ψ. We use quadratic Lagrange elements on semi-structured simplicial meshes, obtained by triangulation of multi-block grids. In the case of uniform refinement the scheme is superconvergent at most mesh vertices, due to local symmetry of the finite element basis with respect to local spatial inversions. We show that in the superconvergent case subsequent unstructured mesh refinements do not improve the quality of our initial data. As proof of concept that this approach is feasible for generating multi-block initial data in three dimensions, after constructing the initial data we evolve them in time using a high-order finite-differencing multi-block approach and extract the gravitational waves from the numerical solution.

A Floating Node Method for the Modelling of Discontinuities Within a Finite Element

Science.gov (United States)

Pinho, Silvestre T.; Chen, B. Y.; DeCarvalho, Nelson V.; Baiz, P. M.; Tay, T. E.

2013-01-01

This paper focuses on the accurate numerical representation of complex networks of evolving discontinuities in solids, with particular emphasis on cracks. The limitation of the standard finite element method (FEM) in approximating discontinuous solutions has motivated the development of re-meshing, smeared crack models, the eXtended Finite Element Method (XFEM) and the Phantom Node Method (PNM). We propose a new method which has some similarities to the PNM, but crucially: (i) does not introduce an error on the crack geometry when mapping to natural coordinates; (ii) does not require numerical integration over only part of a domain; (iii) can incorporate weak discontinuities and cohesive cracks more readily; (iv) is ideally suited for the representation of multiple and complex networks of (weak, strong and cohesive) discontinuities; (v) leads to the same solution as a finite element mesh where the discontinuity is represented explicitly; and (vi) is conceptually simpler than the PNM.

An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics

International Nuclear Information System (INIS)

Kühnlein, Christian; Smolarkiewicz, Piotr K.

2017-01-01

An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-form schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.

An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics

Energy Technology Data Exchange (ETDEWEB)

Kühnlein, Christian, E-mail: christian.kuehnlein@ecmwf.int; Smolarkiewicz, Piotr K., E-mail: piotr.smolarkiewicz@ecmwf.int

2017-04-01

An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-form schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.

A novel hybrid stress-function finite element method immune to severe mesh distortion

International Nuclear Information System (INIS)

Cen Song; Zhou Mingjue; Fu Xiangrong

2010-01-01

This paper introduces a hybrid stress-function finite element method proposed recently for developing 2D finite element models immune to element shapes. Deferent from the first version of the hybrid-stress element constructed by Pian, the stress function φ of 2D elastic or fracture problem is regarded as the functional variable of the complementary energy functional. Then, the basic analytical solutions of φ are taken as the trial functions for finite element models, and meanwhile, the corresponding unknown stress-function constants are introduced. By using the principle of minimum complementary energy, these unknown stress-function constants can be expressed in terms of the displacements along element edges. Finally, the complementary energy functional can be rewritten in terms of element nodal displacement vector, and thus, the element stiffness matrix of such hybrid-function element can be obtained. As examples, two (8- and 12-node) quadrilateral plane elements and an arbitrary polygonal crack element are constructed by employing different basic analytical solutions of different stress functions. Numerical results show that, the 8- and 12-node plane models can produce the exact solutions for pure bending and linear bending problems, respectively, even the element shape degenerates into triangle and concave quadrangle; and the crack element can also predict accurate results with very low computational cost in analysis of stress-singularity problems.

Quasi-automatic 3D finite element model generation for individual single-rooted teeth and periodontal ligament.

Science.gov (United States)

Clement, R; Schneider, J; Brambs, H-J; Wunderlich, A; Geiger, M; Sander, F G

2004-02-01

The paper demonstrates how to generate an individual 3D volume model of a human single-rooted tooth using an automatic workflow. It can be implemented into finite element simulation. In several computational steps, computed tomography data of patients are used to obtain the global coordinates of the tooth's surface. First, the large number of geometric data is processed with several self-developed algorithms for a significant reduction. The most important task is to keep geometrical information of the real tooth. The second main part includes the creation of the volume model for tooth and periodontal ligament (PDL). This is realized with a continuous free form surface of the tooth based on the remaining points. Generating such irregular objects for numerical use in biomechanical research normally requires enormous manual effort and time. The finite element mesh of the tooth, consisting of hexahedral elements, is composed of different materials: dentin, PDL and surrounding alveolar bone. It is capable of simulating tooth movement in a finite element analysis and may give valuable information for a clinical approach without the restrictions of tetrahedral elements. The mesh generator of FE software ANSYS executed the mesh process for hexahedral elements successfully.

FINELM: a multigroup finite element diffusion code. Part II

International Nuclear Information System (INIS)

Davierwalla, D.M.

1981-05-01

The author presents the axisymmetric case in cylindrical coordinates for the finite element multigroup neutron diffusion code, FINELM. The numerical acceleration schemes incorporated viz. the Lebedev extrapolations and the coarse mesh rebalancing, space collapsing, are discussed. A few benchmark computations are presented as validation of the code. (Auth.)

A posteriori estimator and adaptive mesh refinement for finite volume finite element method for monophasic flow and solute transport in porous media

International Nuclear Information System (INIS)

Amor, H.; Bourgeois, M.

2012-01-01

Document available in extended abstract form only. The disposal of high level, long lived waste in deep underground clay formations is investigated by several countries including France. In the safety assessment of such geological repositories, a thoughtful consideration must be given to the mechanisms and possible pathways of migration of radionuclides released from waste packages. However, when modelling the transfer of radionuclides throughout the disposal facilities and geological formations, the numerical simulations must take into consideration, in addition to long durations of concern, the variety in the properties as well as in geometrical scales of the different components of the overall disposal, including the host formation. This task presents significant computational challenges. Numerical methods used in the MELODIE software The MELODIE software is developed by IRSN, and constantly upgraded, with the aim to assess the long-term containment capabilities of underground and surface radioactive waste repositories. The MELODIE software models water flow and the phenomena involved in the transport of radionuclides in saturated and unsaturated porous media in 2 and 3 dimensions; chemical processes are represented by a retardation factor and a solubility limit, for sorption and solubility respectively, integrated in the computational equations. These equations are discretized using a so-called Finite Volume Finite Element method (FVFE), which is based on a Galerkin method to discretize time and variables, together with a Finite Volume method using the Godunov scheme for the convection term. The FVFE method is used to convert partial differential equations into a finite number of algebraic equations that match the number of nodes in the mesh used to model the considered domain. It is also used to stabilise the numerical scheme. In order to manage the variety in properties and geometrical scales of underground disposal components, an a posteriori error estimator

On the development of a three-dimensional finite-element groundwater flow model of the saturated zone, Yucca Mountain, Nevada

International Nuclear Information System (INIS)

Czarnecki, J.B.; Faunt, C.C.; Gable, C.W.; Zyvoloski, G.A.

1996-01-01

Development of a preliminary three-dimensional model of the saturated zone at Yucca Mountain, the potential location for a high-level nuclear waste repository, is presented. The development of the model advances the technology of interfacing: (1)complex three-dimensional hydrogeologic framework modeling; (2) fully three-dimensional, unstructured, finite-element mesh generation; and (3) groundwater flow, heat, and transport simulation. The three-dimensional hydrogeologic framework model is developed using maps, cross sections, and well data. The framework model data are used to feed an automated mesh generator, designed to discretize irregular three-dimensional solids,a nd to assign materials properties from the hydrogeologic framework model to the tetrahedral elements. The mesh generator facilitated the addition of nodes to the finite-element mesh which correspond to the exact three-dimensional position of the potentiometric surface based on water-levels from wells. A ground water flow and heat simulator is run with the resulting finite- element mesh, within a parameter-estimation program. The application of the parameter-estimation program is designed to provide optimal values of permeability and specified fluxes over the model domain to minimize the residual between observed and simulated water levels

FINELM: a multigroup finite element diffusion code

International Nuclear Information System (INIS)

Higgs, C.E.; Davierwalla, D.M.

1981-06-01

FINELM is a FORTRAN IV program to solve the Neutron Diffusion Equation in X-Y, R-Z, R-theta, X-Y-Z and R-theta-Z geometries using the method of Finite Elements. Lagrangian elements of linear or higher degree to approximate the spacial flux distribution have been provided. The method of dissections, coarse mesh rebalancing and Chebyshev acceleration techniques are available. Simple user defined input is achieved through extensive input subroutines. The input preparation is described followed by a program structure description. Sample test cases are provided. (Auth.)

Bessel smoothing filter for spectral-element mesh

Science.gov (United States)

Trinh, P. T.; Brossier, R.; Métivier, L.; Virieux, J.; Wellington, P.

2017-06-01

Smoothing filters are extremely important tools in seismic imaging and inversion, such as for traveltime tomography, migration and waveform inversion. For efficiency, and as they can be used a number of times during inversion, it is important that these filters can easily incorporate prior information on the geological structure of the investigated medium, through variable coherent lengths and orientation. In this study, we promote the use of the Bessel filter to achieve these purposes. Instead of considering the direct application of the filter, we demonstrate that we can rely on the equation associated with its inverse filter, which amounts to the solution of an elliptic partial differential equation. This enhances the efficiency of the filter application, and also its flexibility. We apply this strategy within a spectral-element-based elastic full waveform inversion framework. Taking advantage of this formulation, we apply the Bessel filter by solving the associated partial differential equation directly on the spectral-element mesh through the standard weak formulation. This avoids cumbersome projection operators between the spectral-element mesh and a regular Cartesian grid, or expensive explicit windowed convolution on the finite-element mesh, which is often used for applying smoothing operators. The associated linear system is solved efficiently through a parallel conjugate gradient algorithm, in which the matrix vector product is factorized and highly optimized with vectorized computation. Significant scaling behaviour is obtained when comparing this strategy with the explicit convolution method. The theoretical numerical complexity of this approach increases linearly with the coherent length, whereas a sublinear relationship is observed practically. Numerical illustrations are provided here for schematic examples, and for a more realistic elastic full waveform inversion gradient smoothing on the SEAM II benchmark model. These examples illustrate well the

Final Report of the Project "From the finite element method to the virtual element method"

Energy Technology Data Exchange (ETDEWEB)

Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Gyrya, Vitaliy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2017-12-20

The Finite Element Method (FEM) is a powerful numerical tool that is being used in a large number of engineering applications. The FEM is constructed on triangular/tetrahedral and quadrilateral/hexahedral meshes. Extending the FEM to general polygonal/polyhedral meshes in straightforward way turns out to be extremely difficult and leads to very complex and computationally expensive schemes. The reason for this failure is that the construction of the basis functions on elements with a very general shape is a non-trivial and complex task. In this project we developed a new family of numerical methods, dubbed the Virtual Element Method (VEM) for the numerical approximation of partial differential equations (PDE) of elliptic type suitable to polygonal and polyhedral unstructured meshes. We successfully formulated, implemented and tested these methods and studied both theoretically and numerically their stability, robustness and accuracy for diffusion problems, convection-reaction-diffusion problems, the Stokes equations and the biharmonic equations.

A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

Science.gov (United States)

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.

A Kohn–Sham equation solver based on hexahedral finite elements

International Nuclear Information System (INIS)

Fang Jun; Gao Xingyu; Zhou Aihui

2012-01-01

We design a Kohn–Sham equation solver based on hexahedral finite element discretizations. The solver integrates three schemes proposed in this paper. The first scheme arranges one a priori locally-refined hexahedral mesh with appropriate multiresolution. The second one is a modified mass-lumping procedure which accelerates the diagonalization in the self-consistent field iteration. The third one is a finite element recovery method which enhances the eigenpair approximations with small extra work. We carry out numerical tests on each scheme to investigate the validity and efficiency, and then apply them to calculate the ground state total energies of nanosystems C 60 , C 120 , and C 275 H 172 . It is shown that our solver appears to be computationally attractive for finite element applications in electronic structure study.

Dual-mixed finite elements for the three-field Stokes model as a finite volume method on staggered grids

KAUST Repository

Kou, Jisheng; Sun, Shuyu

2017-01-01

In this paper, a new three-field weak formulation for Stokes problems is developed, and from this, a dual-mixed finite element method is proposed on a rectangular mesh. In the proposed mixed methods, the components of stress tensor are approximated

Mixed finite element - discontinuous finite volume element discretization of a general class of multicontinuum models

Science.gov (United States)

Ruiz-Baier, Ricardo; Lunati, Ivan

2016-10-01

We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation

Application of the finite element method to the neutron transport equation

International Nuclear Information System (INIS)

Martin, W.R.

1976-01-01

This paper examines the theoretical and practical application of the finite element method to the neutron transport equation. It is shown that in principle the system of equations obtained by application of the finite element method can be solved with certain physical restrictions concerning the criticality of the medium. The convergence of this approximate solution to the exact solution with mesh refinement is examined, and a non-optical estimate of the convergence rate is obtained analytically. It is noted that the numerical results indicate a faster convergence rate and several approaches to obtain this result analytically are outlined. The practical application of the finite element method involved the development of a computer code capable of solving the neutron transport equation in 1-D plane geometry. Vacuum, reflecting, or specified incoming boundary conditions may be analyzed, and all are treated as natural boundary conditions. The time-dependent transport equation is also examined and it is shown that the application of the finite element method in conjunction with the Crank-Nicholson time discretization method results in a system of algebraic equations which is readily solved. Numerical results are given for several critical slab eigenvalue problems, including anisotropic scattering, and the results compare extremely well with benchmark results. It is seen that the finite element code is more efficient than a standard discrete ordinates code for certain problems. A problem with severe heterogeneities is considered and it is shown that the use of discontinuous spatial and angular elements results in a marked improvement in the results. Finally, time-dependent problems are examined and it is seen that the phenomenon of angular mode separation makes the numerical treatment of the transport equation in slab geometry a considerable challenge, with the result that the angular mesh has a dominant effect on obtaining acceptable solutions

Extended Finite Element Method with Simplified Spherical Harmonics Approximation for the Forward Model of Optical Molecular Imaging

Directory of Open Access Journals (Sweden)

Wei Li

2012-01-01

Full Text Available An extended finite element method (XFEM for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SPN. In XFEM scheme of SPN equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore, the finite element calculation can be carried out without the time-consuming internal boundary mesh generation. Moreover, the required overly fine mesh conforming to the complex tissue boundary which leads to excess time cost can be avoided. XFEM conveniences its application to tissues with complex internal structure and improves the computational efficiency. Phantom and digital mouse experiments were carried out to validate the efficiency of the proposed method. Compared with standard finite element method and classical Monte Carlo (MC method, the validation results show the merits and potential of the XFEM for optical imaging.

The Fourier-finite-element approximation of the lame equations in axisymmetric domains with edges

International Nuclear Information System (INIS)

Nkemzil, Boniface

2003-10-01

This paper is concerned with a priori error estimates and convergence analysis of the Fourier-finite-element solutions of the Neumann problem for the Lame equations in axisymmetric domains Ω-circumflex is contained in R 3 with reentrant edges. The Fourier-FEM combines the approximating Fourier method with respect to the rotational angle using trigonometric polynomials of degree N (N →∞), with the finite-element method on the plane meridian domain of Ω-circumflex with mesh size h (h → 0) for approximating the Fourier coefficients. The asymptotic behavior of the solution near reentrant edges is described by singular functions in non-tensor product form and treated numerically by means of finite element method on locally graded meshes. For the right-hand side f-circumflex is an element of (L 2 (Ω-circumflex)) 3 , it is proved that the rate of convergence of the combined approximations in the norms of (W 2 1 (Ω-circumflex)) 3 is of the order O(h 2-l +N -(2-l) ) (l=0,1). (author)

Finite element analysis of multilayer coextrusion.

Energy Technology Data Exchange (ETDEWEB)

Hopkins, Matthew Morgan; Schunk, Peter Randall; Baer, Thomas A. (Proctor & Gamble Company, West Chester, OH); Mrozek, Randy A. (Army Research Laboratory, Adelphi, MD); Lenhart, Joseph Ludlow (Army Research Laboratory, Adelphi, MD); Rao, Rekha Ranjana; Collins, Robert (Oak Ridge National Laboratory); Mondy, Lisa Ann

2011-09-01

Multilayer coextrusion has become a popular commercial process for producing complex polymeric products from soda bottles to reflective coatings. A numerical model of a multilayer coextrusion process is developed based on a finite element discretization and two different free-surface methods, an arbitrary-Lagrangian-Eulerian (ALE) moving mesh implementation and an Eulerian level set method, to understand the moving boundary problem associated with the polymer-polymer interface. The goal of this work is to have a numerical capability suitable for optimizing and troubleshooting the coextrusion process, circumventing flow instabilities such as ribbing and barring, and reducing variability in layer thickness. Though these instabilities can be both viscous and elastic in nature, for this work a generalized Newtonian description of the fluid is used. Models of varying degrees of complexity are investigated including stability analysis and direct three-dimensional finite element free surface approaches. The results of this work show how critical modeling can be to reduce build test cycles, improve material choices, and guide mold design.

Comparison of closed-form and finite-element solutions of thick laminated anisotropic rectangular plates

Energy Technology Data Exchange (ETDEWEB)

Reddy, J N; Chao, W C [Virginia Polytechnic Inst. and State Univ., Blacksburg (USA). Dept. of Engineering Science and Mechanics

1981-04-01

In this study the effects of reduced integration, mesh size, and element type (i.e. linear or quadratic) on the accuracy of a penalty-finite element based on the theory governing thick, laminated, anisotropic composite plates are investigated. In order to assess the accuracy of the present finite element, exact closed-form solutions are developed for cross-ply and antisymmetric angle-ply rectangular plates simply supported and subjected to sinusoidally distributed mechanical and/or thermal loadings, and free vibration.

SPIRIT, Plot of Geometry and Results of 2-D Finite Elements Calculation

International Nuclear Information System (INIS)

Lambert, P.

1977-01-01

1 - Nature of the physical problem solved: SPIRIT plots the geometry and the results from a 2-D finite elements calculation. 2 - Method of solution: SPIRIT uses the Benson-Lehner graph plotter. The programme will draw each separate element of the mesh according to the description supplied and a complete picture of the mesh is therefore built up. The program can also construct an isothermal distribution using straight lines. Each line is constructed considering each element in isolation. 3 - Restrictions on the complexity of the problem: The program deals only with bodies entirely contained in the first quadrant and the x-coordinates should be less than 20.0

Anisotropic mesh adaptation for solution of finite element problems using hierarchical edge-based error estimates

Energy Technology Data Exchange (ETDEWEB)

Lipnikov, Konstantin [Los Alamos National Laboratory; Agouzal, Abdellatif [UNIV DE LYON; Vassilevski, Yuri [Los Alamos National Laboratory

2009-01-01

We present a new technology for generating meshes minimizing the interpolation and discretization errors or their gradients. The key element of this methodology is construction of a space metric from edge-based error estimates. For a mesh with N{sub h} triangles, the error is proportional to N{sub h}{sup -1} and the gradient of error is proportional to N{sub h}{sup -1/2} which are optimal asymptotics. The methodology is verified with numerical experiments.

A finite element method for solving the shallow water equations on the sphere

Science.gov (United States)

Comblen, Richard; Legrand, Sébastien; Deleersnijder, Eric; Legat, Vincent

Within the framework of ocean general circulation modeling, the present paper describes an efficient way to discretize partial differential equations on curved surfaces by means of the finite element method on triangular meshes. Our approach benefits from the inherent flexibility of the finite element method. The key idea consists in a dialog between a local coordinate system defined for each element in which integration takes place, and a nodal coordinate system in which all local contributions related to a vectorial degree of freedom are assembled. Since each element of the mesh and each degree of freedom are treated in the same way, the so-called pole singularity issue is fully circumvented. Applied to the shallow water equations expressed in primitive variables, this new approach has been validated against the standard test set defined by [Williamson, D.L., Drake, J.B., Hack, J.J., Jakob, R., Swarztrauber, P.N., 1992. A standard test set for numerical approximations to the shallow water equations in spherical geometry. Journal of Computational Physics 102, 211-224]. Optimal rates of convergence for the P1NC-P1 finite element pair are obtained, for both global and local quantities of interest. Finally, the approach can be extended to three-dimensional thin-layer flows in a straightforward manner.

Finite Element Method for Analysis of Material Properties

DEFF Research Database (Denmark)

Rauhe, Jens Christian

and the finite element method. The material microstructure of the heterogeneous material is non-destructively determined using X-ray microtomography. A software program has been generated which uses the X-ray tomographic data as an input for the mesh generation of the material microstructure. To obtain a proper...... which are used for the determination of the effective properties of the heterogeneous material. Generally, the properties determined using the finite element method coupled with X-ray microtomography are in good agreement with both experimentally determined properties and properties determined using......The use of cellular and composite materials have in recent years become more and more common in all kinds of structural components and accurate knowledge of the effective properties is therefore essential. In this wok the effective properties are determined using the real material microstructure...

Finite element computation of natural convection in enclosures

International Nuclear Information System (INIS)

Kushwaha, H.S.

1982-01-01

Compared to U-V-P-T formulation and stream-vorticity temperature formulation, penalty function formulation is simple and computationally competitive. Incremental New-Raphons method employed in this study is effective and efficient. From this study it is established that very fine mesh is not required for a low Rayleigh number considered in this study. The upwinding finite element may be necessary to avoid oscillations for higher Rayleigh numbers. (author)

Finite element speaker-specific face model generation for the study of speech production.

Science.gov (United States)

Bucki, Marek; Nazari, Mohammad Ali; Payan, Yohan

2010-08-01

In situations where automatic mesh generation is unsuitable, the finite element (FE) mesh registration technique known as mesh-match-and-repair (MMRep) is an interesting option for quickly creating a subject-specific FE model by fitting a predefined template mesh onto the target organ. The irregular or poor quality elements produced by the elastic deformation are corrected by a 'mesh reparation' procedure ensuring that the desired regularity and quality standards are met. Here, we further extend the MMRep capabilities and demonstrate the possibility of taking into account additional relevant anatomical features. We illustrate this approach with an example of biomechanical model generation of a speaker's face comprising face muscle insertions. While taking advantage of the a priori knowledge about tissues conveyed by the template model, this novel, fast and automatic mesh registration technique makes it possible to achieve greater modelling realism by accurately representing the organ surface as well as inner anatomical or functional structures of interest.

An evaluation of a translator for finite element data to resistor/capacitor data for the heat diffusion equation

International Nuclear Information System (INIS)

Manteufel, R.D.; Klein, D.E.; Yoshimura, H.R.

1988-01-01

This paper evaluates a translator for finite element data to resistor/capacitor data (FEM/RC) for the numerical solution of heat diffusion problems. The translator involves the derivation of thermal resistors and capacitors, implicit in the heat balance formulation of the finite difference method. It uses a finite element mesh, which consists of nodes and elements and is implicit in the Galerkin finite element method (GFEM). This hybrid translation method, FEM/RC, has been incorporated in Q/TRAN, a new thermal analysis computer code. This evaluation compares Q/TRAN, HEATING-6, and a research code employing GFEM on a purely mathematical, highly nonlinear steady-state conduction benchmark problem. The evaluation concludes that the FEM/RC technique has numerical characteristics that are consistent with comparable schemes for the benchmark problem. FEM/RC also accurately translates skewed meshes. Because FEM/RC generates resistors and capacitors, it appears to offer a more efficient method than the classical GFEM

Dual-mixed finite elements for the three-field Stokes model as a finite volume method on staggered grids

KAUST Repository

Kou, Jisheng

2017-06-09

In this paper, a new three-field weak formulation for Stokes problems is developed, and from this, a dual-mixed finite element method is proposed on a rectangular mesh. In the proposed mixed methods, the components of stress tensor are approximated by piecewise constant functions or Q1 functions, while the velocity and pressure are discretized by the lowest-order Raviart-Thomas element and the piecewise constant functions, respectively. Using quadrature rules, we demonstrate that this scheme can be reduced into a finite volume method on staggered grid, which is extensively used in computational fluid mechanics and engineering.

Adaptation of an unstructured-mesh, finite-element ocean model to the simulation of ocean circulation beneath ice shelves

Science.gov (United States)

Kimura, Satoshi; Candy, Adam S.; Holland, Paul R.; Piggott, Matthew D.; Jenkins, Adrian

2013-07-01

Several different classes of ocean model are capable of representing floating glacial ice shelves. We describe the incorporation of ice shelves into Fluidity-ICOM, a nonhydrostatic finite-element ocean model with the capacity to utilize meshes that are unstructured and adaptive in three dimensions. This geometric flexibility offers several advantages over previous approaches. The model represents melting and freezing on all ice-shelf surfaces including vertical faces, treats the ice shelf topography as continuous rather than stepped, and does not require any smoothing of the ice topography or any of the additional parameterisations of the ocean mixed layer used in isopycnal or z-coordinate models. The model can also represent a water column that decreases to zero thickness at the 'grounding line', where the floating ice shelf is joined to its tributary ice streams. The model is applied to idealised ice-shelf geometries in order to demonstrate these capabilities. In these simple experiments, arbitrarily coarsening the mesh outside the ice-shelf cavity has little effect on the ice-shelf melt rate, while the mesh resolution within the cavity is found to be highly influential. Smoothing the vertical ice front results in faster flow along the smoothed ice front, allowing greater exchange with the ocean than in simulations with a realistic ice front. A vanishing water-column thickness at the grounding line has little effect in the simulations studied. We also investigate the response of ice shelf basal melting to variations in deep water temperature in the presence of salt stratification.

A parallel finite element method for the analysis of crystalline solids

DEFF Research Database (Denmark)

Sørensen, N.J.; Andersen, B.S.

1996-01-01

A parallel finite element method suitable for the analysis of 3D quasi-static crystal plasticity problems has been developed. The method is based on substructuring of the original mesh into a number of substructures which are treated as isolated finite element models related via the interface...... conditions. The resulting interface equations are solved using a direct solution method. The method shows a good speedup when increasing the number of processors from 1 to 8 and the effective solution of 3D crystal plasticity problems whose size is much too large for a single work station becomes possible....

A Novel Polygonal Finite Element Method: Virtual Node Method

Science.gov (United States)

Tang, X. H.; Zheng, C.; Zhang, J. H.

2010-05-01

Polygonal finite element method (PFEM), which can construct shape functions on polygonal elements, provides greater flexibility in mesh generation. However, the non-polynomial form of traditional PFEM, such as Wachspress method and Mean Value method, leads to inexact numerical integration. Since the integration technique for non-polynomial functions is immature. To overcome this shortcoming, a great number of integration points have to be used to obtain sufficiently exact results, which increases computational cost. In this paper, a novel polygonal finite element method is proposed and called as virtual node method (VNM). The features of present method can be list as: (1) It is a PFEM with polynomial form. Thereby, Hammer integral and Gauss integral can be naturally used to obtain exact numerical integration; (2) Shape functions of VNM satisfy all the requirements of finite element method. To test the performance of VNM, intensive numerical tests are carried out. It found that, in standard patch test, VNM can achieve significantly better results than Wachspress method and Mean Value method. Moreover, it is observed that VNM can achieve better results than triangular 3-node elements in the accuracy test.

Pellet Cladding Mechanical Interaction Modeling Using the Extended Finite Element Method

Energy Technology Data Exchange (ETDEWEB)

Spencer, Benjamin W.; Jiang, Wen; Dolbow, John E.; Peco, Christian

2016-09-01

As a brittle material, the ceramic UO2 used as light water reactor fuel experiences significant fracturing throughout its life, beginning with the first rise to power of fresh fuel. This has multiple effects on the thermal and mechanical response of the fuel/cladding system. One such effect that is particularly important is that when there is mechanical contact between the fuel and cladding, cracks that extending from the outer surface of the fuel into the volume of the fuel cause elevated stresses in the adjacent cladding, which can potentially lead to cladding failure. Modeling the thermal and mechanical response of the cladding in the vicinity of these surface-breaking cracks in the fuel can provide important insights into this behavior to help avoid operating conditions that could lead to cladding failure. Such modeling has traditionally been done in the context of finite-element-based fuel performance analysis by modifying the fuel mesh to introduce discrete cracks. While this approach is effective in capturing the important behavior at the fuel/cladding interface, there are multiple drawbacks to explicitly incorporating the cracks in the finite element mesh. Because the cracks are incorporated in the original mesh, the mesh must be modified for cracks of specified location and depth, so it is difficult to account for crack propagation and the formation of new cracks at other locations. The extended finite element method (XFEM) has emerged in recent years as a powerful method to represent arbitrary, evolving, discrete discontinuities within the context of the finite element method. Development work is underway by the authors to implement XFEM in the BISON fuel performance code, and this capability has previously been demonstrated in simulations of fracture propagation in ceramic nuclear fuel. These preliminary demonstrations have included only the fuel, and excluded the cladding for simplicity. This paper presents initial results of efforts to apply XFEM to

Optimal convergence recovery for the Fourier-finite-element approximation of Maxwell's equations in non-smooth axisymmetric domains

International Nuclear Information System (INIS)

Nkemzi, B.

2005-10-01

Three-dimensional time-harmonic Maxwell's problems in axisymmetric domains Ω-circumflex with edges and conical points on the boundary are treated by means of the Fourier-finite-element method. The Fourier-fem combines the approximating Fourier series expansion of the solution with respect to the rotational angle using trigonometric polynomials of degree N (N → ∞), with the finite element approximation of the Fourier coefficients on the plane meridian domain Ω a is a subset of R + 2 of Ω-circumflex with mesh size h (h → 0). The singular behaviors of the Fourier coefficients near angular points of the domain Ω a are fully described by suitable singular functions and treated numerically by means of the singular function method with the finite element method on graded meshes. It is proved that the rate of convergence of the mixed approximations in H 1 (Ω-circumflex) 3 is of the order O (h+N -1 ) as known for the classical Fourier-finite-element approximation of problems with regular solutions. (author)

A moving mesh finite difference method for equilibrium radiation diffusion equations

Energy Technology Data Exchange (ETDEWEB)

Yang, Xiaobo, E-mail: xwindyb@126.com [Department of Mathematics, College of Science, China University of Mining and Technology, Xuzhou, Jiangsu 221116 (China); Huang, Weizhang, E-mail: whuang@ku.edu [Department of Mathematics, University of Kansas, Lawrence, KS 66045 (United States); Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn [School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen, Fujian 361005 (China)

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.

A moving mesh finite difference method for equilibrium radiation diffusion equations

International Nuclear Information System (INIS)

Yang, Xiaobo; Huang, Weizhang; Qiu, Jianxian

2015-01-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation

Numerical simulation of mechatronic sensors and actuators finite elements for computational multiphysics

CERN Document Server

Kaltenbacher, Manfred

2015-01-01

Like the previous editions also the third edition of this book combines the detailed physical modeling of mechatronic systems and their precise numerical simulation using the Finite Element (FE) method. Thereby, the basic chapter concerning the Finite Element (FE) method is enhanced, provides now also a description of higher order finite elements (both for nodal and edge finite elements) and a detailed discussion of non-conforming mesh techniques. The author enhances and improves many discussions on principles and methods. In particular, more emphasis is put on the description of single fields by adding the flow field. Corresponding to these field, the book is augmented with the new chapter about coupled flow-structural mechanical systems. Thereby, the discussion of computational aeroacoustics is extended towards perturbation approaches, which allows a decomposition of flow and acoustic quantities within the flow region. Last but not least, applications are updated and restructured so that the book meets mode...

QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.

Science.gov (United States)

Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

2014-01-01

We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n -gon, our construction produces 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n ( n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.

Finite-elements modeling of radiant heat transfers between mobile surfaces; Modelisation par elements finis de transferts radiatifs entre surfaces mobiles

Energy Technology Data Exchange (ETDEWEB)

Daurelle, J V; Cadene, V; Occelli, R [Universite de Provence, 13 - Marseille (France)

1997-12-31

In the numerical modeling of thermal industrial problems, radiant heat transfers remain difficult to take into account and require important computer memory and long computing time. These difficulties are enhanced when radiant heat transfers are coupled with finite-elements diffusive heat transfers because finite-elements architecture is complex and requires a lot of memory. In the case of radiant heat transfers along mobile boundaries, the methods must be optimized. The model described in this paper concerns the radiant heat transfers between diffuse grey surfaces. These transfers are coupled with conduction transfers in the limits of the diffusive opaque domain. 2-D and 3-D geometries are analyzed and two configurations of mobile boundaries are considered. In the first configuration, the boundary follows the deformation of the mesh, while in the second, the boundary moves along the fixed mesh. Matter displacement is taken into account in the term of transport of the energy equation, and an appropriate variation of the thermophysical properties of the transition elements between the opaque and transparent media is used. After a description of the introduction of radiative limit conditions in a finite-elements thermal model, the original methods used to optimize calculation time are explained. Two examples of application illustrate the approach used. The first concerns the modeling of radiant heat transfers between fuel rods during a reactor cooling accident, and the second concerns the study of heat transfers inside the air-gap of an electric motor. The method of identification of the mobile surface on the fixed mesh is described. (J.S.) 12 refs.

Finite-elements modeling of radiant heat transfers between mobile surfaces; Modelisation par elements finis de transferts radiatifs entre surfaces mobiles

Energy Technology Data Exchange (ETDEWEB)

Daurelle, J.V.; Cadene, V.; Occelli, R. [Universite de Provence, 13 - Marseille (France)

1996-12-31

In the numerical modeling of thermal industrial problems, radiant heat transfers remain difficult to take into account and require important computer memory and long computing time. These difficulties are enhanced when radiant heat transfers are coupled with finite-elements diffusive heat transfers because finite-elements architecture is complex and requires a lot of memory. In the case of radiant heat transfers along mobile boundaries, the methods must be optimized. The model described in this paper concerns the radiant heat transfers between diffuse grey surfaces. These transfers are coupled with conduction transfers in the limits of the diffusive opaque domain. 2-D and 3-D geometries are analyzed and two configurations of mobile boundaries are considered. In the first configuration, the boundary follows the deformation of the mesh, while in the second, the boundary moves along the fixed mesh. Matter displacement is taken into account in the term of transport of the energy equation, and an appropriate variation of the thermophysical properties of the transition elements between the opaque and transparent media is used. After a description of the introduction of radiative limit conditions in a finite-elements thermal model, the original methods used to optimize calculation time are explained. Two examples of application illustrate the approach used. The first concerns the modeling of radiant heat transfers between fuel rods during a reactor cooling accident, and the second concerns the study of heat transfers inside the air-gap of an electric motor. The method of identification of the mobile surface on the fixed mesh is described. (J.S.) 12 refs.

A high-order multiscale finite-element method for time-domain acoustic-wave modeling

Science.gov (United States)

Gao, Kai; Fu, Shubin; Chung, Eric T.

2018-05-01

Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructs high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss-Lobatto-Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.

Assembly of finite element methods on graphics processors

KAUST Repository

Cecka, Cris

2010-08-23

Recently, graphics processing units (GPUs) have had great success in accelerating many numerical computations. We present their application to computations on unstructured meshes such as those in finite element methods. Multiple approaches in assembling and solving sparse linear systems with NVIDIA GPUs and the Compute Unified Device Architecture (CUDA) are created and analyzed. Multiple strategies for efficient use of global, shared, and local memory, methods to achieve memory coalescing, and optimal choice of parameters are introduced. We find that with appropriate preprocessing and arrangement of support data, the GPU coprocessor using single-precision arithmetic achieves speedups of 30 or more in comparison to a well optimized double-precision single core implementation. We also find that the optimal assembly strategy depends on the order of polynomials used in the finite element discretization. © 2010 John Wiley & Sons, Ltd.

Adaptive Shape Functions and Internal Mesh Adaptation for Modelling Progressive Failure in Adhesively Bonded Joints

Science.gov (United States)

Stapleton, Scott; Gries, Thomas; Waas, Anthony M.; Pineda, Evan J.

2014-01-01

Enhanced finite elements are elements with an embedded analytical solution that can capture detailed local fields, enabling more efficient, mesh independent finite element analysis. The shape functions are determined based on the analytical model rather than prescribed. This method was applied to adhesively bonded joints to model joint behavior with one element through the thickness. This study demonstrates two methods of maintaining the fidelity of such elements during adhesive non-linearity and cracking without increasing the mesh needed for an accurate solution. The first method uses adaptive shape functions, where the shape functions are recalculated at each load step based on the softening of the adhesive. The second method is internal mesh adaption, where cracking of the adhesive within an element is captured by further discretizing the element internally to represent the partially cracked geometry. By keeping mesh adaptations within an element, a finer mesh can be used during the analysis without affecting the global finite element model mesh. Examples are shown which highlight when each method is most effective in reducing the number of elements needed to capture adhesive nonlinearity and cracking. These methods are validated against analogous finite element models utilizing cohesive zone elements.

Soft tissue deformation using a Hierarchical Finite Element Model.

Science.gov (United States)

Faraci, Alessandro; Bello, Fernando; Darzi, Ara

2004-01-01

Simulating soft tissue deformation in real-time has become increasingly important in order to provide a realistic virtual environment for training surgical skills. Several methods have been proposed with the aim of rendering in real-time the mechanical and physiological behaviour of human organs, one of the most popular being Finite Element Method (FEM). In this paper we present a new approach to the solution of the FEM problem introducing the concept of parent and child mesh within the development of a hierarchical FEM. The online selection of the child mesh is presented with the purpose to adapt the mesh hierarchy in real-time. This permits further refinement of the child mesh increasing the detail of the deformation without slowing down the simulation and giving the possibility of integrating force feedback. The results presented demonstrate the application of our proposed framework using a desktop virtual reality (VR) system that incorporates stereo vision with integrated haptics co-location via a desktop Phantom force feedback device.

Accurate evaluation of exchange fields in finite element micromagnetic solvers

Science.gov (United States)

Chang, R.; Escobar, M. A.; Li, S.; Lubarda, M. V.; Lomakin, V.

2012-04-01

Quadratic basis functions (QBFs) are implemented for solving the Landau-Lifshitz-Gilbert equation via the finite element method. This involves the introduction of a set of special testing functions compatible with the QBFs for evaluating the Laplacian operator. The results by using QBFs are significantly more accurate than those via linear basis functions. QBF approach leads to significantly more accurate results than conventionally used approaches based on linear basis functions. Importantly QBFs allow reducing the error of computing the exchange field by increasing the mesh density for structured and unstructured meshes. Numerical examples demonstrate the feasibility of the method.

Error estimates for the Fourier-finite-element approximation of the Lame system in nonsmooth axisymmetric domains

International Nuclear Information System (INIS)

Nkemzi, Boniface

2003-10-01

This paper is concerned with the effective implementation of the Fourier-finite-element method, which combines the approximating Fourier and the finite-element methods, for treating the Derichlet problem for the Lam.6 equations in axisymmetric domains Ω-circumflex is contained in R 3 with conical vertices and reentrant edges. The partial Fourier decomposition reduces the three-dimensional boundary value problem to an infinite sequence of decoupled two-dimensional boundary value problems on the plane meridian domain Ω α is contained in R + 2 of Ω-circumflex with solutions u, n (n = 0,1,2,...) being the Fourier coefficients of the solution u of the 3D problem. The asymptotic behavior of the Fourier coefficients near the angular points of Ω α , is described by appropriate singular vector-functions and treated numerically by linear finite elements on locally graded meshes. For the right-hand side function f-circumflex is an element of (L 2 (Ω-circumflex)) 3 it is proved that with appropriate mesh grading the rate of convergence of the combined approximations in (W 2 1 (Ω-circumflex)) 3 is of the order O(h + N -1 ), where h and N are the parameters of the finite-element and Fourier approximations, respectively, with h → 0 and N → ∞. (author)

A finite element method for netting application to fish cages and fishing gear

CERN Document Server

Priour, Daniel

2014-01-01

This book describes a finite element method for netting that describes the relation between forces and deformation of the netting and takes into account forces due to the twine elasticity, the hydrodynamic forces, the catch effect, the mesh opening stiffness.

An efficient structural finite element for inextensible flexible risers

Science.gov (United States)

Papathanasiou, T. K.; Markolefas, S.; Khazaeinejad, P.; Bahai, H.

2017-12-01

A core part of all numerical models used for flexible riser analysis is the structural component representing the main body of the riser as a slender beam. Loads acting on this structural element are self-weight, buoyant and hydrodynamic forces, internal pressure and others. A structural finite element for an inextensible riser with a point-wise enforcement of the inextensibility constrain is presented. In particular, the inextensibility constraint is applied only at the nodes of the meshed arc length parameter. Among the virtues of the proposed approach is the flexibility in the application of boundary conditions and the easy incorporation of dissipative forces. Several attributes of the proposed finite element scheme are analysed and computation times for the solution of some simplified examples are discussed. Future developments aim at the appropriate implementation of material and geometric parameters for the beam model, i.e. flexural and torsional rigidity.

Formulation of coarse mesh finite difference to calculate mathematical adjoint flux

International Nuclear Information System (INIS)

Pereira, Valmir; Martinez, Aquilino Senra; Silva, Fernando Carvalho da

2002-01-01

The objective of this work is the obtention of the mathematical adjoint flux, having as its support the nodal expansion method (NEM) for coarse mesh problems. Since there are difficulties to evaluate this flux by using NEM. directly, a coarse mesh finite difference program was developed to obtain this adjoint flux. The coarse mesh finite difference formulation (DFMG) adopted uses results of the direct calculation (node average flux and node face averaged currents) obtained by NEM. These quantities (flux and currents) are used to obtain the correction factors which modify the classical finite differences formulation . Since the DFMG formulation is also capable of calculating the direct flux it was also tested to obtain this flux and it was verified that it was able to reproduce with good accuracy both the flux and the currents obtained via NEM. In this way, only matrix transposition is needed to calculate the mathematical adjoint flux. (author)

Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems

KAUST Repository

Cotter, Simon L.; Vejchodský , Tomá š; Erban, Radek

2013-01-01

Stochastic models of chemical systems are often analyzed by solving the corresponding Fokker-Planck equation, which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulation of the underlying chemical system. By observing the stochastic trajectory for a relatively short amount of time, the areas of the state space with nonnegligible probability density are identified. By refining the finite element mesh in these areas, and coarsening elsewhere, a suitable mesh is constructed and used for the computation of the stationary probability density. Numerical examples demonstrate that the presented method is competitive with existing a posteriori methods. © 2013 Society for Industrial and Applied Mathematics.

An object-oriented decomposition of the adaptive-hp finite element method

Energy Technology Data Exchange (ETDEWEB)

Wiley, J.C.

1994-12-13

Adaptive-hp methods are those which use a refinement control strategy driven by a local error estimate to locally modify the element size, h, and polynomial order, p. The result is an unstructured mesh in which each node may be associated with a different polynomial order and which generally require complex data structures to implement. Object-oriented design strategies and languages which support them, e.g., C++, help control the complexity of these methods. Here an overview of the major classes and class structure of an adaptive-hp finite element code is described. The essential finite element structure is described in terms of four areas of computation each with its own dynamic characteristics. Implications of converting the code for a distributed-memory parallel environment are also discussed.

Analysis of dynamic meshing characteristic of planetary gear transmission in wind power increasing gearbox

Directory of Open Access Journals (Sweden)

Wang Jungang

2017-01-01

Full Text Available Dynamic behavior of planetary gear’s tooth contact surface in the different location can better conform operation condition comparing to the general gear pair. Nonlinear finite element algorithm was derived according to the basic control equation of contact dynamics. A finite element model of planetary gear transmission in wind power increasing gearbox was proposed considering different meshing locations based on nonlinear finite element solution. The characteristics of stress distribution at different meshing positions were analyzed. A simulation of the meshing process was conducted using finite element analysis. It was shown that node stresses of external meshing planetary gear varied significantly at different position. The analysis provides some useful insights into the performance of planetary gear’s tooth contact surface.

Finite element approximations of the stokes flow problem based upon various variational principles

International Nuclear Information System (INIS)

Franca, L.P.; Hughers, T.J.R.; Stenberg, R.

1989-05-01

Finite element methods are constructed by adding to the usual Galerkin method terms that are mesh-dependent least-squares forms of the Euler-Lagrange equations. The methods are consistent and possess additional stability compared to the Galerkin method. Finite element interpolations, which are unstable in the Galerkin approach, are now convergent. The methodology is applied to the velocity-pressure formulation, a.k.a., Herrmann's formulation, to the stress-velocity formulation, a.k.a., Hellinger-Reissner's formulation and to a new formulation based on augmented stress, pressure and velocity [pt

Goal-Oriented Self-Adaptive hp Finite Element Simulation of 3D DC Borehole Resistivity Simulations

KAUST Repository

Calo, Victor M.; Pardo, David; Paszyński, Maciej R.

2011-01-01

(adjusting polynomial orders of approximation) or hp (both) refinements on the finite elements. The new parallel implementation utilizes a computational mesh shared between multiple processors. All computational algorithms, including automatic hp goal

Finite Element Method Based Modeling of Resistance Spot-Welded Mild Steel

Directory of Open Access Journals (Sweden)

Miloud Zaoui

Full Text Available Abstract This paper deals with Finite Element refined and simplified models of a mild steel spot-welded specimen, developed and validated based on quasi-static cross-tensile experimental tests. The first model was constructed with a fine discretization of the metal sheet and the spot weld was defined as a special geometric zone of the specimen. This model provided, in combination with experimental tests, the input data for the development of the second model, which was constructed with respect to the mesh size used in the complete car finite element model. This simplified model was developed with coarse shell elements and a spring-type beam element was used to model the spot weld behavior. The global accuracy of the two models was checked by comparing simulated and experimental load-displacement curves and by studying the specimen deformed shapes and the plastic deformation growth in the metal sheets. The obtained results show that both fine and coarse finite element models permit a good prediction of the experimental tests.

Three-dimensional parallel edge-based finite element modeling of electromagnetic data with field redatuming

DEFF Research Database (Denmark)

Cai, Hongzhu; Čuma, Martin; Zhdanov, Michael

2015-01-01

This paper presents a parallelized version of the edge-based finite element method with a novel post-processing approach for numerical modeling of an electromagnetic field in complex media. The method uses an unstructured tetrahedral mesh which can reduce the number of degrees of freedom signific......This paper presents a parallelized version of the edge-based finite element method with a novel post-processing approach for numerical modeling of an electromagnetic field in complex media. The method uses an unstructured tetrahedral mesh which can reduce the number of degrees of freedom...... significantly. The linear system of finite element equations is solved using parallel direct solvers which are robust for ill-conditioned systems and efficient for multiple source electromagnetic (EM) modeling. We also introduce a novel approach to compute the scalar components of the electric field from...... the tangential components along each edge based on field redatuming. The method can produce a more accurate result as compared to conventional approach. We have applied the developed algorithm to compute the EM response for a typical 3D anisotropic geoelectrical model of the off-shore HC reservoir with complex...

Introduction to assembly of finite element methods on graphics processors

International Nuclear Information System (INIS)

Cecka, Cristopher; Lew, Adrian; Darve, Eric

2010-01-01

Recently, graphics processing units (GPUs) have had great success in accelerating numerical computations. We present their application to computations on unstructured meshes such as those in finite element methods. Multiple approaches in assembling and solving sparse linear systems with NVIDIA GPUs and the Compute Unified Device Architecture (CUDA) are presented and discussed. Multiple strategies for efficient use of global, shared, and local memory, methods to achieve memory coalescing, and optimal choice of parameters are introduced. We find that with appropriate preprocessing and arrangement of support data, the GPU coprocessor achieves speedups of 30x or more in comparison to a well optimized serial implementation on the CPU. We also find that the optimal assembly strategy depends on the order of polynomials used in the finite-element discretization.

Modeling hemodynamics in intracranial aneurysms: Comparing accuracy of CFD solvers based on finite element and finite volume schemes.

Science.gov (United States)

Botti, Lorenzo; Paliwal, Nikhil; Conti, Pierangelo; Antiga, Luca; Meng, Hui

2018-06-01

Image-based computational fluid dynamics (CFD) has shown potential to aid in the clinical management of intracranial aneurysms (IAs) but its adoption in the clinical practice has been missing, partially due to lack of accuracy assessment and sensitivity analysis. To numerically solve the flow-governing equations CFD solvers generally rely on two spatial discretization schemes: Finite Volume (FV) and Finite Element (FE). Since increasingly accurate numerical solutions are obtained by different means, accuracies and computational costs of FV and FE formulations cannot be compared directly. To this end, in this study we benchmark two representative CFD solvers in simulating flow in a patient-specific IA model: (1) ANSYS Fluent, a commercial FV-based solver and (2) VMTKLab multidGetto, a discontinuous Galerkin (dG) FE-based solver. The FV solver's accuracy is improved by increasing the spatial mesh resolution (134k, 1.1m, 8.6m and 68.5m tetrahedral element meshes). The dGFE solver accuracy is increased by increasing the degree of polynomials (first, second, third and fourth degree) on the base 134k tetrahedral element mesh. Solutions from best FV and dGFE approximations are used as baseline for error quantification. On average, velocity errors for second-best approximations are approximately 1cm/s for a [0,125]cm/s velocity magnitude field. Results show that high-order dGFE provide better accuracy per degree of freedom but worse accuracy per Jacobian non-zero entry as compared to FV. Cross-comparison of velocity errors demonstrates asymptotic convergence of both solvers to the same numerical solution. Nevertheless, the discrepancy between under-resolved velocity fields suggests that mesh independence is reached following different paths. This article is protected by copyright. All rights reserved.

Finite element modeling of TFTR poloidal field coils

International Nuclear Information System (INIS)

Baumgartner, J.A.; O'Toole, J.A.

1986-01-01

The Tokamak Fusion Test Reactor (TFTR) Poloidal Field (PF) coils were originally analyzed to TFTR design conditions. The coils have been reanalyzed by PPPL and Grumman to determine operating limits under as-built conditions. Critical stress levels, based upon data obtained from the reanalysis of each PF coil, are needed for input to the TFTR simulation code algorithms. The primary objective regarding structural integrity has been to ascertain the magnitude and location of critical internal stresses in each PF coil due to various combinations of electromagnetic and thermally induced loads. For each PF coil, a global finite element model (FEM) of a coil sector is being analyzed to obtain the basic coil internal loads and displacements. Subsequent fine mesh local models of the coil lead stem and lead spur regions produce the magnitudes and locations of peak stresses. Each copper turn and its surrounding insulation are modeled using solid finite elements. The corresponding electromagnetic and thermal analyses are similarly modeled. A series of test beams were developed to determine the best combination of MSC/NASTRAN-type finite elements for use in PF coil analysis. The results of this analysis compare favorably with those obtained by the earlier analysis which was limited in scope

TAURUS, Post-processor of 3-D Finite Elements Plots

International Nuclear Information System (INIS)

Brown, B.E.; Hallquist, J.O.; Kennedy, T.

2002-01-01

Description of program or function: TAURUS reads the binary plot files generated by the LLNL three-dimensional finite element analysis codes, NIKE3D (NESC 9725), DYNA3D (NESC 9909), TACO3D (NESC 9838), TOPAZ3D (NESC9599) and GEMINI and plots contours, time histories, and deformed shapes. Contours of a large number of quantities may be plotted on meshes consisting of plate, shell, and solid type elements. TAURUS can compute a variety of strain measures, reaction forces along constrained boundaries, and momentum. TAURUS has three phases: initialization, geometry display with contouring, and time history processing

Finite Element Analysis of a Four-Cylinder Four Stroke Gasoline Engine Crankshaft

Directory of Open Access Journals (Sweden)

Parman Setyamartana

2014-07-01

Full Text Available Stress analysis of a crankshaft using traditional method is complicated and needs modification by considering its stress concentration factors. To solve this problem, the crankshaft strength of a four-cylinder four stroke gasoline engine is modeled and analyzed using finite element method (FEM in this paper. For this purpose, the crankshaft is modeled using CATIA software in detail. Then, the model is imported in ANSYS. In the recent software, the model is meshed into a number of finite elements. After defining the boundary and loading conditions, the stresses occur in the crankshaft are analyzed in order to identify critical locations on it.

A parallel direct solver for the self-adaptive hp Finite Element Method

KAUST Repository

Paszyński, Maciej R.

2010-03-01

In this paper we present a new parallel multi-frontal direct solver, dedicated for the hp Finite Element Method (hp-FEM). The self-adaptive hp-FEM generates in a fully automatic mode, a sequence of hp-meshes delivering exponential convergence of the error with respect to the number of degrees of freedom (d.o.f.) as well as the CPU time, by performing a sequence of hp refinements starting from an arbitrary initial mesh. The solver constructs an initial elimination tree for an arbitrary initial mesh, and expands the elimination tree each time the mesh is refined. This allows us to keep track of the order of elimination for the solver. The solver also minimizes the memory usage, by de-allocating partial LU factorizations computed during the elimination stage of the solver, and recomputes them for the backward substitution stage, by utilizing only about 10% of the computational time necessary for the original computations. The solver has been tested on 3D Direct Current (DC) borehole resistivity measurement simulations problems. We measure the execution time and memory usage of the solver over a large regular mesh with 1.5 million degrees of freedom as well as on the highly non-regular mesh, generated by the self-adaptive h p-FEM, with finite elements of various sizes and polynomial orders of approximation varying from p = 1 to p = 9. From the presented experiments it follows that the parallel solver scales well up to the maximum number of utilized processors. The limit for the solver scalability is the maximum sequential part of the algorithm: the computations of the partial LU factorizations over the longest path, coming from the root of the elimination tree down to the deepest leaf. © 2009 Elsevier Inc. All rights reserved.

Modeling deformation and chaining of flexible shells in a nematic solvent with finite elements on an adaptive moving mesh

Science.gov (United States)

DeBenedictis, Andrew; Atherton, Timothy J.; Rodarte, Andrea L.; Hirst, Linda S.

2018-03-01

A micrometer-scale elastic shell immersed in a nematic liquid crystal may be deformed by the host if the cost of deformation is comparable to the cost of elastic deformation of the nematic. Moreover, such inclusions interact and form chains due to quadrupolar distortions induced in the host. A continuum theory model using finite elements is developed for this system, using mesh regularization and dynamic refinement to ensure quality of the numerical representation even for large deformations. From this model, we determine the influence of the shell elasticity, nematic elasticity, and anchoring condition on the shape of the shell and hence extract parameter values from an experimental realization. Extending the model to multibody interactions, we predict the alignment angle of the chain with respect to the host nematic as a function of aspect ratio, which is found to be in excellent agreement with experiments.

An h-adaptive finite element solver for the calculations of the electronic structures

International Nuclear Information System (INIS)

Bao Gang; Hu Guanghui; Liu Di

2012-01-01

In this paper, a framework of using h-adaptive finite element method for the Kohn–Sham equation on the tetrahedron mesh is presented. The Kohn–Sham equation is discretized by the finite element method, and the h-adaptive technique is adopted to optimize the accuracy and the efficiency of the algorithm. The locally optimal block preconditioned conjugate gradient method is employed for solving the generalized eigenvalue problem, and an algebraic multigrid preconditioner is used to accelerate the solver. A variety of numerical experiments demonstrate the effectiveness of our algorithm for both the all-electron and the pseudo-potential calculations.

Computational error estimates for Monte Carlo finite element approximation with log normal diffusion coefficients

KAUST Repository

Sandberg, Mattias

2015-01-01

log normal diffusion coefficients with H¨older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible

Straightened cervical lordosis causes stress concentration: a finite element model study

Energy Technology Data Exchange (ETDEWEB)

Wei, Wei; Shi, Shiyuan; Fei, Jun; Wang, Yifan; Chen, Chunyue [Hangzhou Red Cross Hospital, Hangzhou, Zhejiang, (China); Liao, Shenhui [School of Information Science and Engineering, Central South University, Changsha, Hunan (China)

2013-03-15

In this study, we propose a finite element analysis of the complete cervical spine with straightened and normal physiological curvature by using a specially designed modelling system. An accurate finite element model is established to recommend plausible approaches to treatment of cervical spondylosis through the finite element analysis results. There are few reports of biomechanics influence of the straightened cervical curve. It is difficult to measure internal responses of cervical spine directly. However, the finite element method has been reported to have the capability to quantify both external and internal responses to mechanical loading, such as the strain and stress distribution of spinal components. We choose a subject with a straightened cervical spine from whom to collect the CT scan data, which formed the basis of the finite element analysis. By using a specially designed modelling system, a high quality finite element model of the complete cervical spine with straightened curvature was generated, which was then mapped to reconstruct a normal physiological curvature model by a volumetric mesh deformation method based on discrete differential properties. Then, the same boundary conditions were applied to do a comparison. The result demonstrated that the active movement range of straightened cervical spine decreased by 24–33 %, but the stress increased by 5–95 %. The stress was concentrated at the facet joint cartilage, uncovertebral joint and the disk. The results suggest that cervical lordosis may have a direct impact on cervical spondylosis treatment. These results may be useful for clinical treatment of cervical spondylosis with straightened curvature.

Straightened cervical lordosis causes stress concentration: a finite element model study

International Nuclear Information System (INIS)

Wei, Wei; Shi, Shiyuan; Fei, Jun; Wang, Yifan; Chen, Chunyue; Liao, Shenhui

2013-01-01

In this study, we propose a finite element analysis of the complete cervical spine with straightened and normal physiological curvature by using a specially designed modelling system. An accurate finite element model is established to recommend plausible approaches to treatment of cervical spondylosis through the finite element analysis results. There are few reports of biomechanics influence of the straightened cervical curve. It is difficult to measure internal responses of cervical spine directly. However, the finite element method has been reported to have the capability to quantify both external and internal responses to mechanical loading, such as the strain and stress distribution of spinal components. We choose a subject with a straightened cervical spine from whom to collect the CT scan data, which formed the basis of the finite element analysis. By using a specially designed modelling system, a high quality finite element model of the complete cervical spine with straightened curvature was generated, which was then mapped to reconstruct a normal physiological curvature model by a volumetric mesh deformation method based on discrete differential properties. Then, the same boundary conditions were applied to do a comparison. The result demonstrated that the active movement range of straightened cervical spine decreased by 24–33 %, but the stress increased by 5–95 %. The stress was concentrated at the facet joint cartilage, uncovertebral joint and the disk. The results suggest that cervical lordosis may have a direct impact on cervical spondylosis treatment. These results may be useful for clinical treatment of cervical spondylosis with straightened curvature.

Solid Modeling and Finite Element Analysis of an Overhead Crane Bridge

Directory of Open Access Journals (Sweden)

C. Alkin

2005-01-01

Full Text Available The design of an overhead crane bridge with a double box girder has been investigated and a case study of a crane with 35 ton capacity and 13 m span length has been conducted. In the initial phase of the case study, conventional design calculations proposed by F. E. M. Rules and DIN standards were performed to verify the stress and deflection levels. The crane design was modeled using both solids and surfaces. Finite element meshes with 4-node tetrahedral and 4-node quadrilateral shell elements were generated from the solid and shell models, respectively. After a comparison of the finite element analyses, the conventional calculations and performance of the existing crane, the analysis with quadratic shell elements was found to give the most realistic results. As a result of this study, a design optimization method for an overhead crane is proposed. 

Finite element method for computational fluid dynamics with any type of elements; Finite Element Methode zur numerischen Stroemungsberechnung mit beliebigen Elementen

Energy Technology Data Exchange (ETDEWEB)

Steibler, P.

2000-07-01

The unsteady, turbulent flow is to be calculated in a complex geometry. For this purpose a stabilized finite element formulation in which the same functions for velocity and pressure are used is developed. Thus the process remains independent of the type of elements. This simplifies the application. Above all, it is easier to deal with the boundary conditions. The independency from the elements is also achieved by the extended uzawa-algorithm which uses quadratic functions for velocity and an element-constant pressure. This method is also programmed. In order to produce the unstructured grids, an algorithm is implemented which produces meshes consisting of triangular and tetrahedral elements with flow-dependent adaptation. With standard geometries both calculation methods are compared with results. Finally the flow in a draft tube of a Kaplan turbine is calculated and compared with results from model tests. (orig.) [German] Die instationaere, turbulente Stroemung in einer komplexen Geometrie soll berechnet werden. Dazu wird eine Stabilisierte Finite Element Formulierung entwickelt, bei der die gleichen Ansatzfunktionen fuer Geschwindigkeiten und Druck verwendet werden. Das Verfahren wird damit unabhaengig von der Form der Elemente. Dies vereinfacht die Anwendung. Vor allem wird der Umgang mit den Randbedingungen erleichert. Die Elementunabhaengigkeit erreicht man auch mit dem erweiterten Uzawa-Algorithmus, welcher quadratische Ansatzfunktionen fuer die Geschwindigkeiten und elementweisen konstanten Druck verwendet. Dieses Verfahren wird ebenso implementiert. Zur Erstellung der unstrukturierten Gitter wird ein Algorithmus erzeugt, der Netze aus Dreiecks- und Tetraederelementen erstellt, welche stroemungsabhaengige Groessen besitzen koennen. Anhand einiger Standardgeometrien werden die beiden Berechnungsmethoden mit Ergebnissen aus der Literatur verglichen. Als praxisrelevantes Beispiel wird abschliessend die Stroemung in einem Saugrohr einer Kaplanturbine berechnet

Image-Based Geometric Modeling and Mesh Generation

CERN Document Server

2013-01-01

As a new interdisciplinary research area, “image-based geometric modeling and mesh generation” integrates image processing, geometric modeling and mesh generation with finite element method (FEM) to solve problems in computational biomedicine, materials sciences and engineering. It is well known that FEM is currently well-developed and efficient, but mesh generation for complex geometries (e.g., the human body) still takes about 80% of the total analysis time and is the major obstacle to reduce the total computation time. It is mainly because none of the traditional approaches is sufficient to effectively construct finite element meshes for arbitrarily complicated domains, and generally a great deal of manual interaction is involved in mesh generation. This contributed volume, the first for such an interdisciplinary topic, collects the latest research by experts in this area. These papers cover a broad range of topics, including medical imaging, image alignment and segmentation, image-to-mesh conversion,...

Accelerated finite element elastodynamic simulations using the GPU

Energy Technology Data Exchange (ETDEWEB)

Huthwaite, Peter, E-mail: p.huthwaite@imperial.ac.uk

2014-01-15

An approach is developed to perform explicit time domain finite element simulations of elastodynamic problems on the graphical processing unit, using Nvidia's CUDA. Of critical importance for this problem is the arrangement of nodes in memory, allowing data to be loaded efficiently and minimising communication between the independently executed blocks of threads. The initial stage of memory arrangement is partitioning the mesh; both a well established ‘greedy’ partitioner and a new, more efficient ‘aligned’ partitioner are investigated. A method is then developed to efficiently arrange the memory within each partition. The software is applied to three models from the fields of non-destructive testing, vibrations and geophysics, demonstrating a memory bandwidth of very close to the card's maximum, reflecting the bandwidth-limited nature of the algorithm. Comparison with Abaqus, a widely used commercial CPU equivalent, validated the accuracy of the results and demonstrated a speed improvement of around two orders of magnitude. A software package, Pogo, incorporating these developments, is released open source, downloadable from (http://www.pogo-fea.com/) to benefit the community. -- Highlights: •A novel memory arrangement approach is discussed for finite elements on the GPU. •The mesh is partitioned then nodes are arranged efficiently within each partition. •Models from ultrasonics, vibrations and geophysics are run. •The code is significantly faster than an equivalent commercial CPU package. •Pogo, the new software package, is released open source.

Accelerated finite element elastodynamic simulations using the GPU

International Nuclear Information System (INIS)

Huthwaite, Peter

2014-01-01

An approach is developed to perform explicit time domain finite element simulations of elastodynamic problems on the graphical processing unit, using Nvidia's CUDA. Of critical importance for this problem is the arrangement of nodes in memory, allowing data to be loaded efficiently and minimising communication between the independently executed blocks of threads. The initial stage of memory arrangement is partitioning the mesh; both a well established ‘greedy’ partitioner and a new, more efficient ‘aligned’ partitioner are investigated. A method is then developed to efficiently arrange the memory within each partition. The software is applied to three models from the fields of non-destructive testing, vibrations and geophysics, demonstrating a memory bandwidth of very close to the card's maximum, reflecting the bandwidth-limited nature of the algorithm. Comparison with Abaqus, a widely used commercial CPU equivalent, validated the accuracy of the results and demonstrated a speed improvement of around two orders of magnitude. A software package, Pogo, incorporating these developments, is released open source, downloadable from (http://www.pogo-fea.com/) to benefit the community. -- Highlights: •A novel memory arrangement approach is discussed for finite elements on the GPU. •The mesh is partitioned then nodes are arranged efficiently within each partition. •Models from ultrasonics, vibrations and geophysics are run. •The code is significantly faster than an equivalent commercial CPU package. •Pogo, the new software package, is released open source

hp-version discontinuous Galerkin methods on polygonal and polyhedral meshes

CERN Document Server

Cangiani, Andrea; Georgoulis, Emmanuil H; Houston, Paul

2017-01-01

Over the last few decades discontinuous Galerkin finite element methods (DGFEMs) have been witnessed tremendous interest as a computational framework for the numerical solution of partial differential equations. Their success is due to their extreme versatility in the design of the underlying meshes and local basis functions, while retaining key features of both (classical) finite element and finite volume methods. Somewhat surprisingly, DGFEMs on general tessellations consisting of polygonal (in 2D) or polyhedral (in 3D) element shapes have received little attention within the literature, despite the potential computational advantages. This volume introduces the basic principles of hp-version (i.e., locally varying mesh-size and polynomial order) DGFEMs over meshes consisting of polygonal or polyhedral element shapes, presents their error analysis, and includes an extensive collection of numerical experiments. The extreme flexibility provided by the locally variable elemen t-shapes, element-sizes, and elemen...

Analysis of cracked pressure vessel nozzles by finite elements

International Nuclear Information System (INIS)

Reynen, J.

1975-01-01

The paper describes various algorithms, their computer implementations and relative merits to define in an effective way strain energy release rates along the tip front of arbitrary 3D cracks under arbitrary load including thermal strains. These techniques are basically equivalent to substructuring techniques and consequently they can be implemented to any FEM program able to deal with the data handling problems of the substructuring technique. Special finite elements with a built-in stress-singularity are not necessary although their use contributes to accuracy and the mesh can be coarser. Examples are given carried out with a substructure version of the BERSAFE system. These examples include a corner crack in a pressure vessel nozzle loaded by internal pressure and by thermal stresses. Although not of any fundamental importance, in practice the difficulties consist in generating an appropriate mesh to represent the crack front. For the example of the corner crack in a nozzle the problem has been solved by developing a special purpose mesh generation program (EURCRACK)

High Order Finite Element Method for the Lambda modes problem on hexagonal geometry

International Nuclear Information System (INIS)

Gonzalez-Pintor, S.; Ginestar, D.; Verdu, G.

2009-01-01

A High Order Finite Element Method to approximate the Lambda modes problem for reactors with hexagonal geometry has been developed. This method is based on the expansion of the neutron flux in terms of the modified Dubiner's polynomials on a triangular mesh. This mesh is fixed and the accuracy of the method is improved increasing the degree of the polynomial expansions without the necessity of remeshing. The performance of method has been tested obtaining the dominant Lambda modes of different 2D reactor benchmark problems.

Finite Element Analysis of the Propagation of Acoustic Waves Along Waveguides Immersed in Water

Science.gov (United States)

Hladky-Hennion, A.-C.; Langlet, P.; de Billy, M.

1997-03-01

The finite element approach has previously been used, with the help of the ATILA code, to model the propagation of acoustic waves in waveguides [A.-C. Hladky-Hennion, Journal of Sound and Vibration, 194,119-136 (1996)]. In this paper an extension of the technique to the analysis of the propagation of acoustic waves in immersed waveguides is presented. In the proposed approach, the problem is reduced to a bidimensional problem, in which only the cross-section of the guide and the surrounding fluid domain are meshed by using finite elements. Then, wedges the top angles of which vary, are studied and the finite element results of the wedge wave speed are compared with experimental results. Finally, the conclusion indicates a way to extend this approach to waveguides of any cross-section.

High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics [High Order Curvilinear Finite Elements for Lagrangian Hydrodynamics

Energy Technology Data Exchange (ETDEWEB)

Dobrev, Veselin A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kolev, Tzanio V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rieben, Robert N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2012-09-20

The numerical approximation of the Euler equations of gas dynamics in a movingLagrangian frame is at the heart of many multiphysics simulation algorithms. Here, we present a general framework for high-order Lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements. This method is an extension of the approach outlined in [Dobrev et al., Internat. J. Numer. Methods Fluids, 65 (2010), pp. 1295--1310] and can be formulated for any finite dimensional approximation of the kinematic and thermodynamic fields, including generic finite elements on two- and three-dimensional meshes with triangular, quadrilateral, tetrahedral, or hexahedral zones. We discretize the kinematic variables of position and velocity using a continuous high-order basis function expansion of arbitrary polynomial degree which is obtained via a corresponding high-order parametric mapping from a standard reference element. This enables the use of curvilinear zone geometry, higher-order approximations for fields within a zone, and a pointwise definition of mass conservation which we refer to as strong mass conservation. Moreover, we discretize the internal energy using a piecewise discontinuous high-order basis function expansion which is also of arbitrary polynomial degree. This facilitates multimaterial hydrodynamics by treating material properties, such as equations of state and constitutive models, as piecewise discontinuous functions which vary within a zone. To satisfy the Rankine--Hugoniot jump conditions at a shock boundary and generate the appropriate entropy, we introduce a general tensor artificial viscosity which takes advantage of the high-order kinematic and thermodynamic information available in each zone. Finally, we apply a generic high-order time discretization process to the semidiscrete equations to develop the fully discrete numerical algorithm. Our method can be viewed as the high-order generalization of the so-called staggered

Arbitrary-Lagrangian-Eulerian Discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes

Science.gov (United States)

Boscheri, Walter; Dumbser, Michael

2017-10-01

We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes, like molecular viscosity or heat conduction. High order piecewise polynomials of degree N are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach, making use of an element-local space-time Galerkin finite element predictor. A novel nodal solver algorithm based on the HLL flux is derived to compute the velocity for each nodal degree of freedom that describes the current mesh geometry. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Each technique generates a corresponding number of geometrical degrees of freedom needed to describe the current mesh configuration and which must be considered by the nodal solver for determining the grid velocity. The connection of the old mesh configuration at time tn with the new one at time t n + 1 provides the space-time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our numerical method belongs to the category of so-called direct Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation formulation of the governing PDE system is considered and which already takes into account the new grid geometry (including a possible rezoning step) directly during the computation of the numerical fluxes. We emphasize that our method is a moving mesh method, as opposed to total

Adaptive finite element methods for differential equations

CERN Document Server

Bangerth, Wolfgang

2003-01-01

These Lecture Notes discuss concepts of `self-adaptivity' in the numerical solution of differential equations, with emphasis on Galerkin finite element methods. The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. `Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. At the end of each chapter some exercises are posed in order ...

Hierarchical Material Properties in Finite Element Analysis: The Oilfield Infrastructure Problem.

Science.gov (United States)

Weiss, C. J.; Wilson, G. A.

2017-12-01

Geophysical simulation of low-frequency electromagnetic signals within built environments such as urban centers and industrial landscapes facilities is a challenging computational problem because strong conductors (e.g., pipes, fences, rail lines, rebar, etc.) are not only highly conductive and/or magnetic relative to the surrounding geology, but they are very small in one or more of their physical length coordinates. Realistic modeling of such structures as idealized conductors has long been the standard approach; however this strategy carries with it computational burdens such as cumbersome implementation of internal boundary conditions, and limited flexibility for accommodating realistic geometries. Another standard approach is "brute force" discretization (often coupled with an equivalent medium model) whereby 100's of millions of voxels are used to represent these strong conductors, but at the cost of extreme computation times (and mesh design) for a simulation result when possible. To minimize these burdens, a new finite element scheme (Weiss, Geophysics, 2017) has been developed in which the material properties reside on a hierarchy of geometric simplicies (i.e., edges, facets and volumes) within an unstructured tetrahedral mesh. This allows thin sheet—like structures, such as subsurface fractures, to be economically represented by a connected set of triangular facets, for example, that freely conform to arbitrary "real world" geometries. The same holds thin pipe/wire-like structures, such as casings or pipelines. The hierarchical finite element scheme has been applied to problems in electro- and magnetostatics for oilfield problems where the elevated, but finite, conductivity and permeability of the steel-cased oil wells must be properly accounted for, yielding results that are otherwise unobtainable, with run times as low as a few 10s of seconds. Extension of the hierarchical finite element concept to broadband electromagnetics is presently underway, as

User Manual for the PROTEUS Mesh Tools

Energy Technology Data Exchange (ETDEWEB)

Smith, Micheal A. [Argonne National Lab. (ANL), Argonne, IL (United States); Shemon, Emily R [Argonne National Lab. (ANL), Argonne, IL (United States)

2016-09-19

PROTEUS is built around a finite element representation of the geometry for visualization. In addition, the PROTEUS-SN solver was built to solve the even-parity transport equation on a finite element mesh provided as input. Similarly, PROTEUS-MOC and PROTEUS-NEMO were built to apply the method of characteristics on unstructured finite element meshes. Given the complexity of real world problems, experience has shown that using commercial mesh generator to create rather simple input geometries is overly complex and slow. As a consequence, significant effort has been put into place to create multiple codes that help assist in the mesh generation and manipulation. There are three input means to create a mesh in PROTEUS: UFMESH, GRID, and NEMESH. At present, the UFMESH is a simple way to generate two-dimensional Cartesian and hexagonal fuel assembly geometries. The UFmesh input allows for simple assembly mesh generation while the GRID input allows the generation of Cartesian, hexagonal, and regular triangular structured grid geometry options. The NEMESH is a way for the user to create their own mesh or convert another mesh file format into a PROTEUS input format. Given that one has an input mesh format acceptable for PROTEUS, we have constructed several tools which allow further mesh and geometry construction (i.e. mesh extrusion and merging). This report describes the various mesh tools that are provided with the PROTEUS code giving both descriptions of the input and output. In many cases the examples are provided with a regression test of the mesh tools. The most important mesh tools for any user to consider using are the MT_MeshToMesh.x and the MT_RadialLattice.x codes. The former allows the conversion between most mesh types handled by PROTEUS while the second allows the merging of multiple (assembly) meshes into a radial structured grid. Note that the mesh generation process is recursive in nature and that each input specific for a given mesh tool (such as .axial

A Novel Virtual Node Hexahedral Element with Exact Integration and Octree Meshing

Directory of Open Access Journals (Sweden)

Logah Perumal

2016-01-01

Full Text Available The method presented in this work is a 3-dimensional polyhedral finite element (3D PFEM based on virtual node method. Novel virtual node polyhedral elements (termed as VPHE are developed here, particularly virtual node hexahedral element (termed as VHE. Stiffness matrices of these polyhedral elements consist of simple polynomials. Thus, a new algorithm is introduced in this paper, which enables exact integration of monomials without a need for high number of integration points and weights. The number of nodes for VHE elements is not restricted, as opposed to the conventional hexahedral elements. This feature enables formulation of transition elements (termed as T-VHE which are useful to adaptive computation. Performances of the new VHE elements in solid mechanics and conductive heat transfer phenomena are examined through numerical simulations. The new T-VHE elements are utilized in octree mesh. The VHE elements are found to produce good results and T-VHE elements help to reduce number of global nodes for the analysis.

Application of finite-element method to three-dimensional nuclear reactor analysis

International Nuclear Information System (INIS)

Cheung, K.Y.

1985-01-01

The application of the finite element method to solve a realistic one-or-two energy group, multiregion, three-dimensional static neutron diffusion problem is studied. Linear, quadratic, and cubic serendipity box-shape elements are used. The resulting sets of simultaneous algebraic equations with thousands of unknowns are solved by the conjugate gradient method, without forming the large coefficient matrix explicitly. This avoids the complicated data management schemes to store such a large coefficient matrix. Three finite-element computer programs: FEM-LINEAR, FEM-QUADRATIC and FEM-CUBIC were developed, using the linear, quadratic, and cubic box-shape elements respectively. They are self-contained, using simple nodal labeling schemes, without the need for separate finite element mesh generating routines. The efficiency and accuracy of these computer programs are then compared among themselves, and with other computer codes. The cubic element model is not recommended for practical usage because it gives almost identical results as the quadratic model, but it requires considerably longer computation time. The linear model is less accurate than the quadratic model, but it requires much shorter computation time. For a large 3-D problem, the linear model is to be preferred since it gives acceptable accuracy. The quadratic model may be used if improved accuracy is desired

An automatic granular structure generation and finite element analysis of heterogeneous semi-solid materials

International Nuclear Information System (INIS)

Sharifi, Hamid; Larouche, Daniel

2015-01-01

The quality of cast metal products depends on the capacity of the semi-solid metal to sustain the stresses generated during the casting. Predicting the evolution of these stresses with accuracy in the solidification interval should be highly helpful to avoid the formation of defects like hot tearing. This task is however very difficult because of the heterogeneous nature of the material. In this paper, we propose to evaluate the mechanical behaviour of a metal during solidification using a mesh generation technique of the heterogeneous semi-solid material for a finite element analysis at the microscopic level. This task is done on a two-dimensional (2D) domain in which the granular structure of the solid phase is generated surrounded by an intergranular and interdendritc liquid phase. Some basic solid grains are first constructed and projected in the 2D domain with random orientations and scale factors. Depending on their orientation, the basic grains are combined to produce larger grains or separated by a liquid film. Different basic grain shapes can produce different granular structures of the mushy zone. As a result, using this automatic grain generation procedure, we can investigate the effect of grain shapes and sizes on the thermo-mechanical behaviour of the semi-solid material. The granular models are automatically converted to the finite element meshes. The solid grains and the liquid phase are meshed properly using quadrilateral elements. This method has been used to simulate the microstructure of a binary aluminium–copper alloy (Al–5.8 wt% Cu) when the fraction solid is 0.92. Using the finite element method and the Mie–Grüneisen equation of state for the liquid phase, the transient mechanical behaviour of the mushy zone under tensile loading has been investigated. The stress distribution and the bridges, which are formed during the tensile loading, have been detected. (paper)

Finite-element solutions of the AER-2 rod ejection benchmark by CRONOS

International Nuclear Information System (INIS)

Kolev, N.P.; Lenain, R.; Fedon-Magnaud, C.

2001-01-01

The finite-element option in CRONOS was used to analyse the AER-2 rod-ejection benchmark for WWER-440. The objective is to obtain spatially converged solutions by means of node subdivision and approximation refinement. This paper presents the first phase of analysis dealing with the initial and just-ejected states used for calculation of the initial reactivity. Fine-mesh and extrapolated to zero mesh size solutions were obtained and verified by comparison to MAG code solutions. These differences provide potential for large deviations in the transient results and deserve further attention in reactor safety analysis (Authors)

Basic Finite Element Method

International Nuclear Information System (INIS)

Lee, Byeong Hae

1992-02-01

This book gives descriptions of basic finite element method, which includes basic finite element method and data, black box, writing of data, definition of VECTOR, definition of matrix, matrix and multiplication of matrix, addition of matrix, and unit matrix, conception of hardness matrix like spring power and displacement, governed equation of an elastic body, finite element method, Fortran method and programming such as composition of computer, order of programming and data card and Fortran card, finite element program and application of nonelastic problem.

MHD simulations on an unstructured mesh

International Nuclear Information System (INIS)

Strauss, H.R.; Park, W.

1996-01-01

We describe work on a full MHD code using an unstructured mesh. MH3D++ is an extension of the PPPL MH3D resistive full MHD code. MH3D++ replaces the structured mesh and finite difference / fourier discretization of MH3D with an unstructured mesh and finite element / fourier discretization. Low level routines which perform differential operations, solution of PDEs such as Poisson's equation, and graphics, are encapsulated in C++ objects to isolate the finite element operations from the higher level code. The high level code is the same, whether it is run in structured or unstructured mesh versions. This allows the unstructured mesh version to be benchmarked against the structured mesh version. As a preliminary example, disruptions in DIIID reverse shear equilibria are studied numerically with the MH3D++ code. Numerical equilibria were first produced starting with an EQDSK file containing equilibrium data of a DIII-D L-mode negative central shear discharge. Using these equilibria, the linearized equations are time advanced to get the toroidal mode number n = 1 linear growth rate and eigenmode, which is resistively unstable. The equilibrium and linear mode are used to initialize 3D nonlinear runs. An example shows poloidal slices of 3D pressure surfaces: initially, on the left, and at an intermediate time, on the right

High order curvilinear finite elements for elastic–plastic Lagrangian dynamics

International Nuclear Information System (INIS)

Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.

2014-01-01

This paper presents a high-order finite element method for calculating elastic–plastic flow on moving curvilinear meshes and is an extension of our general high-order curvilinear finite element approach for solving the Euler equations of gas dynamics in a Lagrangian frame [1,2]. In order to handle transition to plastic flow, we formulate the stress–strain relation in rate (or incremental) form and augment our semi-discrete equations for Lagrangian hydrodynamics with an additional evolution equation for the deviatoric stress which is valid for arbitrary order spatial discretizations of the kinematic and thermodynamic variables. The semi-discrete equation for the deviatoric stress rate is developed for 2D planar, 2D axisymmetric and full 3D geometries. For each case, the strain rate is approximated via a collocation method at zone quadrature points while the deviatoric stress is approximated using an L 2 projection onto the thermodynamic basis. We apply high order, energy conserving, explicit time stepping methods to the semi-discrete equations to develop the fully discrete method. We conclude with numerical results from an extensive series of verification tests that demonstrate several practical advantages of using high-order finite elements for elastic–plastic flow

Coupled porohyperelastic mass transport (PHEXPT) finite element models for soft tissues using ABAQUS.

Science.gov (United States)

Vande Geest, Jonathan P; Simon, B R; Rigby, Paul H; Newberg, Tyler P

2011-04-01

Finite element models (FEMs) including characteristic large deformations in highly nonlinear materials (hyperelasticity and coupled diffusive/convective transport of neutral mobile species) will allow quantitative study of in vivo tissues. Such FEMs will provide basic understanding of normal and pathological tissue responses and lead to optimization of local drug delivery strategies. We present a coupled porohyperelastic mass transport (PHEXPT) finite element approach developed using a commercially available ABAQUS finite element software. The PHEXPT transient simulations are based on sequential solution of the porohyperelastic (PHE) and mass transport (XPT) problems where an Eulerian PHE FEM is coupled to a Lagrangian XPT FEM using a custom-written FORTRAN program. The PHEXPT theoretical background is derived in the context of porous media transport theory and extended to ABAQUS finite element formulations. The essential assumptions needed in order to use ABAQUS are clearly identified in the derivation. Representative benchmark finite element simulations are provided along with analytical solutions (when appropriate). These simulations demonstrate the differences in transient and steady state responses including finite deformations, total stress, fluid pressure, relative fluid, and mobile species flux. A detailed description of important model considerations (e.g., material property functions and jump discontinuities at material interfaces) is also presented in the context of finite deformations. The ABAQUS-based PHEXPT approach enables the use of the available ABAQUS capabilities (interactive FEM mesh generation, finite element libraries, nonlinear material laws, pre- and postprocessing, etc.). PHEXPT FEMs can be used to simulate the transport of a relatively large neutral species (negligible osmotic fluid flux) in highly deformable hydrated soft tissues and tissue-engineered materials.

Finite-element 3D simulation tools for high-current relativistic electron beams

Science.gov (United States)

Humphries, Stanley; Ekdahl, Carl

2002-08-01

The DARHT second-axis injector is a challenge for computer simulations. Electrons are subject to strong beam-generated forces. The fields are fully three-dimensional and accurate calculations at surfaces are critical. We describe methods applied in OmniTrak, a 3D finite-element code suite that can address DARHT and the full range of charged-particle devices. The system handles mesh generation, electrostatics, magnetostatics and self-consistent particle orbits. The MetaMesh program generates meshes of conformal hexahedrons to fit any user geometry. The code has the unique ability to create structured conformal meshes with cubic logic. Organized meshes offer advantages in speed and memory utilization in the orbit and field solutions. OmniTrak is a versatile charged-particle code that handles 3D electric and magnetic field solutions on independent meshes. The program can update both 3D field solutions from the calculated beam space-charge and current-density. We shall describe numerical methods for orbit tracking on a hexahedron mesh. Topics include: 1) identification of elements along the particle trajectory, 2) fast searches and adaptive field calculations, 3) interpolation methods to terminate orbits on material surfaces, 4) automatic particle generation on multiple emission surfaces to model space-charge-limited emission and field emission, 5) flexible Child law algorithms, 6) implementation of the dual potential model for 3D magnetostatics, and 7) assignment of charge and current from model particle orbits for self-consistent fields.

A voxel-based finite element model for the prediction of bladder deformation

Energy Technology Data Exchange (ETDEWEB)

Xiangfei, Chai; Herk, Marcel van; Hulshof, Maarten C. C. M.; Bel, Arjan [Radiation Oncology Department, Academic Medical Center, University of Amsterdam, 1105 AZ Amsterdam (Netherlands); Radiation Oncology Department, Netherlands Cancer Institute, 1066 CX Amsterdam (Netherlands); Radiation Oncology Department, Academic Medical Center, University of Amsterdam, 1105 AZ Amsterdam (Netherlands)

2012-01-15

Purpose: A finite element (FE) bladder model was previously developed to predict bladder deformation caused by bladder filling change. However, two factors prevent a wide application of FE models: (1) the labor required to construct a FE model with high quality mesh and (2) long computation time needed to construct the FE model and solve the FE equations. In this work, we address these issues by constructing a low-resolution voxel-based FE bladder model directly from the binary segmentation images and compare the accuracy and computational efficiency of the voxel-based model used to simulate bladder deformation with those of a classical FE model with a tetrahedral mesh. Methods: For ten healthy volunteers, a series of MRI scans of the pelvic region was recorded at regular intervals of 10 min over 1 h. For this series of scans, the bladder volume gradually increased while rectal volume remained constant. All pelvic structures were defined from a reference image for each volunteer, including bladder wall, small bowel, prostate (male), uterus (female), rectum, pelvic bone, spine, and the rest of the body. Four separate FE models were constructed from these structures: one with a tetrahedral mesh (used in previous study), one with a uniform hexahedral mesh, one with a nonuniform hexahedral mesh, and one with a low-resolution nonuniform hexahedral mesh. Appropriate material properties were assigned to all structures and uniform pressure was applied to the inner bladder wall to simulate bladder deformation from urine inflow. Performance of the hexahedral meshes was evaluated against the performance of the standard tetrahedral mesh by comparing the accuracy of bladder shape prediction and computational efficiency. Results: FE model with a hexahedral mesh can be quickly and automatically constructed. No substantial differences were observed between the simulation results of the tetrahedral mesh and hexahedral meshes (<1% difference in mean dice similarity coefficient to

A voxel-based finite element model for the prediction of bladder deformation

International Nuclear Information System (INIS)

Chai Xiangfei; Herk, Marcel van; Hulshof, Maarten C. C. M.; Bel, Arjan

2012-01-01

Purpose: A finite element (FE) bladder model was previously developed to predict bladder deformation caused by bladder filling change. However, two factors prevent a wide application of FE models: (1) the labor required to construct a FE model with high quality mesh and (2) long computation time needed to construct the FE model and solve the FE equations. In this work, we address these issues by constructing a low-resolution voxel-based FE bladder model directly from the binary segmentation images and compare the accuracy and computational efficiency of the voxel-based model used to simulate bladder deformation with those of a classical FE model with a tetrahedral mesh. Methods: For ten healthy volunteers, a series of MRI scans of the pelvic region was recorded at regular intervals of 10 min over 1 h. For this series of scans, the bladder volume gradually increased while rectal volume remained constant. All pelvic structures were defined from a reference image for each volunteer, including bladder wall, small bowel, prostate (male), uterus (female), rectum, pelvic bone, spine, and the rest of the body. Four separate FE models were constructed from these structures: one with a tetrahedral mesh (used in previous study), one with a uniform hexahedral mesh, one with a nonuniform hexahedral mesh, and one with a low-resolution nonuniform hexahedral mesh. Appropriate material properties were assigned to all structures and uniform pressure was applied to the inner bladder wall to simulate bladder deformation from urine inflow. Performance of the hexahedral meshes was evaluated against the performance of the standard tetrahedral mesh by comparing the accuracy of bladder shape prediction and computational efficiency. Results: FE model with a hexahedral mesh can be quickly and automatically constructed. No substantial differences were observed between the simulation results of the tetrahedral mesh and hexahedral meshes (<1% difference in mean dice similarity coefficient to

On constitutive modelling in finite element analysis

International Nuclear Information System (INIS)

Bathe, K.J.; Snyder, M.D.; Cleary, M.P.

1979-01-01

This compact contains a brief introduction to the problems involved in constitutive modeling as well as an outline of the final paper to be submitted. Attention is focussed on three important areas: (1) the need for using theoretically sound material models and the importance of recognizing the limitations of the models, (2) the problem of developing stable and effective numerical representations of the models, and (3) the necessity for selection of an appropriate finite element mesh that can capture the actual physical response of the complete structure. In the final paper, we will be presenting our recent research results pertaining to each of these problem areas. (orig.)

Finite Element Analysis Modeling of Chemical Vapor Deposition of Silicon Carbide

Science.gov (United States)

2014-06-19

concentrations. This is the method by which species adsorb to the surface of the substrate. The movement resulting from diffusion is governed by...itself. This can be treacherous, however. The mesh is what the entire finite element method is built upon. If the movement of the backbone has... Brownian Motion Algorithm for Tow Scale Modeling of Chemical Vapor Infiltration. Computational Materials Science, 1871-1878. !178 23. Wang, C. & D

An element-based finite-volume method approach for naturally fractured compositional reservoir simulation

Energy Technology Data Exchange (ETDEWEB)

Marcondes, Francisco [Federal University of Ceara, Fortaleza (Brazil). Dept. of Metallurgical Engineering and Material Science], e-mail: marcondes@ufc.br; Varavei, Abdoljalil; Sepehrnoori, Kamy [The University of Texas at Austin (United States). Petroleum and Geosystems Engineering Dept.], e-mails: varavei@mail.utexas.edu, kamys@mail.utexas.edu

2010-07-01

An element-based finite-volume approach in conjunction with unstructured grids for naturally fractured compositional reservoir simulation is presented. In this approach, both the discrete fracture and the matrix mass balances are taken into account without any additional models to couple the matrix and discrete fractures. The mesh, for two dimensional domains, can be built of triangles, quadrilaterals, or a mix of these elements. However, due to the available mesh generator to handle both matrix and discrete fractures, only results using triangular elements will be presented. The discrete fractures are located along the edges of each element. To obtain the approximated matrix equation, each element is divided into three sub-elements and then the mass balance equations for each component are integrated along each interface of the sub-elements. The finite-volume conservation equations are assembled from the contribution of all the elements that share a vertex, creating a cell vertex approach. The discrete fracture equations are discretized only along the edges of each element and then summed up with the matrix equations in order to obtain a conservative equation for both matrix and discrete fractures. In order to mimic real field simulations, the capillary pressure is included in both matrix and discrete fracture media. In the implemented model, the saturation field in the matrix and discrete fractures can be different, but the potential of each phase in the matrix and discrete fracture interface needs to be the same. The results for several naturally fractured reservoirs are presented to demonstrate the applicability of the method. (author)

Evaluation of Strip Footing Bearing Capacity Built on the Anthropogenic Embankment by Random Finite Element Method

Science.gov (United States)

Pieczynska-Kozlowska, Joanna

2014-05-01

One of a geotechnical problem in the area of Wroclaw is an anthropogenic embankment layer delaying to the depth of 4-5m, arising as a result of historical incidents. In such a case an assumption of bearing capacity of strip footing might be difficult. The standard solution is to use a deep foundation or foundation soil replacement. However both methods generate significant costs. In the present paper the authors focused their attention on the influence of anthropogenic embankment variability on bearing capacity. Soil parameters were defined on the basis of CPT test and modeled as 2D anisotropic random fields and the assumption of bearing capacity were made according deterministic finite element methods. Many repeated of the different realizations of random fields lead to stable expected value of bearing capacity. The algorithm used to estimate the bearing capacity of strip footing was the random finite element method (e.g. [1]). In traditional approach of bearing capacity the formula proposed by [2] is taken into account. qf = c'Nc + qNq + 0.5γBN- γ (1) where: qf is the ultimate bearing stress, cis the cohesion, qis the overburden load due to foundation embedment, γ is the soil unit weight, Bis the footing width, and Nc, Nq and Nγ are the bearing capacity factors. The method of evaluation the bearing capacity of strip footing based on finite element method incorporate five parameters: Young's modulus (E), Poisson's ratio (ν), dilation angle (ψ), cohesion (c), and friction angle (φ). In the present study E, ν and ψ are held constant while c and φ are randomized. Although the Young's modulus does not affect the bearing capacity it governs the initial elastic response of the soil. Plastic stress redistribution is accomplished using a viscoplastic algorithm merge with an elastic perfectly plastic (Mohr - Coulomb) failure criterion. In this paper a typical finite element mesh was assumed with 8-node elements consist in 50 columns and 20 rows. Footings width B

Computable error estimates for Monte Carlo finite element approximation of elliptic PDE with lognormal diffusion coefficients

KAUST Repository

Hall, Eric; Haakon, Hoel; Sandberg, Mattias; Szepessy, Anders; Tempone, Raul

2016-01-01

lognormal diffusion coefficients with H´ older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible

Coarse mesh code development

Energy Technology Data Exchange (ETDEWEB)

Lieberoth, J.

1975-06-15

The numerical solution of the neutron diffusion equation plays a very important role in the analysis of nuclear reactors. A wide variety of numerical procedures has been proposed, at which most of the frequently used numerical methods are fundamentally based on the finite- difference approximation where the partial derivatives are approximated by the finite difference. For complex geometries, typical of the practical reactor problems, the computational accuracy of the finite-difference method is seriously affected by the size of the mesh width relative to the neutron diffusion length and by the heterogeneity of the medium. Thus, a very large number of mesh points are generally required to obtain a reasonably accurate approximate solution of the multi-dimensional diffusion equation. Since the computation time is approximately proportional to the number of mesh points, a detailed multidimensional analysis, based on the conventional finite-difference method, is still expensive even with modern large-scale computers. Accordingly, there is a strong incentive to develop alternatives that can reduce the number of mesh-points and still retain accuracy. One of the promising alternatives is the finite element method, which consists of the expansion of the neutron flux by piecewise polynomials. One of the advantages of this procedure is its flexibility in selecting the locations of the mesh points and the degree of the expansion polynomial. The small number of mesh points of the coarse grid enables to store the results of several of the least outer iterations and to calculate well extrapolated values of them by comfortable formalisms. This holds especially if only one energy distribution of fission neutrons is assumed for all fission processes in the reactor, because the whole information of an outer iteration is contained in a field of fission rates which has the size of all mesh points of the coarse grid.

Computational error estimates for Monte Carlo finite element approximation with log normal diffusion coefficients

KAUST Repository

Sandberg, Mattias

2015-01-07

The Monte Carlo (and Multi-level Monte Carlo) finite element method can be used to approximate observables of solutions to diffusion equations with log normal distributed diffusion coefficients, e.g. modelling ground water flow. Typical models use log normal diffusion coefficients with H¨older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible and can be larger than the computable low frequency error. This talk will address how the total error can be estimated by the computable error.

On the relationship between some nodal schemes and the finite element method in static diffusion calculations

International Nuclear Information System (INIS)

Fedon-Magnaud, C.; Hennart, J.P.; Lautard, J.J.

1983-03-01

An unified formulation of non conforming finite elements with quadrature formula and simple nodal scheme is presented. The theoretical convergence is obtained for the previous scheme when the mesh is refined. Numerical tests are provided in order to bear out the theorical results

Comparison of computed tomography based parametric and patient-specific finite element models of the healthy and metastatic spine using a mesh-morphing algorithm.

Science.gov (United States)

O'Reilly, Meaghan Anne; Whyne, Cari Marisa

2008-08-01

A comparative analysis of parametric and patient-specific finite element (FE) modeling of spinal motion segments. To develop patient-specific FE models of spinal motion segments using mesh-morphing methods applied to a parametric FE model. To compare strain and displacement patterns in parametric and morphed models for both healthy and metastatically involved vertebrae. Parametric FE models may be limited in their ability to fully represent patient-specific geometries and material property distributions. Generation of multiple patient-specific FE models has been limited because of computational expense. Morphing methods have been successfully used to generate multiple specimen-specific FE models of caudal rat vertebrae. FE models of a healthy and a metastatic T6-T8 spinal motion segment were analyzed with and without patient-specific material properties. Parametric and morphed models were compared using a landmark-based morphing algorithm. Morphing of the parametric FE model and including patient-specific material properties both had a strong impact on magnitudes and patterns of vertebral strain and displacement. Small but important geometric differences can be represented through morphing of parametric FE models. The mesh-morphing algorithm developed provides a rapid method for generating patient-specific FE models of spinal motion segments.

Simplified Qualitative Discrete Numerical Model to Determine Cracking Pattern in Brittle Materials by Means of Finite Element Method

Directory of Open Access Journals (Sweden)

J. Ochoa-Avendaño

2017-01-01

Full Text Available This paper presents the formulation, implementation, and validation of a simplified qualitative model to determine the crack path of solids considering static loads, infinitesimal strain, and plane stress condition. This model is based on finite element method with a special meshing technique, where nonlinear link elements are included between the faces of the linear triangular elements. The stiffness loss of some link elements represents the crack opening. Three experimental tests of bending beams are simulated, where the cracking pattern calculated with the proposed numerical model is similar to experimental result. The advantages of the proposed model compared to discrete crack approaches with interface elements can be the implementation simplicity, the numerical stability, and the very low computational cost. The simulation with greater values of the initial stiffness of the link elements does not affect the discontinuity path and the stability of the numerical solution. The exploded mesh procedure presented in this model avoids a complex nonlinear analysis and regenerative or adaptive meshes.

A direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D

Science.gov (United States)

Boscheri, Walter; Dumbser, Michael

2014-10-01

In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final Lagrangian finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with

Generalized finite elements

International Nuclear Information System (INIS)

Wachspress, E.

2009-01-01

Triangles and rectangles are the ubiquitous elements in finite element studies. Only these elements admit polynomial basis functions. Rational functions provide a basis for elements having any number of straight and curved sides. Numerical complexities initially associated with rational bases precluded extensive use. Recent analysis has reduced these difficulties and programs have been written to illustrate effectiveness. Although incorporation in major finite element software requires considerable effort, there are advantages in some applications which warrant implementation. An outline of the basic theory and of recent innovations is presented here. (authors)

Automatic generation of accurate subject-specific bone finite element models to be used in clinical studies.

Science.gov (United States)

Viceconti, Marco; Davinelli, Mario; Taddei, Fulvia; Cappello, Angelo

2004-10-01

Most of the finite element models of bones used in orthopaedic biomechanics research are based on generic anatomies. However, in many cases it would be useful to generate from CT data a separate finite element model for each subject of a study group. In a recent study a hexahedral mesh generator based on a grid projection algorithm was found very effective in terms of accuracy and automation. However, so far the use of this method has been documented only on data collected in vitro and only for long bones. The present study was aimed at verifying if this method represents a procedure for the generation of finite element models of human bones from data collected in vivo, robust, accurate, automatic and general enough to be used in clinical studies. Robustness, automation and numerical accuracy of the proposed method were assessed on five femoral CT data sets of patients affected by various pathologies. The generality of the method was verified by processing a femur, an ileum, a phalanx, a proximal femur reconstruction, and the micro-CT of a small sample of spongy bone. The method was found robust enough to cope with the variability of the five femurs, producing meshes with a numerical accuracy and a computational weight comparable to those found in vitro. Even when the method was used to process the other bones the levels of mesh conditioning remained within acceptable limits. Thus, it may be concluded that the method presents a generality sufficient to cope with almost any orthopaedic application.

A Novel Mesh Quality Improvement Method for Boundary Elements

Directory of Open Access Journals (Sweden)

Hou-lin Liu

2012-01-01

Full Text Available In order to improve the boundary mesh quality while maintaining the essential characteristics of discrete surfaces, a new approach combining optimization-based smoothing and topology optimization is developed. The smoothing objective function is modified, in which two functions denoting boundary and interior quality, respectively, and a weight coefficient controlling boundary quality are taken into account. In addition, the existing smoothing algorithm can improve the mesh quality only by repositioning vertices of the interior mesh. Without destroying boundary conformity, bad elements with all their vertices on the boundary cannot be eliminated. Then, topology optimization is employed, and those elements are converted into other types of elements whose quality can be improved by smoothing. The practical application shows that the worst elements can be eliminated and, with the increase of weight coefficient, the average quality of boundary mesh can also be improved. Results obtained with the combined approach are compared with some common approach. It is clearly shown that it performs better than the existing approach.

Simulation of incompressible flows with heat and mass transfer using parallel finite element method

Directory of Open Access Journals (Sweden)

Jalal Abedi

2003-02-01

Full Text Available The stabilized finite element formulations based on the SUPG (Stream-line-Upwind/Petrov-Galerkin and PSPG (Pressure-Stabilization/Petrov-Galerkin methods are developed and applied to solve buoyancy-driven incompressible flows with heat and mass transfer. The SUPG stabilization term allows us to solve flow problems at high speeds (advection dominant flows and the PSPG term eliminates instabilities associated with the use of equal order interpolation functions for both pressure and velocity. The finite element formulations are implemented in parallel using MPI. In parallel computations, the finite element mesh is partitioned into contiguous subdomains using METIS, which are then assigned to individual processors. To ensure a balanced load, the number of elements assigned to each processor is approximately equal. To solve nonlinear systems in large-scale applications, we developed a matrix-free GMRES iterative solver. Here we totally eliminate a need to form any matrices, even at the element levels. To measure the accuracy of the method, we solve 2D and 3D example of natural convection flows at moderate to high Rayleigh numbers.

Electric field calculations in brain stimulation based on finite elements

DEFF Research Database (Denmark)

Windhoff, Mirko; Opitz, Alexander; Thielscher, Axel

2013-01-01

The need for realistic electric field calculations in human noninvasive brain stimulation is undisputed to more accurately determine the affected brain areas. However, using numerical techniques such as the finite element method (FEM) is methodologically complex, starting with the creation...... of accurate head models to the integration of the models in the numerical calculations. These problems substantially limit a more widespread application of numerical methods in brain stimulation up to now. We introduce an optimized processing pipeline allowing for the automatic generation of individualized...... the successful usage of the pipeline in six subjects, including field calculations for transcranial magnetic stimulation and transcranial direct current stimulation. The quality of the head volume meshes is validated both in terms of capturing the underlying anatomy and of the well-shapedness of the mesh...

Solution of three-dimensional energy equation using finite element method

International Nuclear Information System (INIS)

Bhasin, V.; Singh, R.K.; Dutta, B.K.; Kushwaha, H.S.

1993-01-01

In the present work an attempt has been made to formulate an efficient 3-D finite element program for solving coupled momentum-energy equation with unsymmetric frontal solver and a suitable upwinding scheme. Based on the above solution technique of energy equation it can be concluded that upwinding scheme can lead to fairly accurate and smooth results even with coarse mesh. Otherwise the mesh size requirement will be extremely stringent for most of the practical problems. With upwinding the additional computer time required is marginally more. This effort has resulted in getting practical solution for large size real life problems in nuclear industry. The program was used for computation of temperature field in heavy water moderator of Madras Atomic Power Station (MAPS) reactor, in new mode of operation. (author). 9 refs., 7 figs

Adaptive Multilevel Methods with Local Smoothing for $H^1$- and $H^{\\mathrm{curl}}$-Conforming High Order Finite Element Methods

KAUST Repository

Janssen, Bä rbel; Kanschat, Guido

2011-01-01

A multilevel method on adaptive meshes with hanging nodes is presented, and the additional matrices appearing in the implementation are derived. Smoothers of overlapping Schwarz type are discussed; smoothing is restricted to the interior of the subdomains refined to the current level; thus it has optimal computational complexity. When applied to conforming finite element discretizations of elliptic problems and Maxwell equations, the method's convergence rates are very close to those for the nonadaptive version. Furthermore, the smoothers remain efficient for high order finite elements. We discuss the implementation in a general finite element code using the example of the deal.II library. © 2011 Societ y for Industrial and Applied Mathematics.

Model of Random Polygon Particles for Concrete and Mesh Automatic Subdivision

Institute of Scientific and Technical Information of China (English)

无

2001-01-01

In order to study the constitutive behavior of concrete in mesoscopic level, a new method is proposed in this paper. This method uses random polygon particles to simulate full grading broken aggregates of concrete. Based on computational geometry, we carry out the automatic generation of the triangle finite element mesh for the model of random polygon particles of concrete. The finite element mesh generated in this paper is also applicable to many other numerical methods.

Development and application of a third order scheme of finite differences centered in mesh

International Nuclear Information System (INIS)

Delfin L, A.; Alonso V, G.; Valle G, E. del

2003-01-01

In this work the development of a third order scheme of finite differences centered in mesh is presented and it is applied in the numerical solution of those diffusion equations in multi groups in stationary state and X Y geometry. Originally this scheme was developed by Hennart and del Valle for the monoenergetic diffusion equation with a well-known source and they show that the one scheme is of third order when comparing the numerical solution with the analytical solution of a model problem using several mesh refinements and boundary conditions. The scheme by them developed it also introduces the application of numeric quadratures to evaluate the rigidity matrices and of mass that its appear when making use of the finite elements method of Galerkin. One of the used quadratures is the open quadrature of 4 points, no-standard, of Newton-Cotes to evaluate in approximate form the elements of the rigidity matrices. The other quadrature is that of 3 points of Radau that it is used to evaluate the elements of all the mass matrices. One of the objectives of these quadratures are to eliminate the couplings among the Legendre moments 0 and 1 associated to the left and right faces as those associated to the inferior and superior faces of each cell of the discretization. The other objective is to satisfy the particles balance in weighed form in each cell. In this work it expands such development to multiplicative means considering several energy groups. There are described diverse details inherent to the technique, particularly those that refer to the simplification of the algebraic systems that appear due to the space discretization. Numerical results for several test problems are presented and are compared with those obtained with other nodal techniques. (Author)

A software platform for continuum modeling of ion channels based on unstructured mesh

International Nuclear Information System (INIS)

Tu, B; Bai, S Y; Xie, Y; Zhang, L B; Lu, B Z; Chen, M X

2014-01-01

Most traditional continuum molecular modeling adopted finite difference or finite volume methods which were based on a structured mesh (grid). Unstructured meshes were only occasionally used, but an increased number of applications emerge in molecular simulations. To facilitate the continuum modeling of biomolecular systems based on unstructured meshes, we are developing a software platform with tools which are particularly beneficial to those approaches. This work describes the software system specifically for the simulation of a typical, complex molecular procedure: ion transport through a three-dimensional channel system that consists of a protein and a membrane. The platform contains three parts: a meshing tool chain for ion channel systems, a parallel finite element solver for the Poisson–Nernst–Planck equations describing the electrodiffusion process of ion transport, and a visualization program for continuum molecular modeling. The meshing tool chain in the platform, which consists of a set of mesh generation tools, is able to generate high-quality surface and volume meshes for ion channel systems. The parallel finite element solver in our platform is based on the parallel adaptive finite element package PHG which wass developed by one of the authors [1]. As a featured component of the platform, a new visualization program, VCMM, has specifically been developed for continuum molecular modeling with an emphasis on providing useful facilities for unstructured mesh-based methods and for their output analysis and visualization. VCMM provides a graphic user interface and consists of three modules: a molecular module, a meshing module and a numerical module. A demonstration of the platform is provided with a study of two real proteins, the connexin 26 and hemolysin ion channels. (paper)

Space and Time Adaptive Two-Mesh hp-Finite Element Method for Transient Microwave Heating Problems

Czech Academy of Sciences Publication Activity Database

Dubcová, Lenka; Šolín, Pavel; Červený, Jakub; Kůs, Pavel

1-2, č. 30 (2010), s. 23-40 ISSN 0272-6343 R&D Projects: GA ČR(CZ) GA102/07/0496; GA AV ČR IAA100760702 Institutional research plan: CEZ:AV0Z20570509 Keywords : hp-finite element method * microwave heating * edge elements Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 0.844, year: 2010

An h-adaptive finite element method for turbulent heat transfer

Energy Technology Data Exchange (ETDEWEB)

Carriington, David B [Los Alamos National Laboratory

2009-01-01

A two-equation turbulence closure model (k-{omega}) using an h-adaptive grid technique and finite element method (FEM) has been developed to simulate low Mach flow and heat transfer. These flows are applicable to many flows in engineering and environmental sciences. Of particular interest in the engineering modeling areas are: combustion, solidification, and heat exchanger design. Flows for indoor air quality modeling and atmospheric pollution transport are typical types of environmental flows modeled with this method. The numerical method is based on a hybrid finite element model using an equal-order projection process. The model includes thermal and species transport, localized mesh refinement (h-adaptive) and Petrov-Galerkin weighting for the stabilizing the advection. This work develops the continuum model of a two-equation turbulence closure method. The fractional step solution method is stated along with the h-adaptive grid method (Carrington and Pepper, 2002). Solutions are presented for 2d flow over a backward-facing step.

Hybrid Direct and Iterative Solver with Library of Multi-criteria Optimal Orderings for h Adaptive Finite Element Method Computations

KAUST Repository

AbouEisha, Hassan M.

2016-06-02

In this paper we present a multi-criteria optimization of element partition trees and resulting orderings for multi-frontal solver algorithms executed for two dimensional h adaptive finite element method. In particular, the problem of optimal ordering of elimination of rows in the sparse matrices resulting from adaptive finite element method computations is reduced to the problem of finding of optimal element partition trees. Given a two dimensional h refined mesh, we find all optimal element partition trees by using the dynamic programming approach. An element partition tree defines a prescribed order of elimination of degrees of freedom over the mesh. We utilize three different metrics to estimate the quality of the element partition tree. As the first criterion we consider the number of floating point operations(FLOPs) performed by the multi-frontal solver. As the second criterion we consider the number of memory transfers (MEMOPS) performed by the multi-frontal solver algorithm. As the third criterion we consider memory usage (NONZEROS) of the multi-frontal direct solver. We show the optimization results for FLOPs vs MEMOPS as well as for the execution time estimated as FLOPs+100MEMOPS vs NONZEROS. We obtain Pareto fronts with multiple optimal trees, for each mesh, and for each refinement level. We generate a library of optimal elimination trees for small grids with local singularities. We also propose an algorithm that for a given large mesh with identified local sub-grids, each one with local singularity. We compute Schur complements over the sub-grids using the optimal trees from the library, and we submit the sequence of Schur complements into the iterative solver ILUPCG.

Nonlinear magnetohydrodynamics simulation using high-order finite elements

International Nuclear Information System (INIS)

Plimpton, Steven James; Schnack, D.D.; Tarditi, A.; Chu, M.S.; Gianakon, T.A.; Kruger, S.E.; Nebel, R.A.; Barnes, D.C.; Sovinec, C.R.; Glasser, A.H.

2005-01-01

A conforming representation composed of 2D finite elements and finite Fourier series is applied to 3D nonlinear non-ideal magnetohydrodynamics using a semi-implicit time-advance. The self-adjoint semi-implicit operator and variational approach to spatial discretization are synergistic and enable simulation in the extremely stiff conditions found in high temperature plasmas without sacrificing the geometric flexibility needed for modeling laboratory experiments. Growth rates for resistive tearing modes with experimentally relevant Lundquist number are computed accurately with time-steps that are large with respect to the global Alfven time and moderate spatial resolution when the finite elements have basis functions of polynomial degree (p) two or larger. An error diffusion method controls the generation of magnetic divergence error. Convergence studies show that this approach is effective for continuous basis functions with p (ge) 2, where the number of test functions for the divergence control terms is less than the number of degrees of freedom in the expansion for vector fields. Anisotropic thermal conduction at realistic ratios of parallel to perpendicular conductivity (x(parallel)/x(perpendicular)) is computed accurately with p (ge) 3 without mesh alignment. A simulation of tearing-mode evolution for a shaped toroidal tokamak equilibrium demonstrates the effectiveness of the algorithm in nonlinear conditions, and its results are used to verify the accuracy of the numerical anisotropic thermal conduction in 3D magnetic topologies.

Finite element analysis of trabecular bone structures : a comparison of image-based meshing techniques

NARCIS (Netherlands)

Ulrich, D.; Rietbergen, van B.; Weinans, H.; Rüegsegger, P.

1998-01-01

In this study, we investigate if finite element (FE) analyses of human trabecular bone architecture based on 168 microm images can provide relevant information about the bone mechanical characteristics. Three human trabecular bone samples, one taken from the femoral head, one from the iliac crest,

Finite element investigation of explosively formed projectiles (EFP)

International Nuclear Information System (INIS)

Ahmad, I.

1999-01-01

This thesis report represents the numerical simulation of explosively formed projectiles (EFP), a type of linear self-forging fragment device. The simulation is performed using a finite element code DYNA2D. It also explicates that how the shape, velocity and kinetic energy of an explosively formed projectile is effected by various parameters. Different parameters investigated are mesh density, material, thickness, contour and types of liner. Effect of shape of casing and material model is also analyzed. The shapes of projectiles at different times after detonation are shown. The maximum velocity and kinetic energy of the projectile have been used to ascertain the effect of above mentioned parameters. (author)

Computable error estimates for Monte Carlo finite element approximation of elliptic PDE with lognormal diffusion coefficients

KAUST Repository

Hall, Eric

2016-01-09

The Monte Carlo (and Multi-level Monte Carlo) finite element method can be used to approximate observables of solutions to diffusion equations with lognormal distributed diffusion coefficients, e.g. modeling ground water flow. Typical models use lognormal diffusion coefficients with H´ older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible and can be larger than the computable low frequency error. We address how the total error can be estimated by the computable error.

Studies on the numerical solution of three-dimensional stationary diffusion equations using the finite element method

International Nuclear Information System (INIS)

Franke, H.P.

1976-05-01

The finite element method is applied to the solution of the stationary 3D group diffusion equations. For this, a programme system with the name of FEM3D is established which also includes a module for semi-automatic mesh generation. Tetrahedral finite elements are used. The neutron fluxes are described by complete first- or second-order Lagrangian polynomials. General homogeneous boundary conditions are allowed. The studies show that realistic three-dimensional problems can be solved at less expense by iterative methods, in particular so when especially adapted matrix handling and storage schemes are used efficiently. (orig./RW) [de

3D CSEM inversion based on goal-oriented adaptive finite element method

Science.gov (United States)

Zhang, Y.; Key, K.

2016-12-01

We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with

Eigenvalue solutions in finite element thermal transient problems

International Nuclear Information System (INIS)

Stoker, J.R.

1975-01-01

The eigenvalue economiser concept can be useful in solving large finite element transient heat flow problems in which the boundary heat transfer coefficients are constant. The usual economiser theory is equivalent to applying a unit thermal 'force' to each of a small sub-set of nodes on the finite element mesh, and then calculating sets of resulting steady state temperatures. Subsequently it is assumed that the required transient temperature distributions can be approximated by a linear combination of this comparatively small set of master temperatures. The accuracy of a reduced eigenvalue calculation depends upon a good choice of master nodes, which presupposes at least a little knowledge about what sort of shape is expected in the unknown temperature distributions. There are some instances, however, where a reasonably good idea exists of the required shapes, permitting a modification to the economiser process which leads to greater economy in the number of master temperatures. The suggested new approach is to use manually prescribed temperature distributions as the master distributions, rather than using temperatures resulting from unit thermal forces. Thus, with a little pre-knowledge one may write down a set of master distributions which, as a linear combination, can represent the required solution over the range of interest to a reasonable engineering accuracy, and using the minimum number of variables. The proposed modified eigenvalue economiser technique then uses the master distributions in an automatic way to arrive at the required solution. The technique is illustrated by some simple finite element examples

Feature-Sensitive Tetrahedral Mesh Generation with Guaranteed Quality

OpenAIRE

Wang, Jun; Yu, Zeyun

2012-01-01

Tetrahedral meshes are being extensively used in finite element methods (FEM). This paper proposes an algorithm to generate feature-sensitive and high-quality tetrahedral meshes from an arbitrary surface mesh model. A top-down octree subdivision is conducted on the surface mesh and a set of tetrahedra are constructed using adaptive body-centered cubic (BCC) lattices. Special treatments are given to the tetrahedra near the surface such that the quality of the resulting tetrahedral mesh is prov...

Non-linear finite element analyses of wide plate fracture mechanics experiments

International Nuclear Information System (INIS)

Harrop, L.P.; Gibson, S.

1988-06-01

A series of centre-cracked, wide plate fracture mechanics tests is being conducted with plates made from 0.36% carbon steel. This report gives an account of post-test finite element analyses performed to compare with the results of one of these tests (designated CSTP4) and a pre-test analysis of the next test which has a slightly different geometry (CSTP5). The plates are relatively thick (75mm) and have a width of 1.62m. The finite element analyses use a two-dimensional plane stress mesh. The work shows good agreement between the post-test analysis results and the overall experimental results for CSTP4. It is not expected that the analysis results will be accurate within the dimensions of the process zone ahead of the crack tip; the mesh is not sufficient for this. A vital ingredient in attaining the good overall agreement is the representation of the actual stress-strain curve of the material. The predicted response of test CSTP5 is markedly different from that of CSTP4 even though the only change is the increase in the height of the plate. In particular the shape and size of the plastic zone ahead of the crack tip is quite different in the two tests at the same nominal remote applied load. (author)

Symplectic finite element scheme: application to a driven problem with a regular singularity

Energy Technology Data Exchange (ETDEWEB)

Pletzer, A. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)

1996-02-01

A new finite element (FE) scheme, based on the decomposition of a second order differential equation into a set of first order symplectic (Hamiltonian) equations, is presented and tested on one-dimensional, driven Sturm-Liouville problem. Error analysis shows improved cubic convergence in the energy norm for piecewise linear `tent` elements, as compared to quadratic convergence for the standard and hybrid FE methods. The convergence deteriorates in the presence of a regular singular point, but can be recovered by appropriate mesh node packing. Optimal mesh packing exponents are derived to ensure cubic (respectively quadratic) convergence with minimal numerical error. A further suppression of the numerical error by a factor proportional to the square of the leading exponent of the singular solution, is achieved for a model problem based on determining the nonideal magnetohydrodynamic stability of a fusion plasma. (author) 7 figs., 14 refs.

Symplectic finite element scheme: application to a driven problem with a regular singularity

International Nuclear Information System (INIS)

Pletzer, A.

1996-02-01

A new finite element (FE) scheme, based on the decomposition of a second order differential equation into a set of first order symplectic (Hamiltonian) equations, is presented and tested on one-dimensional, driven Sturm-Liouville problem. Error analysis shows improved cubic convergence in the energy norm for piecewise linear 'tent' elements, as compared to quadratic convergence for the standard and hybrid FE methods. The convergence deteriorates in the presence of a regular singular point, but can be recovered by appropriate mesh node packing. Optimal mesh packing exponents are derived to ensure cubic (respectively quadratic) convergence with minimal numerical error. A further suppression of the numerical error by a factor proportional to the square of the leading exponent of the singular solution, is achieved for a model problem based on determining the nonideal magnetohydrodynamic stability of a fusion plasma. (author) 7 figs., 14 refs

Adaptive Multilevel Methods with Local Smoothing for $H^1$- and $H^{\\mathrm{curl}}$-Conforming High Order Finite Element Methods

KAUST Repository

Janssen, Bärbel

2011-01-01

A multilevel method on adaptive meshes with hanging nodes is presented, and the additional matrices appearing in the implementation are derived. Smoothers of overlapping Schwarz type are discussed; smoothing is restricted to the interior of the subdomains refined to the current level; thus it has optimal computational complexity. When applied to conforming finite element discretizations of elliptic problems and Maxwell equations, the method\\'s convergence rates are very close to those for the nonadaptive version. Furthermore, the smoothers remain efficient for high order finite elements. We discuss the implementation in a general finite element code using the example of the deal.II library. © 2011 Societ y for Industrial and Applied Mathematics.

A maximum-principle preserving finite element method for scalar conservation equations

KAUST Repository

Guermond, Jean-Luc; Nazarov, Murtazo

2014-01-01

This paper introduces a first-order viscosity method for the explicit approximation of scalar conservation equations with Lipschitz fluxes using continuous finite elements on arbitrary grids in any space dimension. Provided the lumped mass matrix is positive definite, the method is shown to satisfy the local maximum principle under a usual CFL condition. The method is independent of the cell type; for instance, the mesh can be a combination of tetrahedra, hexahedra, and prisms in three space dimensions. © 2014 Elsevier B.V.

A maximum-principle preserving finite element method for scalar conservation equations

KAUST Repository

Guermond, Jean-Luc

2014-04-01

This paper introduces a first-order viscosity method for the explicit approximation of scalar conservation equations with Lipschitz fluxes using continuous finite elements on arbitrary grids in any space dimension. Provided the lumped mass matrix is positive definite, the method is shown to satisfy the local maximum principle under a usual CFL condition. The method is independent of the cell type; for instance, the mesh can be a combination of tetrahedra, hexahedra, and prisms in three space dimensions. © 2014 Elsevier B.V.

Lagrangian and Eulerian finite element techniques for transient fluid-structure interaction problems

International Nuclear Information System (INIS)

Donea, J.; Fasoli-Stella, P.; Giuliani, S.

1977-01-01

The basic finite element equations for transient compressible fluid flow are presented in a form that allows the elements to be moved with the fluid in normal Lagrangian fashion, to be held fixed in a Eulerian manner, or to be moved in some arbitrarily specified way. The co-existence of Lagrangian and Eulerian regions within the finite element mesh will permit to handle greater distortions in the fluid motion than would be allowed by a purely Lagrangian method, with more resolution than is afforded by a purely Eulerian method. To achieve a mixed formulation, the conservation statements of mass, momentum and energy are expressed in integral form over a reference volume whose surface may be moving with an arbitrarily prescribed velocity. Direct use can be made of the integral forms of the mass and energy equations to adjust the element density and specific internal energy. The Galerkin process is employed to formulate a variational statement associated with the momentum equation. The difficulties associated with the presence of convective terms in the conservation equations are handled by expressing transports of mass, momentum and energy terms of intermediate velocities derived at each cycle from the previous cycle velocities and accelerations. The hydrodynamic elements presented are triangles, quadrilaterals with constant pressure and density. The finite element equations associated with these elements are described in the necessary detail. Numerical results are presented based on purely Lagrangian, purely Eulerian and mixed formulations. Simple problems with analytic solution are solved first to show the validity and accuracy of the proposed mixed finite element formulation. Then, practical problems are illustrated in the field of fast reactor safety analysis

Simplified Qualitative Discrete Numerical Model to Determine Cracking Pattern in Brittle Materials by Means of Finite Element Method

OpenAIRE

Ochoa-Avendaño, J.; Garzon-Alvarado, D. A.; Linero, Dorian L.; Cerrolaza, M.

2017-01-01

This paper presents the formulation, implementation, and validation of a simplified qualitative model to determine the crack path of solids considering static loads, infinitesimal strain, and plane stress condition. This model is based on finite element method with a special meshing technique, where nonlinear link elements are included between the faces of the linear triangular elements. The stiffness loss of some link elements represents the crack opening. Three experimental tests of bending...

Mechanical stress calculations for toroidal field coils by the finite element method

International Nuclear Information System (INIS)

Soell, M.; Jandl, O.; Gorenflo, H.

1976-09-01

After discussing fundamental relationships of the finite element method, this report describes the calculation steps worked out for mechanical stress calculations in the case of magnetic forces and forces produced by thermal expansion or compression of toroidal field coils using the SOLID SAP IV computer program. The displacement and stress analysis are based on the 20-node isoparametric solid element. The calculation of the nodal forces produced by magnetic body forces are discussed in detail. The computer programs, which can be used generally for mesh generation and determination of the nodal forces, are published elsewhere. (orig.) [de

A fluid-solid finite element method for the analysis of reactor safety problems

International Nuclear Information System (INIS)

Mitra, Santanu; Kumar, Ashutosh; Sinhamahapatra, K.P.

2006-01-01

The work presented herein can broadly be categorized as a fluid-structure interaction problem. The response of a circular cylindrical structure subjected to cross flow is examined using the finite element method for both the liquid and the structure domains. The cylindrical tube is mounted elastically at the ends and is free to move under the action of the unsteady flow-induced forces. The fluid is considered to be acoustic compressible and viscous. A Galerkin finite element method implemented on a triangular mesh is used to solve the time-dependent Navier-Stokes equations. The cylinder motion is modeled using a five-degrees of freedom generalized shell element structural dynamics model. The numerical simulations of the response of the calandria tubes/pressure tubes, adjustor rod and shut-off rod of a nuclear reactor are presented. A few typical results are presented to assess the accuracy and applicability of the developed modules

Compatible-strain mixed finite element methods for incompressible nonlinear elasticity

Science.gov (United States)

Faghih Shojaei, Mostafa; Yavari, Arash

2018-05-01

We introduce a new family of mixed finite elements for incompressible nonlinear elasticity - compatible-strain mixed finite element methods (CSFEMs). Based on a Hu-Washizu-type functional, we write a four-field mixed formulation with the displacement, the displacement gradient, the first Piola-Kirchhoff stress, and a pressure-like field as the four independent unknowns. Using the Hilbert complexes of nonlinear elasticity, which describe the kinematics and the kinetics of motion, we identify the solution spaces of the independent unknown fields. In particular, we define the displacement in H1, the displacement gradient in H (curl), the stress in H (div), and the pressure field in L2. The test spaces of the mixed formulations are chosen to be the same as the corresponding solution spaces. Next, in a conforming setting, we approximate the solution and the test spaces with some piecewise polynomial subspaces of them. Among these approximation spaces are the tensorial analogues of the Nédélec and Raviart-Thomas finite element spaces of vector fields. This approach results in compatible-strain mixed finite element methods that satisfy both the Hadamard compatibility condition and the continuity of traction at the discrete level independently of the refinement level of the mesh. By considering several numerical examples, we demonstrate that CSFEMs have a good performance for bending problems and for bodies with complex geometries. CSFEMs are capable of capturing very large strains and accurately approximating stress and pressure fields. Using CSFEMs, we do not observe any numerical artifacts, e.g., checkerboarding of pressure, hourglass instability, or locking in our numerical examples. Moreover, CSFEMs provide an efficient framework for modeling heterogeneous solids.

ImageParser: a tool for finite element generation from three-dimensional medical images

Directory of Open Access Journals (Sweden)

Yamada T

2004-10-01

Full Text Available Abstract Background The finite element method (FEM is a powerful mathematical tool to simulate and visualize the mechanical deformation of tissues and organs during medical examinations or interventions. It is yet a challenge to build up an FEM mesh directly from a volumetric image partially because the regions (or structures of interest (ROIs may be irregular and fuzzy. Methods A software package, ImageParser, is developed to generate an FEM mesh from 3-D tomographic medical images. This software uses a semi-automatic method to detect ROIs from the context of image including neighboring tissues and organs, completes segmentation of different tissues, and meshes the organ into elements. Results The ImageParser is shown to build up an FEM model for simulating the mechanical responses of the breast based on 3-D CT images. The breast is compressed by two plate paddles under an overall displacement as large as 20% of the initial distance between the paddles. The strain and tangential Young's modulus distributions are specified for the biomechanical analysis of breast tissues. Conclusion The ImageParser can successfully exact the geometry of ROIs from a complex medical image and generate the FEM mesh with customer-defined segmentation information.

MP Salsa: a finite element computer program for reacting flow problems. Part 1--theoretical development

Energy Technology Data Exchange (ETDEWEB)

Shadid, J.N.; Moffat, H.K.; Hutchinson, S.A.; Hennigan, G.L.; Devine, K.D.; Salinger, A.G.

1996-05-01

The theoretical background for the finite element computer program, MPSalsa, is presented in detail. MPSalsa is designed to solve laminar, low Mach number, two- or three-dimensional incompressible and variable density reacting fluid flows on massively parallel computers, using a Petrov-Galerkin finite element formulation. The code has the capability to solve coupled fluid flow, heat transport, multicomponent species transport, and finite-rate chemical reactions, and to solver coupled multiple Poisson or advection-diffusion- reaction equations. The program employs the CHEMKIN library to provide a rigorous treatment of multicomponent ideal gas kinetics and transport. Chemical reactions occurring in the gas phase and on surfaces are treated by calls to CHEMKIN and SURFACE CHEMKIN, respectively. The code employs unstructured meshes, using the EXODUS II finite element data base suite of programs for its input and output files. MPSalsa solves both transient and steady flows by using fully implicit time integration, an inexact Newton method and iterative solvers based on preconditioned Krylov methods as implemented in the Aztec solver library.

Conforming to interface structured adaptive mesh refinement: 3D algorithm and implementation

Science.gov (United States)

Nagarajan, Anand; Soghrati, Soheil

2018-03-01

A new non-iterative mesh generation algorithm named conforming to interface structured adaptive mesh refinement (CISAMR) is introduced for creating 3D finite element models of problems with complex geometries. CISAMR transforms a structured mesh composed of tetrahedral elements into a conforming mesh with low element aspect ratios. The construction of the mesh begins with the structured adaptive mesh refinement of elements in the vicinity of material interfaces. An r-adaptivity algorithm is then employed to relocate selected nodes of nonconforming elements, followed by face-swapping a small fraction of them to eliminate tetrahedrons with high aspect ratios. The final conforming mesh is constructed by sub-tetrahedralizing remaining nonconforming elements, as well as tetrahedrons with hanging nodes. In addition to studying the convergence and analyzing element-wise errors in meshes generated using CISAMR, several example problems are presented to show the ability of this method for modeling 3D problems with intricate morphologies.

Modular 3-D solid finite element model for fatigue analyses of a PWR coolant system

International Nuclear Information System (INIS)

Garrido, Oriol Costa; Cizelj, Leon; Simonovski, Igor

2012-01-01

Highlights: ► A 3-D model of a reactor coolant system for fatigue usage assessment. ► The performed simulations are a heat transfer and stress analyses. ► The main results are the expected ranges of fatigue loadings. - Abstract: The extension of operational licenses of second generation pressurized water reactor (PWR) nuclear power plants depends to a large extent on the analyses of fatigue usage of the reactor coolant pressure boundary. The reliable estimation of the fatigue usage requires detailed thermal and stress analyses of the affected components. Analyses, based upon the in-service transient loads should be compared to the loads analyzed at the design stage. The thermal and stress transients can be efficiently analyzed using the finite element method. This requires that a 3-D solid model of a given system is discretized with finite elements (FE). The FE mesh density is crucial for both the accuracy and the cost of the analysis. The main goal of the paper is to propose a set of computational tools which assist a user in a deployment of modular spatial FE model of main components of a typical reactor coolant system, e.g., pipes, pressure vessels and pumps. The modularity ensures that the components can be analyzed individually or in a system. Also, individual components can be meshed with different mesh densities, as required by the specifics of the particular transient studied. For optimal accuracy, all components are meshed with hexahedral elements with quadratic interpolation. The performance of the model is demonstrated with simulations performed with a complete two-loop PWR coolant system (RCS). Heat transfer analysis and stress analysis for a complete loading and unloading cycle of the RCS are performed. The main results include expected ranges of fatigue loading for the pipe lines and coolant pump components under the given conditions.

On accuracy of the wave finite element predictions of wavenumbers and power flow: A benchmark problem

Science.gov (United States)

Søe-Knudsen, Alf; Sorokin, Sergey

2011-06-01

This rapid communication is concerned with justification of the 'rule of thumb', which is well known to the community of users of the finite element (FE) method in dynamics, for the accuracy assessment of the wave finite element (WFE) method. An explicit formula linking the size of a window in the dispersion diagram, where the WFE method is trustworthy, with the coarseness of a FE mesh employed is derived. It is obtained by the comparison of the exact Pochhammer-Chree solution for an elastic rod having the circular cross-section with its WFE approximations. It is shown that the WFE power flow predictions are also valid within this window.

A robust and efficient finite volume scheme for the discretization of diffusive flux on extremely skewed meshes in complex geometries

Science.gov (United States)

Traoré, Philippe; Ahipo, Yves Marcel; Louste, Christophe

2009-08-01

In this paper an improved finite volume scheme to discretize diffusive flux on a non-orthogonal mesh is proposed. This approach, based on an iterative technique initially suggested by Khosla [P.K. Khosla, S.G. Rubin, A diagonally dominant second-order accurate implicit scheme, Computers and Fluids 2 (1974) 207-209] and known as deferred correction, has been intensively utilized by Muzaferija [S. Muzaferija, Adaptative finite volume method for flow prediction using unstructured meshes and multigrid approach, Ph.D. Thesis, Imperial College, 1994] and later Fergizer and Peric [J.H. Fergizer, M. Peric, Computational Methods for Fluid Dynamics, Springer, 2002] to deal with the non-orthogonality of the control volumes. Using a more suitable decomposition of the normal gradient, our scheme gives accurate solutions in geometries where the basic idea of Muzaferija fails. First the performances of both schemes are compared for a Poisson problem solved in quadrangular domains where control volumes are increasingly skewed in order to test their robustness and efficiency. It is shown that convergence properties and the accuracy order of the solution are not degraded even on extremely skewed mesh. Next, the very stable behavior of the method is successfully demonstrated on a randomly distorted grid as well as on an anisotropically distorted one. Finally we compare the solution obtained for quadrilateral control volumes to the ones obtained with a finite element code and with an unstructured version of our finite volume code for triangular control volumes. No differences can be observed between the different solutions, which demonstrates the effectiveness of our approach.

Computational performance of Free Mesh Method applied to continuum mechanics problems

Science.gov (United States)

YAGAWA, Genki

2011-01-01

The free mesh method (FMM) is a kind of the meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, or a node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm. The aim of the present paper is to review some unique numerical solutions of fluid and solid mechanics by employing FMM as well as the Enriched Free Mesh Method (EFMM), which is a new version of FMM, including compressible flow and sounding mechanism in air-reed instruments as applications to fluid mechanics, and automatic remeshing for slow crack growth, dynamic behavior of solid as well as large-scale Eigen-frequency of engine block as applications to solid mechanics. PMID:21558753

Finite-Element 2D and 3D PIC Modeling of RF Devices with Applications to Multipacting

CERN Document Server

De Ford, John F; Petillo, John

2005-01-01

Multipacting currently limits the performance of many high power radio-frequency (RF) devices, particularly couplers and windows. Models have helped researchers understand and mitigate this problem in 2D structures, but useful multipacting models for complicated 3D structures are still a challenge. A combination of three recent technologies that have been developed in the Analyst and MICHELLE codes begin to address this challenge: high-order adaptive finite-element RF field calculations, advanced particle tracking on unstructured grids, and comprehensive secondary emission models. Analyst employs high-order adaptive finite-element methods to accurately compute driven RF fields and eigenmodes in complex geometries, particularly near edges, corners, and curved surfaces. To perform a multipacting analysis, we use the mesh and fields from Analyst in a modified version of the self-consistent, finite-element gun code MICHELLE. MICHELLE has both a fast, accurate, and reliable particle tracker for unstructured grids ...

Finite element computational fluid mechanics

International Nuclear Information System (INIS)

Baker, A.J.

1983-01-01

This book analyzes finite element theory as applied to computational fluid mechanics. It includes a chapter on using the heat conduction equation to expose the essence of finite element theory, including higher-order accuracy and convergence in a common knowledge framework. Another chapter generalizes the algorithm to extend application to the nonlinearity of the Navier-Stokes equations. Other chapters are concerned with the analysis of a specific fluids mechanics problem class, including theory and applications. Some of the topics covered include finite element theory for linear mechanics; potential flow; weighted residuals/galerkin finite element theory; inviscid and convection dominated flows; boundary layers; parabolic three-dimensional flows; and viscous and rotational flows

Evaluating the performance of the particle finite element method in parallel architectures

Science.gov (United States)

Gimenez, Juan M.; Nigro, Norberto M.; Idelsohn, Sergio R.

2014-05-01

This paper presents a high performance implementation for the particle-mesh based method called particle finite element method two (PFEM-2). It consists of a material derivative based formulation of the equations with a hybrid spatial discretization which uses an Eulerian mesh and Lagrangian particles. The main aim of PFEM-2 is to solve transport equations as fast as possible keeping some level of accuracy. The method was found to be competitive with classical Eulerian alternatives for these targets, even in their range of optimal application. To evaluate the goodness of the method with large simulations, it is imperative to use of parallel environments. Parallel strategies for Finite Element Method have been widely studied and many libraries can be used to solve Eulerian stages of PFEM-2. However, Lagrangian stages, such as streamline integration, must be developed considering the parallel strategy selected. The main drawback of PFEM-2 is the large amount of memory needed, which limits its application to large problems with only one computer. Therefore, a distributed-memory implementation is urgently needed. Unlike a shared-memory approach, using domain decomposition the memory is automatically isolated, thus avoiding race conditions; however new issues appear due to data distribution over the processes. Thus, a domain decomposition strategy for both particle and mesh is adopted, which minimizes the communication between processes. Finally, performance analysis running over multicore and multinode architectures are presented. The Courant-Friedrichs-Lewy number used influences the efficiency of the parallelization and, in some cases, a weighted partitioning can be used to improve the speed-up. However the total cputime for cases presented is lower than that obtained when using classical Eulerian strategies.

Elastic-plastic finite element analyses for reducers with constant-depth internal circumferential surface cracks

International Nuclear Information System (INIS)

Wu, Szu-Ying; Tsai, Bor-Jiun; Chen, Jien-Jong

2015-01-01

In this study, a 3-D automatic elastic-plastic finite element mesh generator is established to accurately predict the J-integral value of an arbitrary reducer with a constant-depth internal circumferential surface crack under bending and axial force. The contact pairs are used on the crack surfaces to simulate the actual contact behaviors of the crack model under loadings. In order to verify the accuracy of the proposed elastic-plastic finite element model for a reducer with a surface crack, the cracked straight pipe models are generated according to a special modeling procedure for a flawed reducer. The J-integral values along the crack front of surface crack are calculated and compared with the straight pipe models which have been verified in the previous published studies. Based on the comparison of computed results, good agreements are obtained to show the accuracy of present numerical models. More confidence on using the 3-D elastic-plastic finite element analysis for reducers with internal circumferential surface cracks can be thus established in this work

Fiber-reinforced materials: finite elements for the treatment of the inextensibility constraint

Science.gov (United States)

Auricchio, Ferdinando; Scalet, Giulia; Wriggers, Peter

2017-12-01

The present paper proposes a numerical framework for the analysis of problems involving fiber-reinforced anisotropic materials. Specifically, isotropic linear elastic solids, reinforced by a single family of inextensible fibers, are considered. The kinematic constraint equation of inextensibility in the fiber direction leads to the presence of an undetermined fiber stress in the constitutive equations. To avoid locking-phenomena in the numerical solution due to the presence of the constraint, mixed finite elements based on the Lagrange multiplier, perturbed Lagrangian, and penalty method are proposed. Several boundary-value problems under plane strain conditions are solved and numerical results are compared to analytical solutions, whenever the derivation is possible. The performed simulations allow to assess the performance of the proposed finite elements and to discuss several features of the developed formulations concerning the effective approximation for the displacement and fiber stress fields, mesh convergence, and sensitivity to penalty parameters.

Spectral decomposition in advection-diffusion analysis by finite element methods

International Nuclear Information System (INIS)

Nickell, R.E.; Gartling, D.K.; Strang, G.

1978-01-01

In a recent study of the convergence properties of finite element methods in nonlinear fluid mechanics, an indirect approach was taken. A two-dimensional example with a known exact solution was chosen as the vehicle for the study, and various mesh refinements were tested in an attempt to extract information on the effect of the local Reynolds number. However, more direct approaches are usually preferred. In this study one such direct approach is followed, based upon the spectral decomposition of the solution operator. Spectral decomposition is widely employed as a solution technique for linear structural dynamics problems and can be applied readily to linear, transient heat transfer analysis; in this case, the extension to nonlinear problems is of interest. It was shown previously that spectral techniques were applicable to stiff systems of rate equations, while recent studies of geometrically and materially nonlinear structural dynamics have demonstrated the increased information content of the numerical results. The use of spectral decomposition in nonlinear problems of heat and mass transfer would be expected to yield equally increased flow of information to the analyst, and this information could include a quantitative comparison of various solution strategies, meshes, and element hierarchies

A parallel finite element procedure for contact-impact problems using edge-based smooth triangular element and GPU

Science.gov (United States)

Cai, Yong; Cui, Xiangyang; Li, Guangyao; Liu, Wenyang

2018-04-01

The edge-smooth finite element method (ES-FEM) can improve the computational accuracy of triangular shell elements and the mesh partition efficiency of complex models. In this paper, an approach is developed to perform explicit finite element simulations of contact-impact problems with a graphical processing unit (GPU) using a special edge-smooth triangular shell element based on ES-FEM. Of critical importance for this problem is achieving finer-grained parallelism to enable efficient data loading and to minimize communication between the device and host. Four kinds of parallel strategies are then developed to efficiently solve these ES-FEM based shell element formulas, and various optimization methods are adopted to ensure aligned memory access. Special focus is dedicated to developing an approach for the parallel construction of edge systems. A parallel hierarchy-territory contact-searching algorithm (HITA) and a parallel penalty function calculation method are embedded in this parallel explicit algorithm. Finally, the program flow is well designed, and a GPU-based simulation system is developed, using Nvidia's CUDA. Several numerical examples are presented to illustrate the high quality of the results obtained with the proposed methods. In addition, the GPU-based parallel computation is shown to significantly reduce the computing time.

3D controlled-source electromagnetic modeling in anisotropic medium using edge-based finite element method

DEFF Research Database (Denmark)

Cai, Hongzhu; Xiong, Bin; Han, Muran

2014-01-01

This paper presents a linear edge-based finite element method for numerical modeling of 3D controlled-source electromagnetic data in an anisotropic conductive medium. We use a nonuniform rectangular mesh in order to capture the rapid change of diffusive electromagnetic field within the regions of...... are in a good agreement with the solutions obtained by the integral equation method....

Superconvergence of mixed finite element approximations to 3-D Maxwell's equations in metamaterials

KAUST Repository

Huang, Yunqing

2011-09-01

Numerical simulation of metamaterials has attracted more and more attention since 2000, after the first metamaterial with negative refraction index was successfully constructed. In this paper we construct a fully-discrete leap-frog type finite element scheme to solve the three-dimensional time-dependent Maxwell\\'s equations when metamaterials are involved. First, we obtain some superclose results between the interpolations of the analytical solutions and finite element solutions obtained using arbitrary orders of Raviart-Thomas-Nédélec mixed spaces on regular cubic meshes. Then we prove the superconvergence result in the discrete l2 norm achieved for the lowest-order Raviart-Thomas-Nédélec space. To our best knowledge, such superconvergence results have never been obtained elsewhere. Finally, we implement the leap-frog scheme and present numerical results justifying our theoretical analysis. © 2011 Elsevier Inc.

Superconvergence of mixed finite element approximations to 3-D Maxwell's equations in metamaterials

KAUST Repository

Huang, Yunqing; Li, Jichun; Yang, Wei; Sun, Shuyu

2011-01-01

Numerical simulation of metamaterials has attracted more and more attention since 2000, after the first metamaterial with negative refraction index was successfully constructed. In this paper we construct a fully-discrete leap-frog type finite element scheme to solve the three-dimensional time-dependent Maxwell's equations when metamaterials are involved. First, we obtain some superclose results between the interpolations of the analytical solutions and finite element solutions obtained using arbitrary orders of Raviart-Thomas-Nédélec mixed spaces on regular cubic meshes. Then we prove the superconvergence result in the discrete l2 norm achieved for the lowest-order Raviart-Thomas-Nédélec space. To our best knowledge, such superconvergence results have never been obtained elsewhere. Finally, we implement the leap-frog scheme and present numerical results justifying our theoretical analysis. © 2011 Elsevier Inc.

A piecewise bi-linear discontinuous finite element spatial discretization of the Sn transport equation

International Nuclear Information System (INIS)

Bailey, Teresa S.; Warsa, James S.; Chang, Jae H.; Adams, Marvin L.

2011-01-01

We present a new spatial discretization of the discrete-ordinates transport equation in two dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretization that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems. (author)

A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

International Nuclear Information System (INIS)

Bailey, T.S.; Chang, J.H.; Warsa, J.S.; Adams, M.L.

2010-01-01

We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.

A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

Energy Technology Data Exchange (ETDEWEB)

Bailey, T S; Chang, J H; Warsa, J S; Adams, M L

2010-12-22

We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.

Electromagnetic Extended Finite Elements for High-Fidelity Multimaterial Problems LDRD Final Report

Energy Technology Data Exchange (ETDEWEB)

Siefert, Christopher [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bochev, Pavel Blagoveston [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Kramer, Richard Michael Jack [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Voth, Thomas Eugene [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Cox, James [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2014-09-01

Surface effects are critical to the accurate simulation of electromagnetics (EM) as current tends to concentrate near material surfaces. Sandia EM applications, which include exploding bridge wires for detonator design, electromagnetic launch of flyer plates for material testing and gun design, lightning blast-through for weapon safety, electromagnetic armor, and magnetic flux compression generators, all require accurate resolution of surface effects. These applications operate in a large deformation regime, where body-fitted meshes are impractical and multimaterial elements are the only feasible option. State-of-the-art methods use various mixture models to approximate the multi-physics of these elements. The empirical nature of these models can significantly compromise the accuracy of the simulation in this very important surface region. We propose to substantially improve the predictive capability of electromagnetic simulations by removing the need for empirical mixture models at material surfaces. We do this by developing an eXtended Finite Element Method (XFEM) and an associated Conformal Decomposition Finite Element Method (CDFEM) which satisfy the physically required compatibility conditions at material interfaces. We demonstrate the effectiveness of these methods for diffusion and diffusion-like problems on node, edge and face elements in 2D and 3D. We also present preliminary work on h -hierarchical elements and remap algorithms.

Finite element modelling of the creep deformation of T91 steel weldments at 600 C

Energy Technology Data Exchange (ETDEWEB)

Bhadrui, A.K. [Indira Gandhi Centre for Atomic Research, Kalpakkam (India); Gaudig, W. [Stuttgart Univ. (Germany). Staatliche Materialpruefungsanstalt; Theofel, H. [Stuttgart Univ. (Germany). Staatliche Materialpruefungsanstalt; Maile, K. [Stuttgart Univ. (Germany). Staatliche Materialpruefungsanstalt

1996-05-01

Finite element modelling of the creep deformation of T91 steel weldments, welded using the manual metal arc (MMA) and submerged arc (SA) welding processes, was carried out to predict creep curves for both of the weldments under different stresses and compared with the experimental data. The stress and strain redistribution across the length of the transverse-weld specimens has also been predicted. Data of creep tests at 600 C at stresses between 90-130 MPa for the base metal, the MMA and SA weld metals, and the simulated heat-affected zone were used to determine Garofalo`s equation for creep strain. Finite element meshes for both of the weldments were constructed after calculating the HAZ locations using Rosenthal`s heat flow equation. (orig.)

Band-limited Green's Functions for Quantitative Evaluation of Acoustic Emission Using the Finite Element Method

Science.gov (United States)

Leser, William P.; Yuan, Fuh-Gwo; Leser, William P.

2013-01-01

A method of numerically estimating dynamic Green's functions using the finite element method is proposed. These Green's functions are accurate in a limited frequency range dependent on the mesh size used to generate them. This range can often match or exceed the frequency sensitivity of the traditional acoustic emission sensors. An algorithm is also developed to characterize an acoustic emission source by obtaining information about its strength and temporal dependence. This information can then be used to reproduce the source in a finite element model for further analysis. Numerical examples are presented that demonstrate the ability of the band-limited Green's functions approach to determine the moment tensor coefficients of several reference signals to within seven percent, as well as accurately reproduce the source-time function.

Finite elements and approximation

CERN Document Server

Zienkiewicz, O C

2006-01-01

A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o

A first course in finite elements

CERN Document Server

Fish, Jacob

2007-01-01

Developed from the authors, combined total of 50 years undergraduate and graduate teaching experience, this book presents the finite element method formulated as a general-purpose numerical procedure for solving engineering problems governed by partial differential equations.  Focusing on the formulation and application of the finite element method through the integration of finite element theory, code development, and software application, the book is both introductory and self-contained, as well as being a hands-on experience for any student. This authoritative text on Finite Elements:Adopts

Finite element analysis of fatigue crack closure under plane strain state

International Nuclear Information System (INIS)

Lee, Hak Joo; Kang, Jae Youn; Song, Ji Ho

2004-01-01

An elastic-plastic finite element analysis of fatigue crack closure is performed for plane strain conditions. The stabilization behavior of crack opening level and the effect of mesh size on the crack opening stress are investigated. In order to obtain a stabilized crack opening level for plane strain conditions, the crack must be advanced through approximately four times the initial monotonic plastic zone. The crack opening load tends to increase with the decrease of mesh size. The mesh size nearly equal to the theoretical plane strain cyclic plastic zone size may provide reasonable numerical results comparable with experimental crack opening data. The crack opening behavior is influenced by the crack growth increment and discontinuous opening behavior is observed. A procedure to predict the most appropriate mesh size for different stress ratio is suggested. Crack opening loads predicted by the FE analysis based on the procedure suggested resulted in good agreement with experimental ones within the error of 5 %. Effect of the distance behind the crack tip on the crack opening load determined by the ASTM compliance offset method based on the load-displacement relation and by the rotational offset method based on the load-differential displacement relation is investigated. Optimal gage location and method to determine the crack opening load is suggested

Coarse-mesh method for multidimensional, mixed-lattice diffusion calculations

International Nuclear Information System (INIS)

Dodds, H.L. Jr.; Honeck, H.C.; Hostetler, D.E.

1977-01-01

A coarse-mesh finite difference method has been developed for multidimensional, mixed-lattice reactor diffusion calculations, both statics and kinetics, in hexagonal geometry. Results obtained with the coarse-mesh (CM) method have been compared with a conventional mesh-centered finite difference method and with experiment. The results of this comparison indicate that the accuracy of the CM method for highly heterogeneous (mixed) lattices using one point per hexagonal mesh element (''hex'') is about the same as the conventional method with six points per hex. Furthermore, the computing costs (i.e., central processor unit time and core storage requirements) of the CM method with one point per hex are about the same as the conventional method with one point per hex

Mesh distortion immunity of finite elements and the best-fit paradigm

Indian Academy of Sciences (India)

relatively (and, sometimes, dramatically) poor results. ... why the unsymmetric parametric-metric formulation is effective is because the stress repre- .... competing requirements of managing continuity and equilibrium under mesh distortion to.

[Establishment of a 3D finite element model of human skull using MSCT images and mimics software].

Science.gov (United States)

Huang, Ping; Li, Zheng-dong; Shao, Yu; Zou, Dong-hua; Liu, Ning-guo; Li, Li; Chen, Yuan-yuan; Wan, Lei; Chen, Yi-jiu

2011-02-01

To establish a human 3D finite element skull model, and to explore its value in biomechanics analysis. The cadaveric head was scanned and then 3D skull model was created using Mimics software based on 2D CT axial images. The 3D skull model was optimized by preprocessor along with creation of the surface and volume meshes. The stress changes, after the head was struck by an object or the head hit the ground directly, were analyzed using ANSYS software. The original 3D skull model showed a large number of triangles with a poor quality and high similarity with the real head, while the optimized model showed high quality surface and volume meshes with a small number of triangles comparatively. The model could show the local and global stress changes effectively. The human 3D skull model can be established using MSCT and Mimics software and provides a good finite element model for biomechanics analysis. This model may also provide a base for the study of head stress changes following different forces.

Modelling optimization involving different types of elements in finite element analysis

International Nuclear Information System (INIS)

Wai, C M; Rivai, Ahmad; Bapokutty, Omar

2013-01-01

Finite elements are used to express the mechanical behaviour of a structure in finite element analysis. Therefore, the selection of the elements determines the quality of the analysis. The aim of this paper is to compare and contrast 1D element, 2D element, and 3D element used in finite element analysis. A simple case study was carried out on a standard W460x74 I-beam. The I-beam was modelled and analyzed statically with 1D elements, 2D elements and 3D elements. The results for the three separate finite element models were compared in terms of stresses, deformation and displacement of the I-beam. All three finite element models yield satisfactory results with acceptable errors. The advantages and limitations of these elements are discussed. 1D elements offer simplicity although lacking in their ability to model complicated geometry. 2D elements and 3D elements provide more detail yet sophisticated results which require more time and computer memory in the modelling process. It is also found that the choice of element in finite element analysis is influence by a few factors such as the geometry of the structure, desired analysis results, and the capability of the computer

Application of 3D X-ray CT data sets to finite element analysis

International Nuclear Information System (INIS)

Bossart, P.L.; Martz, H.E.; Brand, H.R.; Hollerbach, K.

1995-01-01

Finite Element Modeling (FEM) is becoming more important as industry drives toward concurrent engineering. A fundamental hindrance to fully exploiting the power of FEM is the human effort required to acquire complex part geometry, particularly as-built geometry, as a FEM mesh. Many Quantitative Non Destructive Evaluation (QNDE) techniques that produce three-dimensional (3D) data sets provide a substantial reduction in the effort required to apply FEM to as-built parts. This paper describes progress at LLNL on the application of 3D X-ray computed tomography (CT) data sets to more rapidly produce high-quality FEM meshes of complex, as-built geometries. Issues related to the volume segmentation of the 3D CT data as well as the use of this segmented data to tailor generic hexahedral FEM meshes to part specific geometries are discussed. The application of these techniques to FEM analysis in the medical field is reported here

On mesh refinement and accuracy of numerical solutions

NARCIS (Netherlands)

Zhou, Hong; Peters, Maria; van Oosterom, Adriaan

1993-01-01

This paper investigates mesh refinement and its relation with the accuracy of the boundary element method (BEM) and the finite element method (FEM). TO this end an isotropic homogeneous spherical volume conductor, for which the analytical solution is available, wag used. The numerical results

High speed finite element simulations on the graphics card

Energy Technology Data Exchange (ETDEWEB)

Huthwaite, P.; Lowe, M. J. S. [Department of Mechanical Engineering, Imperial College, London, SW7 2AZ (United Kingdom)

2014-02-18

A software package is developed to perform explicit time domain finite element simulations of ultrasonic propagation on the graphical processing unit, using Nvidia’s CUDA. Of critical importance for this problem is the arrangement of nodes in memory, allowing data to be loaded efficiently and minimising communication between the independently executed blocks of threads. The initial stage of memory arrangement is partitioning the mesh; both a well established ‘greedy’ partitioner and a new, more efficient ‘aligned’ partitioner are investigated. A method is then developed to efficiently arrange the memory within each partition. The technique is compared to a commercial CPU equivalent, demonstrating an overall speedup of at least 100 for a non-destructive testing weld model.

High speed finite element simulations on the graphics card

International Nuclear Information System (INIS)

Huthwaite, P.; Lowe, M. J. S.

2014-01-01

A software package is developed to perform explicit time domain finite element simulations of ultrasonic propagation on the graphical processing unit, using Nvidia’s CUDA. Of critical importance for this problem is the arrangement of nodes in memory, allowing data to be loaded efficiently and minimising communication between the independently executed blocks of threads. The initial stage of memory arrangement is partitioning the mesh; both a well established ‘greedy’ partitioner and a new, more efficient ‘aligned’ partitioner are investigated. A method is then developed to efficiently arrange the memory within each partition. The technique is compared to a commercial CPU equivalent, demonstrating an overall speedup of at least 100 for a non-destructive testing weld model

On the time-stepping stability of continuous mass-lumped and discontinuous Galerkin finite elements for the 3D acoustic wave equation

NARCIS (Netherlands)

Zhebel, E.; Minisini, S.; Mulder, W.A.

2012-01-01

We solve the three-dimensional acoustic wave equation, discretized on tetrahedral meshes. Two methods are considered: mass-lumped continuous finite elements and the symmetric interior-penalty discontinuous Galerkin method (SIP-DG). Combining the spatial discretization with the leap-frog

Three-dimensional geometric model of the middle segment of the thoracic spine based on graphical images for finite element analysis

Directory of Open Access Journals (Sweden)

Rozilene Maria Cota Aroeira

2017-05-01

Full Text Available Abstract Introduction: Biomedical studies involve complex anatomical structures, which require specific methodology to generate their geometric models. The middle segment of the thoracic spine (T5-T10 is the site of the highest incidence of vertebral deformity in adolescents. Traditionally, its geometries are derived from computed tomography or magnetic resonance imaging data. However, this approach may restrict certain studies. The study aimed to generate two 3D geometric model of the T5-T10 thoracic spine segment, obtained from graphical images, and to create mesh for finite element studies. Methods A 3D geometric model of T5-T10 was generated using two anatomical images of T6 vertebra (side and top. The geometric model was created in Autodesk® Maya® 3D 2013, and the mesh process in HiperMesh and MeshMixer (v11.0.544 Autodesk. Results The T5-T10 thoracic segment model is presented with its passive components, bones, intervertebral discs and flavum, intertransverse and supraspinous ligaments, in different views, as well as the volumetric mesh. Conclusion The 3D geometric model generated from graphical images is suitable for application in non-patient-specific finite element model studies or, with restrictions, in the use of computed tomography or magnetic resonance imaging. This model may be useful for biomechanical studies related to the middle thoracic spine, the most vulnerable site for vertebral deformations.

Discontinuous finite elements applied to solution of problems about heat transfer in heterogeneous media

International Nuclear Information System (INIS)

Ferreira, Monica Barcellos Jansen; Carmo, Eduardo Gomes Dutra do

2000-01-01

Heat transfer problems in heterogenous media with large variation of thermal conductivity are notorious for the difficulties in obtaining good numerical results. In this work it is proposed an application of a new mixed discontinuous finite element formulation to this class of problems, which produces good results without the need of high mesh refinement. Stability and consistency aspects are considered and numerical results are presented to show the efficacy of the method. (author)

An assessment of finite element synthesis model using 3D FEM

International Nuclear Information System (INIS)

Jagannathan, V.; Rastogi, B.P

1983-01-01

For the solution of multigroup diffusion theory equations a code system called FEMSYN has been developed. The code FEMSYN incorporates a finite difference (FD) module, a finite element (FE) module and one module based on single channel flux synthesis (SCFS) method, which uses trial functions generated by either FD or FE method. The 3D problems can be tackled by all the three modules. The 3D FE solutions are cheaper in comparison with fine mesh FD computations and are quite accurate. The accuracy is improved by proper choice of rectangular and triangular right prismatic elements and polynomial order in case of 3D FE analyses. Synthesis method using FE trial functions provides the fastest means of solution for 3D problems. In this paper, the FE synthesis method has been compared with 3D FE technique for the case of IAEA PWR benchmark problem. It is concluded from the above comparison that FE synthesis method can give at negligible computational efforts, accurate eigenvalue estimates and satisfactory prediction of reactor core power profiles

Parametric Quadrilateral Meshes for the Design and Optimization of Superconducting Magnets

CERN Document Server

Aleksa, Martin; Völlinger, Christine

2002-01-01

The program package ROXIE has been developed at CERN for the design and optimization of accelerator magnets. The necessity of extremely uniform fields in the superconducting accelerator magnets for LHC requires very accurate methods of field computation. For this purpose the coupled boundary-element / finite-element technique (BEM-FEM) is used. Quadrilateral higher order finite-element meshes are generated for the discretization of the iron domain (yoke) and stainless steel collars. A new mesh generator using geometrically optimized domain decomposition which was developed at the University of Stuttgart, Germany has been implemented into the ROXIE program providing fully automatic and user friendly mesh generation. The structure of the magnet cross-section can be modeled using parametric objects such as holes of different forms, elliptic, parabolic or hyperbolic arcs, notches, slots, .... For sensitivity analysis and parametric studies, point based morphing algorithms are applied to guarantee smooth adaptatio...

MHD simulations on an unstructured mesh

International Nuclear Information System (INIS)

Strauss, H.R.; Park, W.; Belova, E.; Fu, G.Y.; Sugiyama, L.E.

1998-01-01

Two reasons for using an unstructured computational mesh are adaptivity, and alignment with arbitrarily shaped boundaries. Two codes which use finite element discretization on an unstructured mesh are described. FEM3D solves 2D and 3D RMHD using an adaptive grid. MH3D++, which incorporates methods of FEM3D into the MH3D generalized MHD code, can be used with shaped boundaries, which might be 3D

Two-dimensional multigroup finite element calculation of fast reactor in diffusion approximation

International Nuclear Information System (INIS)

Schmid, J.

1986-06-01

When a linear element of triangular shape is used the actual finite element calculation is relatively simple. Extensive programs for mesh generation were written for easy inputting the configuration of reactors. A number of other programs were written for plotting neutron flux fields in individual groups, the power distribution, spatial plotting of fields, etc. The operation of selected programs, data preparation and operating instructions are described and examples given of data and results. All programs are written in GIER ALGOL. The used method and the developed programs have demonstrated that they are a useful instrument for the calculation of criticality and the distribution of neutron flux and power of both fast and thermal reactors. (J.B.)

Efficient CUDA Polynomial Preconditioned Conjugate Gradient Solver for Finite Element Computation of Elasticity Problems

Directory of Open Access Journals (Sweden)

Jianfei Zhang

2013-01-01

Full Text Available Graphics processing unit (GPU has obtained great success in scientific computations for its tremendous computational horsepower and very high memory bandwidth. This paper discusses the efficient way to implement polynomial preconditioned conjugate gradient solver for the finite element computation of elasticity on NVIDIA GPUs using compute unified device architecture (CUDA. Sliced block ELLPACK (SBELL format is introduced to store sparse matrix arising from finite element discretization of elasticity with fewer padding zeros than traditional ELLPACK-based formats. Polynomial preconditioning methods have been investigated both in convergence and running time. From the overall performance, the least-squares (L-S polynomial method is chosen as a preconditioner in PCG solver to finite element equations derived from elasticity for its best results on different example meshes. In the PCG solver, mixed precision algorithm is used not only to reduce the overall computational, storage requirements and bandwidth but to make full use of the capacity of the GPU devices. With SBELL format and mixed precision algorithm, the GPU-based L-S preconditioned CG can get a speedup of about 7–9 to CPU-implementation.

Use of heterogeneous finite elements generated by collision probability solutions to calculate a pool reactor core

International Nuclear Information System (INIS)

Calabrese, C.R.; Grant, C.R.

1990-01-01

This work presents comparisons between measured fluxes obtained by activation of Manganese foils in the light water, enriched uranium research pool reactor RA-2 MTR (Materials Testing Reactors) fuel element) and fluxes calculated by the finite element method FEM using DELFIN code, and describes the heterogeneus finite elements by a set of solutions of the transport equations for several different configurations obtained using the collision probability code HUEMUL. The agreement between calculated and measured fluxes is good, and the advantage of using FEM is showed because to obtain the flux distribution with same detail using an usual diffusion calculation it would be necessary 12000 mesh points against the 2000 points that FEM uses, hence the processing time is reduced in a factor ten. An interesting alternative to use in MTR fuel management is presented. (Author) [es

Non-linear finite element modeling

DEFF Research Database (Denmark)

Mikkelsen, Lars Pilgaard

The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...

Structural modeling techniques by finite element method

International Nuclear Information System (INIS)

Kang, Yeong Jin; Kim, Geung Hwan; Ju, Gwan Jeong

1991-01-01

This book includes introduction table of contents chapter 1 finite element idealization introduction summary of the finite element method equilibrium and compatibility in the finite element solution degrees of freedom symmetry and anti symmetry modeling guidelines local analysis example references chapter 2 static analysis structural geometry finite element models analysis procedure modeling guidelines references chapter 3 dynamic analysis models for dynamic analysis dynamic analysis procedures modeling guidelines and modeling guidelines.

Detent Force Calculations of a PMLSM Using the Finite Element Method

Science.gov (United States)

Remy, Ghislain; Krebs, Guillaume; Tounzi, Abdelmounaïm; Barre, Pierre-Jean

This paper presents a Finite Element Analysis of a Permanent Magnet Linear Synchronous Motor. The aim is to obtain an accurate estimation of the detent force without oversize computation. First, some usual techniques dedicated to the calculation of the forces in electromagnetic devices, such as the Virtual Work Method and the Maxwell Stress Tensor, are described. Some keypoints of the meshing method using a commercial FEM software are presented and used in order to improve the thrust computations. After that, the topology and features of the studied motor are described to highlight specific problems of the modelling process. In the 2D FEM case, new meshing techniques are proposed, according to the force calculations. The FEM results obtained from the different methods are analysed and compared with the experimental ones. Second, using FEM results, a study of the independence of the cogging and the end-effect forces is presented. Particularly, an original approach is suggested in order to compute the cogging force only, using the same mesh for each motion step. Then, the PMLSM geometry is adapted to calculate the end-effect forces only.

Modeling of heterogeneous elastic materials by the multiscale hp-adaptive finite element method

Science.gov (United States)

Klimczak, Marek; Cecot, Witold

2018-01-01

We present an enhancement of the multiscale finite element method (MsFEM) by combining it with the hp-adaptive FEM. Such a discretization-based homogenization technique is a versatile tool for modeling heterogeneous materials with fast oscillating elasticity coefficients. No assumption on periodicity of the domain is required. In order to avoid direct, so-called overkill mesh computations, a coarse mesh with effective stiffness matrices is used and special shape functions are constructed to account for the local heterogeneities at the micro resolution. The automatic adaptivity (hp-type at the macro resolution and h-type at the micro resolution) increases efficiency of computation. In this paper details of the modified MsFEM are presented and a numerical test performed on a Fichera corner domain is presented in order to validate the proposed approach.

Element-topology-independent preconditioners for parallel finite element computations

Science.gov (United States)

Park, K. C.; Alexander, Scott

1992-01-01

A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.

Hybrid mesh finite volume CFD code for studying heat transfer in a forward-facing step

Energy Technology Data Exchange (ETDEWEB)

Jayakumar, J S; Kumar, Inder [Bhabha Atomic Research Center, Mumbai (India); Eswaran, V, E-mail: jsjayan@gmail.com, E-mail: inderk@barc.gov.in, E-mail: eswar@iitk.ac.in [Indian Institute of Technology, Kanpur (India)

2010-12-15

Computational fluid dynamics (CFD) methods employ two types of grid: structured and unstructured. Developing the solver and data structures for a finite-volume solver is easier than for unstructured grids. But real-life problems are too complicated to be fitted flexibly by structured grids. Therefore, unstructured grids are widely used for solving real-life problems. However, using only one type of unstructured element consumes a lot of computational time because the number of elements cannot be controlled. Hence, a hybrid grid that contains mixed elements, such as the use of hexahedral elements along with tetrahedral and pyramidal elements, gives the user control over the number of elements in the domain, and thus only the domain that requires a finer grid is meshed finer and not the entire domain. This work aims to develop such a finite-volume hybrid grid solver capable of handling turbulence flows and conjugate heat transfer. It has been extended to solving flow involving separation and subsequent reattachment occurring due to sudden expansion or contraction. A significant effect of mixing high- and low-enthalpy fluid occurs in the reattached regions of these devices. This makes the study of the backward-facing and forward-facing step with heat transfer an important field of research. The problem of the forward-facing step with conjugate heat transfer was taken up and solved for turbulence flow using a two-equation model of k-{omega}. The variation in the flow profile and heat transfer behavior has been studied with the variation in Re and solid to fluid thermal conductivity ratios. The results for the variation in local Nusselt number, interface temperature and skin friction factor are presented.

Hybrid mesh finite volume CFD code for studying heat transfer in a forward-facing step

Science.gov (United States)

Jayakumar, J. S.; Kumar, Inder; Eswaran, V.

2010-12-01

Computational fluid dynamics (CFD) methods employ two types of grid: structured and unstructured. Developing the solver and data structures for a finite-volume solver is easier than for unstructured grids. But real-life problems are too complicated to be fitted flexibly by structured grids. Therefore, unstructured grids are widely used for solving real-life problems. However, using only one type of unstructured element consumes a lot of computational time because the number of elements cannot be controlled. Hence, a hybrid grid that contains mixed elements, such as the use of hexahedral elements along with tetrahedral and pyramidal elements, gives the user control over the number of elements in the domain, and thus only the domain that requires a finer grid is meshed finer and not the entire domain. This work aims to develop such a finite-volume hybrid grid solver capable of handling turbulence flows and conjugate heat transfer. It has been extended to solving flow involving separation and subsequent reattachment occurring due to sudden expansion or contraction. A significant effect of mixing high- and low-enthalpy fluid occurs in the reattached regions of these devices. This makes the study of the backward-facing and forward-facing step with heat transfer an important field of research. The problem of the forward-facing step with conjugate heat transfer was taken up and solved for turbulence flow using a two-equation model of k-ω. The variation in the flow profile and heat transfer behavior has been studied with the variation in Re and solid to fluid thermal conductivity ratios. The results for the variation in local Nusselt number, interface temperature and skin friction factor are presented.

Hybrid mesh finite volume CFD code for studying heat transfer in a forward-facing step

International Nuclear Information System (INIS)

Jayakumar, J S; Kumar, Inder; Eswaran, V

2010-01-01

Computational fluid dynamics (CFD) methods employ two types of grid: structured and unstructured. Developing the solver and data structures for a finite-volume solver is easier than for unstructured grids. But real-life problems are too complicated to be fitted flexibly by structured grids. Therefore, unstructured grids are widely used for solving real-life problems. However, using only one type of unstructured element consumes a lot of computational time because the number of elements cannot be controlled. Hence, a hybrid grid that contains mixed elements, such as the use of hexahedral elements along with tetrahedral and pyramidal elements, gives the user control over the number of elements in the domain, and thus only the domain that requires a finer grid is meshed finer and not the entire domain. This work aims to develop such a finite-volume hybrid grid solver capable of handling turbulence flows and conjugate heat transfer. It has been extended to solving flow involving separation and subsequent reattachment occurring due to sudden expansion or contraction. A significant effect of mixing high- and low-enthalpy fluid occurs in the reattached regions of these devices. This makes the study of the backward-facing and forward-facing step with heat transfer an important field of research. The problem of the forward-facing step with conjugate heat transfer was taken up and solved for turbulence flow using a two-equation model of k-ω. The variation in the flow profile and heat transfer behavior has been studied with the variation in Re and solid to fluid thermal conductivity ratios. The results for the variation in local Nusselt number, interface temperature and skin friction factor are presented.

Finite element and node point generation computer programs used for the design of toroidal field coils in tokamak fusion devices

International Nuclear Information System (INIS)

Smith, R.A.

1975-06-01

The structural analysis of toroidal field coils in Tokamak fusion machines can be performed with the finite element method. This technique has been employed for design evaluations of toroidal field coils on the Princeton Large Torus (PLT), the Poloidal Diverter Experiment (PDX), and the Tokamak Fusion Test Reactor (TFTR). The application of the finite element method can be simplified with computer programs that are used to generate the input data for the finite element code. There are three areas of data input where significant automation can be provided by supplementary computer codes. These concern the definition of geometry by a node point mesh, the definition of the finite elements from the geometric node points, and the definition of the node point force/displacement boundary conditions. The node point forces in a model of a toroidal field coil are computed from the vector cross product of the coil current and the magnetic field. The computer programs named PDXNODE and ELEMENT are described. The program PDXNODE generates the geometric node points of a finite element model for a toroidal field coil. The program ELEMENT defines the finite elements of the model from the node points and from material property considerations. The program descriptions include input requirements, the output, the program logic, the methods of generating complex geometries with multiple runs, computational time and computer compatibility. The output format of PDXNODE and ELEMENT make them compatible with PDXFORC and two general purpose finite element computer codes: (ANSYS) the Engineering Analysis System written by the Swanson Analysis Systems, Inc., and (WECAN) the Westinghouse Electric Computer Analysis general purpose finite element program. The Fortran listings of PDXNODE and ELEMENT are provided

Electromagnetic characteristics and static torque of a solid salient poles synchronous motor computed by 3D-finite element method magnetics

International Nuclear Information System (INIS)

Popnikolova Radevska, Mirka; Cundev, Milan; Petkovska, Lidija

2002-01-01

In these paper is presented a methodology for numerical determination and complex analysis of the electromagnetic characteristics of the Solid Salient Poles Synchronous Motor, with rated data: 2.5 kW, 240 V and 1500 r.p.m.. A mathematical model and original algorithm for the nonlinear and iterative calculations by using Finite Element Method in 3D domain will be given. The program package FEM-3D will be used to perform automatically mesh generation of the finite elements in the 3D domain, calculation of the magnetic field distribution, as well as electromagnetic characteristics and Static torque in SSPSM. (Author)

High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster

International Nuclear Information System (INIS)

Komatitsch, Dimitri; Erlebacher, Gordon; Goeddeke, Dominik; Michea, David

2010-01-01

We implement a high-order finite-element application, which performs the numerical simulation of seismic wave propagation resulting for instance from earthquakes at the scale of a continent or from active seismic acquisition experiments in the oil industry, on a large cluster of NVIDIA Tesla graphics cards using the CUDA programming environment and non-blocking message passing based on MPI. Contrary to many finite-element implementations, ours is implemented successfully in single precision, maximizing the performance of current generation GPUs. We discuss the implementation and optimization of the code and compare it to an existing very optimized implementation in C language and MPI on a classical cluster of CPU nodes. We use mesh coloring to efficiently handle summation operations over degrees of freedom on an unstructured mesh, and non-blocking MPI messages in order to overlap the communications across the network and the data transfer to and from the device via PCIe with calculations on the GPU. We perform a number of numerical tests to validate the single-precision CUDA and MPI implementation and assess its accuracy. We then analyze performance measurements and depending on how the problem is mapped to the reference CPU cluster, we obtain a speedup of 20x or 12x.

Probabilistic finite elements

Science.gov (United States)

Belytschko, Ted; Wing, Kam Liu

1987-01-01

In the Probabilistic Finite Element Method (PFEM), finite element methods have been efficiently combined with second-order perturbation techniques to provide an effective method for informing the designer of the range of response which is likely in a given problem. The designer must provide as input the statistical character of the input variables, such as yield strength, load magnitude, and Young's modulus, by specifying their mean values and their variances. The output then consists of the mean response and the variance in the response. Thus the designer is given a much broader picture of the predicted performance than with simply a single response curve. These methods are applicable to a wide class of problems, provided that the scale of randomness is not too large and the probabilistic density functions possess decaying tails. By incorporating the computational techniques we have developed in the past 3 years for efficiency, the probabilistic finite element methods are capable of handling large systems with many sources of uncertainties. Sample results for an elastic-plastic ten-bar structure and an elastic-plastic plane continuum with a circular hole subject to cyclic loadings with the yield stress on the random field are given.

Obtuse triangle suppression in anisotropic meshes

KAUST Repository

Sun, Feng; Choi, Yi King; Wang, Wen Ping; Yan, Dongming; Liu, Yang; Lé vy, Bruno L.

2011-01-01

Anisotropic triangle meshes are used for efficient approximation of surfaces and flow data in finite element analysis, and in these applications it is desirable to have as few obtuse triangles as possible to reduce the discretization error. We present a variational approach to suppressing obtuse triangles in anisotropic meshes. Specifically, we introduce a hexagonal Minkowski metric, which is sensitive to triangle orientation, to give a new formulation of the centroidal Voronoi tessellation (CVT) method. Furthermore, we prove several relevant properties of the CVT method with the newly introduced metric. Experiments show that our algorithm produces anisotropic meshes with much fewer obtuse triangles than using existing methods while maintaining mesh anisotropy. © 2011 Elsevier B.V. All rights reserved.

Obtuse triangle suppression in anisotropic meshes

KAUST Repository

Sun, Feng

2011-12-01

Anisotropic triangle meshes are used for efficient approximation of surfaces and flow data in finite element analysis, and in these applications it is desirable to have as few obtuse triangles as possible to reduce the discretization error. We present a variational approach to suppressing obtuse triangles in anisotropic meshes. Specifically, we introduce a hexagonal Minkowski metric, which is sensitive to triangle orientation, to give a new formulation of the centroidal Voronoi tessellation (CVT) method. Furthermore, we prove several relevant properties of the CVT method with the newly introduced metric. Experiments show that our algorithm produces anisotropic meshes with much fewer obtuse triangles than using existing methods while maintaining mesh anisotropy. © 2011 Elsevier B.V. All rights reserved.

Parametric Quadrilateral Meshes for the Design and Optimization of Superconducting Magnets

CERN Document Server

Aleksa, Martin; Völlinger, Christine

2000-01-01

The program package ROXIE [1] has been developed at CERN for the design and optimization of the superconducting magnets for the LHC.The necessity of extremely uniform (coil dominated) fields in accelerator magnets requires very accurate methods of .eld computation. For this purpose a coupled boundary-element/ finite-element technique (BEM-FEM) is used [2]. Quadrilateral higher order finite-elements are used for the discretization of the iron domain.This is necessary for the accurate modeling of the iron contours and is favorable for 3D meshes. A new quadrilateral mesh generator using geometrically optimized domain decomposition which was developed at the University of Stuttgart, Germany [3] has been implemented into the ROXIE program providing fully automatic and user friendly mesh generation.The frequent application of mathematical optimization techniques requires parametric models which are set-up using a feature-based approach.The structure of the magnet cross-section can be modeled using parametric object...

Numerical simulation of a flow-like landslide using the particle finite element method

Science.gov (United States)

Zhang, Xue; Krabbenhoft, Kristian; Sheng, Daichao; Li, Weichao

2015-01-01

In this paper, an actual landslide process that occurred in Southern China is simulated by a continuum approach, the particle finite element method (PFEM). The PFEM attempts to solve the boundary-value problems in the framework of solid mechanics, satisfying the governing equations including momentum conservation, displacement-strain relation, constitutive relation as well as the frictional contact between the sliding mass and the slip surface. To warrant the convergence behaviour of solutions, the problem is formulated as a mathematical programming problem, while the particle finite element procedure is employed to tackle the issues of mesh distortion and free-surface evolution. The whole procedure of the landslide, from initiation, sliding to deposition, is successfully reproduced by the continuum approach. It is shown that the density of the mass has little influence on the sliding process in the current landslide, whereas both the geometry and the roughness of the slip surface play important roles. Comparative studies are also conducted where a satisfactory agreement is obtained.

Finite element and finite difference methods in electromagnetic scattering

CERN Document Server

Morgan, MA

2013-01-01

This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca

Modeling fragmentation with new high order finite element technology and node splitting

Directory of Open Access Journals (Sweden)

Olovsson Lars

2015-01-01

Full Text Available The modeling of fragmentation has historically been linked to the weapons industry where the main goal is to optimize a bomb or to design effective blast shields. Numerical modeling of fragmentation from dynamic loading has traditionally been modeled by legacy finite element solvers that rely on element erosion to model material failure. However this method results in the removal of too much material. This is not realistic as retaining the mass of the structure is critical to modeling the event correctly. We propose a new approach implemented in the IMPETUS AFEA SOLVER® based on the following: New High Order Finite Elements that can easily deal with very large deformations; Stochastic distribution of initial damage that allows for a non homogeneous distribution of fragments; and a Node Splitting Algorithm that allows for material fracture without element erosion that is mesh independent. The approach is evaluated for various materials and scenarios: -Titanium ring electromagnetic compression; Hard steel Taylor bar impact, Fused silica Taylor bar impact, Steel cylinder explosion, The results obtained from the simulations are representative of the failure mechanisms observed experimentally. The main benefit of this approach is good energy conservation (no loss of mass and numerical robustness even in complex situations.

Mesh Association by Projection along Smoothed-Normal-Vector Fields : Association of Closed Manifolds

NARCIS (Netherlands)

Van Brummelen, E.H.

2006-01-01

The necessity to associate two geometrically distinct meshes arises in many engineering applications. Current mesh-association algorithms are generally unsuitable for the high-order geometry representations associated with high-order finite-element discretizations. In the present work we therefore

Neurosurgery simulation using non-linear finite element modeling and haptic interaction

Science.gov (United States)

Lee, Huai-Ping; Audette, Michel; Joldes, Grand R.; Enquobahrie, Andinet

2012-02-01

Real-time surgical simulation is becoming an important component of surgical training. To meet the realtime requirement, however, the accuracy of the biomechancial modeling of soft tissue is often compromised due to computing resource constraints. Furthermore, haptic integration presents an additional challenge with its requirement for a high update rate. As a result, most real-time surgical simulation systems employ a linear elasticity model, simplified numerical methods such as the boundary element method or spring-particle systems, and coarse volumetric meshes. However, these systems are not clinically realistic. We present here an ongoing work aimed at developing an efficient and physically realistic neurosurgery simulator using a non-linear finite element method (FEM) with haptic interaction. Real-time finite element analysis is achieved by utilizing the total Lagrangian explicit dynamic (TLED) formulation and GPU acceleration of per-node and per-element operations. We employ a virtual coupling method for separating deformable body simulation and collision detection from haptic rendering, which needs to be updated at a much higher rate than the visual simulation. The system provides accurate biomechancial modeling of soft tissue while retaining a real-time performance with haptic interaction. However, our experiments showed that the stability of the simulator depends heavily on the material property of the tissue and the speed of colliding objects. Hence, additional efforts including dynamic relaxation are required to improve the stability of the system.

Predicting thermal distortion of synchrotron radiation mirrors with finite element analysis

International Nuclear Information System (INIS)

DiGennaro, R.; Edwards, W.R.; Hoyer, E.

1985-10-01

High power and high power densities due to absorbed radiation are significant design considerations which can limit performance of mirrors receiving highly collimated synchrotron radiation from insertion devices and bending magnet sources. Although the grazing incidence angles needed for x-ray optics spread the thermal load, localized, non-uniform heating can cause distortions which exceed allowable surface figure errors and limit focusing resolution. This paper discusses the suitability of numerical approximations using finite element methods for heat transfer, deformation, and stress analysis of optical elements. The primary analysis objectives are (1) to estimate optical surface figure under maximum heat loads, (2) to correctly predict thermal stresses in order to select suitable materials and mechanical design configurations, and (3) to minimize fabrication costs by specifying appropriate tolerances for surface figure. Important factors which determine accuracy of results include finite element model mesh refinement, accuracy of boundary condition modeling, and reliability of material property data. Some methods to verify accuracy are suggested. Design analysis for an x-ray mirror is presented. Some specific configurations for internal water-cooling are evaluated in order to determine design sensitivity with respect to structural geometry, material properties, fabrication tolerances, absorbed heat magnitude and distribution, and heat transfer approximations. Estimated accuracy of these results is discussed

Dynamic Response of a Planetary Gear System Using a Finite Element/Contact Mechanics Model

Science.gov (United States)

Parker, Robert G.; Agashe, Vinayak; Vijayakar, Sandeep M.

2000-01-01

The dynamic response of a helicopter planetary gear system is examined over a wide range of operating speeds and torques. The analysis tool is a unique, semianalytical finite element formulation that admits precise representation of the tooth geometry and contact forces that are crucial in gear dynamics. Importantly, no a priori specification of static transmission error excitation or mesh frequency variation is required; the dynamic contact forces are evaluated internally at each time step. The calculated response shows classical resonances when a harmonic of mesh frequency coincides with a natural frequency. However, peculiar behavior occurs where resonances expected to be excited at a given speed are absent. This absence of particular modes is explained by analytical relationships that depend on the planetary configuration and mesh frequency harmonic. The torque sensitivity of the dynamic response is examined and compared to static analyses. Rotation mode response is shown to be more sensitive to input torque than translational mode response.

Electrical machine analysis using finite elements

CERN Document Server

Bianchi, Nicola

2005-01-01

OUTLINE OF ELECTROMAGNETIC FIELDSVector AnalysisElectromagnetic FieldsFundamental Equations SummaryReferencesBASIC PRINCIPLES OF FINITE ELEMENT METHODSIntroductionField Problems with Boundary ConditionsClassical Method for the Field Problem SolutionThe Classical Residual Method (Galerkin's Method)The Classical Variational Method (Rayleigh-Ritz's Method)The Finite Element MethodReferencesAPPLICATIONS OF THE FINITE ELEMENT METHOD TO TWO-DIMENSIONAL FIELDSIntroductionLinear Interpolation of the Function fApplication of the Variational MethodSimple Descriptions of Electromagnetic FieldsAppendix: I

Comparison between a finite difference model (PUMA) and a finite element model (DELFIN) for simulation of the reactor of the atomic power plant of Atucha I

International Nuclear Information System (INIS)

Grant, C.R.

1996-01-01

The reactor code PUMA, developed in CNEA, simulates nuclear reactors discretizing space in finite difference elements. Core representation is performed by means a cylindrical mesh, but the reactor channels are arranged in an hexagonal lattice. That is why a mapping using volume intersections must be used. This spatial treatment is the reason of an overestimation of the control rod reactivity values, which must be adjusted modifying the incremental cross sections. Also, a not very good treatment of the continuity conditions between core and reflector leads to an overestimation of channel power of the peripherical fuel elements between 5 to 8 per cent. Another code, DELFIN, developed also in CNEA, treats the spatial discretization using heterogeneous finite elements, allowing a correct treatment of the continuity of fluxes and current among elements and a more realistic representation of the hexagonal lattice of the reactor. A comparison between results obtained using both methods in done in this paper. (author). 4 refs., 3 figs

New Multigrid Method Including Elimination Algolithm Based on High-Order Vector Finite Elements in Three Dimensional Magnetostatic Field Analysis

Science.gov (United States)

Hano, Mitsuo; Hotta, Masashi

A new multigrid method based on high-order vector finite elements is proposed in this paper. Low level discretizations in this method are obtained by using low-order vector finite elements for the same mesh. Gauss-Seidel method is used as a smoother, and a linear equation of lowest level is solved by ICCG method. But it is often found that multigrid solutions do not converge into ICCG solutions. An elimination algolithm of constant term using a null space of the coefficient matrix is also described. In three dimensional magnetostatic field analysis, convergence time and number of iteration of this multigrid method are discussed with the convectional ICCG method.

Adaptive mesh refinement for a finite volume method for flow and transport of radionuclides in heterogeneous porous media

International Nuclear Information System (INIS)

Amaziane, Brahim; Bourgeois, Marc; El Fatini, Mohamed

2014-01-01

In this paper, we consider adaptive numerical simulation of miscible displacement problems in porous media, which are modeled by single phase flow equations. A vertex-centred finite volume method is employed to discretize the coupled system: the Darcy flow equation and the diffusion-convection concentration equation. The convection term is approximated with a Godunov scheme over the dual finite volume mesh, whereas the diffusion-dispersion term is discretized by piecewise linear conforming finite elements. We introduce two kinds of indicators, both of them of residual type. The first one is related to time discretization and is local with respect to the time discretization: thus, at each time, it provides an appropriate information for the choice of the next time step. The second is related to space discretization and is local with respect to both the time and space variable and the idea is that at each time it is an efficient tool for mesh adaptivity. An error estimation procedure evaluates where additional refinement is needed and grid generation procedures dynamically create or remove fine-grid patches as resolution requirements change. The method was implemented in the software MELODIE, developed by the French Institute for Radiological Protection and Nuclear Safety (IRSN, Institut de Radioprotection et de Surete Nucleaire). The algorithm is then used to simulate the evolution of radionuclide migration from the waste packages through a heterogeneous disposal, demonstrating its capability to capture complex behavior of the resulting flow. (authors)

Determination of the ultimate load in concrete slabs by the yield line finite element method

International Nuclear Information System (INIS)

Vaz, L.E.; Feijo, B.; Martha, L.F.R.; Lopes, M.M.

1984-01-01

A method for calculating the ultimate load in reinforced concrete slabs is proposed. The method follows the finite element aproach representating the continuum slab as an assembly of rigid triangular plates connected along their sides through yield line elements. This approach leads to the definition of the displacement configuration of the plate only as a function of the transversal displacement at the nodes of the mesh (1 DOF per node) reducing significantly the number of DOF's in relation to the conventional formulation by means of the finite element method (minimum of 3 DOF per node). Nonlinear behaviour of the reinforced concrete section is considered in the definition of the moment rotation curve of the yield lines. The effect of the in plane forces acting in the middle surface of the plate is also taken into account. The validity of the model is verified comparing the numerical solutions with the results of the classical yield line theory. (Author) [pt

Hybrid finite elements nanocomposite characterization by stochastic microstructuring

Science.gov (United States)

Esteva, Milton

In this thesis the impact of entangled and non-straight fibers in the determination of the effective elastic and thermal properties of polymer nanocomposite (PNC) is addressed. Most of the models in recent studies assume nanotubes to be well dispersed straight fibers with fixed size. Nonetheless experiments reveal that nanotube formation become wavy during the manufacturing process, due to their high aspect ratio and low bending stiffness. Furthermore, experiments also show that nanotubes come in a variety of diameters and lengths. In the thesis an attempt to model the behavior of entangled fibers is made in which the distributions regarding the nanotube length and diameter are incorporated. First, an approach to generate random microstructures is developed. Then, using the finite element (FE) method with embedded fibers, the effective properties are computed for each of the random microstructures. This approach requires only a regular grid for the FE mesh, circumventing the requisite computationally costly and human labor intensive mesh refinement of ordinary FE in order to capture the local morphology of the composite material. Finally, a Monte Carlo simulation approach is used to obtain statistics of the computed effective physical properties. The numerical results are found in good agreement with experimental data reported in the open literature.

Automatic mesh generation with QMESH program

International Nuclear Information System (INIS)

Ise, Takeharu; Tsutsui, Tsuneo

1977-05-01

Usage of the two-dimensional self-organizing mesh generation program, QMESH, is presented together with the descriptions and the experience, as it has recently been converted and reconstructed from the NEACPL version to the FACOM. The program package consists of the QMESH code to generate quadrilaterial meshes with smoothing techniques, the QPLOT code to plot the data obtained from the QMESH on the graphic COM, and the RENUM code to renumber the meshes by using a bandwidth minimization procedure. The technique of mesh reconstructuring coupled with smoothing techniques is especially useful when one generates the meshes for computer codes based on the finite element method. Several typical examples are given for easy access to the QMESH program, which is registered in the R.B-disks of JAERI for users. (auth.)

A three-dimensional finite element model for biomechanical analysis of the hip.

Science.gov (United States)

Chen, Guang-Xing; Yang, Liu; Li, Kai; He, Rui; Yang, Bin; Zhan, Yan; Wang, Zhi-Jun; Yu, Bing-Nin; Jian, Zhe

2013-11-01

The objective of this study was to construct a three-dimensional (3D) finite element model of the hip. The images of the hip were obtained from Chinese visible human dataset. The hip model includes acetabular bone, cartilage, labrum, and bone. The cartilage of femoral head was constructed using the AutoCAD and Solidworks software. The hip model was imported into ABAQUS analysis system. The contact surface of the hip joint was meshed. To verify the model, the single leg peak force was loaded, and contact area of the cartilage and labrum of the hip and pressure distribution in these structures were observed. The constructed 3D hip model reflected the real hip anatomy. Further, this model reflected biomechanical behavior similar to previous studies. In conclusion, this 3D finite element hip model avoids the disadvantages of other construction methods, such as imprecision of cartilage construction and the absence of labrum. Further, it provides basic data critical for accurately modeling normal and abnormal loads, and the effects of abnormal loads on the hip.

CONSTRUCTION OF AN ELECTRICAL GENERATOR USING THE FINITE ELEMENT ANALYSIS IN ELECTROMAGNETISM, ANSOFT MAXWELL

OpenAIRE

SAVULESCU Adrian

2014-01-01

This paper attempts to present the necessary steps in designing a electrical generator represented in 2D, 3D, finite element analysis software of Ansoft Maxwell magnetic fields. This work includes modeling form of generator, boundaries, excitations, parameterization, the analysis of the mesh, optimization, performance and representation fields: A (Flux Vector Lines and A), H (Mag_H and H Vector), B (Mag_B and B vector) J (Jz and J vector) and the energy and other analyzes as CoreLoss, Ohmic_L...

Trabecular bone strains around a dental implant and associated micromotions--a micro-CT-based three-dimensional finite element study.

Science.gov (United States)

Limbert, Georges; van Lierde, Carl; Muraru, O Luiza; Walboomers, X Frank; Frank, Milan; Hansson, Stig; Middleton, John; Jaecques, Siegfried

2010-05-07

The first objective of this computational study was to assess the strain magnitude and distribution within the three-dimensional (3D) trabecular bone structure around an osseointegrated dental implant loaded axially. The second objective was to investigate the relative micromotions between the implant and the surrounding bone. The work hypothesis adopted was that these virtual measurements would be a useful indicator of bone adaptation (resorption, homeostasis, formation). In order to reach these objectives, a microCT-based finite element model of an oral implant implanted into a Berkshire pig mandible was developed along with a robust software methodology. The finite element mesh of the 3D trabecular bone architecture was generated from the segmentation of microCT scans. The implant was meshed independently from its CAD file obtained from the manufacturer. The meshes of the implant and the bone sample were registered together in an integrated software environment. A series of non-linear contact finite element (FE) analyses considering an axial load applied to the top of the implant in combination with three sets of mechanical properties for the trabecular bone tissue was devised. Complex strain distribution patterns are reported and discussed. It was found that considering the Young's modulus of the trabecular bone tissue to be 5, 10 and 15GPa resulted in maximum peri-implant bone microstrains of about 3000, 2100 and 1400. These results indicate that, for the three sets of mechanical properties considered, the magnitude of maximum strain lies within an homeostatic range known to be sufficient to maintain/form bone. The corresponding micro-motions of the implant with respect to the bone microstructure were shown to be sufficiently low to prevent fibrous tissue formation and to favour long-term osseointegration. Copyright 2010 Elsevier Ltd. All rights reserved.

Application of the finite element method to neutronics problems with inhomogeneous boundray conditions

International Nuclear Information System (INIS)

Yoo, K.J.

1982-01-01

The albedo boundary conditions are incorporated into the finite element method using bicubic Hermite element functions in order to reduce the computer memory and computation time in two-group diffusion calculations by excluding the reflector regions in computation space. The basis functions at the core-reflector interfaces are newly established to satisfy the albedo boundary conditions, and then the ''weak'' form of two-group diffusion equations is discretized using the principle of the weighted residual method in combination with the Galerkin approximation. The discretized two-group diffusion equation is then solved by the Gaussian elimination method with the scaled column pivoting algorithm in one-dimensional problem and Gauss-Seidel method in two-dimensional problem. Prior to the application of the method to two-group diffusion problems, the same method is applied to the one-speed neutron transport equation in a bare slab reactor with the vacuum boundary condition to confirm its usefulness in the diffusion calculations. To investigate the applicability of our diffusion method, several numerical calculations are performed: two-dimensional IAEA benchmark problem and two-dimensional ZION problem. The results are compared with the available results from the conventional finite difference and other finite element methods. If the albedo values are appropriately adjusted, our results of the two-dimensional IAEA benchmark problem are agreed within 0.002% of ksub(eff) with the fine mesh PDQ results. Comparing with CITATION results, one-eighth of core memory and one-fifteenth of computing time are required to obtain the same accuracy even though no acceleration technique is used in the present case. Also, it is found that the results are comparable with the other finite element results. However, no significant saving is obtained in computation time comparing with the other finite element results, where the reflector regions are explicity included. This mainly comes from

A new algorithm for finite element simulation of wedge osteotomies in voxel models with application to the tibia

Directory of Open Access Journals (Sweden)

Thomas Pressel

2010-01-01

Full Text Available Thomas Pressel1, Markus D Schofer1, Jörg Meiforth2, Markus Lengsfeld1, Jan Schmitt11Department of Orthopaedics and Rheumatology, University Hospital Marburg, Marburg, Germany; 2St. Vincentius Kliniken, Klinik für Orthopädie, Karlsruhe, GermanyAbstract: Wedge osteotomies are used to correct bone deformities or change the forces acting on bones and joints in the human body. Finite element models can be employed to simulate the effect of such operations on the bone or adjacent joints. The automatic generation of voxel models derived from computed tomography data is a common procedure, but the major drawback of the method lies in irregular model surfaces. Therefore, the concept of hybrid models combining voxel and tetrahedron meshes was developed. We present an algorithm to simulate wedge osteotomies in voxel models by adding tetrahedron to brick elements. Applicability of the procedure was tested by performing a parametric study using a tibia model created from computed tomography scans taken in vivo applying individually calculated force conditions. The osteotomy angle largely affected maximum stresses: at 2.5 degrees valgus, the stresses at the medial and lateral tibial plateau were equivalent, while increasing valgus angles reduced medial stresses. The algorithm described here is an improvement of former mesh generation procedures and allows a better representation of the geometry at the osteotomy level. The algorithm can be used for all wedge osteotomies and is not limited to the tibia.Keywords: finite element/osteotomy/voxel/pre-operative planning, simulation, mesh algorithm

Permeability computation on a REV with an immersed finite element method

International Nuclear Information System (INIS)

Laure, P.; Puaux, G.; Silva, L.; Vincent, M.

2011-01-01

An efficient method to compute permeability of fibrous media is presented. An immersed domain approach is used to represent the porous material at its microscopic scale and the flow motion is computed with a stabilized mixed finite element method. Therefore the Stokes equation is solved on the whole domain (including solid part) using a penalty method. The accuracy is controlled by refining the mesh around the solid-fluid interface defined by a level set function. Using homogenisation techniques, the permeability of a representative elementary volume (REV) is computed. The computed permeabilities of regular fibre packings are compared to classical analytical relations found in the bibliography.

Structural optimisation of cage induction motors using finite element analysis

Science.gov (United States)

Palko, S.

The current trend in motor design is to have highly efficient, low noise, low cost, and modular motors with a high power factor. High torque motors are useful in applications like servo motors, lifts, cranes, and rolling mills. This report contains a detailed review of different optimization methods applicable in various design problems. Special attention is given to the performance of different methods, when they are used with finite element analysis (FEA) as an objective function, and accuracy problems arising from the numerical simulations. Also an effective method for designing high starting torque and high efficiency motors is presented. The method described in this work utilizes FEA combined with algorithms for the optimization of the slot geometry. The optimization algorithm modifies the position of the nodal points in the element mesh. The number of independent variables ranges from 14 to 140 in this work.

The intervals method: a new approach to analyse finite element outputs using multivariate statistics

Directory of Open Access Journals (Sweden)

Jordi Marcé-Nogué

2017-10-01

Full Text Available Background In this paper, we propose a new method, named the intervals’ method, to analyse data from finite element models in a comparative multivariate framework. As a case study, several armadillo mandibles are analysed, showing that the proposed method is useful to distinguish and characterise biomechanical differences related to diet/ecomorphology. Methods The intervals’ method consists of generating a set of variables, each one defined by an interval of stress values. Each variable is expressed as a percentage of the area of the mandible occupied by those stress values. Afterwards these newly generated variables can be analysed using multivariate methods. Results Applying this novel method to the biological case study of whether armadillo mandibles differ according to dietary groups, we show that the intervals’ method is a powerful tool to characterize biomechanical performance and how this relates to different diets. This allows us to positively discriminate between specialist and generalist species. Discussion We show that the proposed approach is a useful methodology not affected by the characteristics of the finite element mesh. Additionally, the positive discriminating results obtained when analysing a difficult case study suggest that the proposed method could be a very useful tool for comparative studies in finite element analysis using multivariate statistical approaches.

The intervals method: a new approach to analyse finite element outputs using multivariate statistics

Science.gov (United States)

De Esteban-Trivigno, Soledad; Püschel, Thomas A.; Fortuny, Josep

2017-01-01

Background In this paper, we propose a new method, named the intervals’ method, to analyse data from finite element models in a comparative multivariate framework. As a case study, several armadillo mandibles are analysed, showing that the proposed method is useful to distinguish and characterise biomechanical differences related to diet/ecomorphology. Methods The intervals’ method consists of generating a set of variables, each one defined by an interval of stress values. Each variable is expressed as a percentage of the area of the mandible occupied by those stress values. Afterwards these newly generated variables can be analysed using multivariate methods. Results Applying this novel method to the biological case study of whether armadillo mandibles differ according to dietary groups, we show that the intervals’ method is a powerful tool to characterize biomechanical performance and how this relates to different diets. This allows us to positively discriminate between specialist and generalist species. Discussion We show that the proposed approach is a useful methodology not affected by the characteristics of the finite element mesh. Additionally, the positive discriminating results obtained when analysing a difficult case study suggest that the proposed method could be a very useful tool for comparative studies in finite element analysis using multivariate statistical approaches. PMID:29043107

A proposal for a determination method of element division on an analytical model for finite element elastic waves propagation analysis

International Nuclear Information System (INIS)

Ishida, Hitoshi; Meshii, Toshiyuki

2010-01-01

This study proposes an element size selection method named the 'Impact-Meshing (IM) method' for a finite element waves propagation analysis model, which is characterized by (1) determination of element division of the model with strain energy in the whole model, (2) static analysis (dynamic analysis in a single time step) with boundary conditions which gives a maximum change of displacement in the time increment and inertial (impact) force caused by the displacement change. In this paper, an example of application of the IM method to 3D ultrasonic wave propagation problem in an elastic solid is described. These examples showed an analysis result with a model determined by the IM method was convergence and calculation time for determination of element subdivision was reduced to about 1/6 by the IM Method which did not need determination of element subdivision by a dynamic transient analysis with 100 time steps. (author)

A novel finite volume discretization method for advection-diffusion systems on stretched meshes

Science.gov (United States)

Merrick, D. G.; Malan, A. G.; van Rooyen, J. A.

2018-06-01

This work is concerned with spatial advection and diffusion discretization technology within the field of Computational Fluid Dynamics (CFD). In this context, a novel method is proposed, which is dubbed the Enhanced Taylor Advection-Diffusion (ETAD) scheme. The model equation employed for design of the scheme is the scalar advection-diffusion equation, the industrial application being incompressible laminar and turbulent flow. Developed to be implementable into finite volume codes, ETAD places specific emphasis on improving accuracy on stretched structured and unstructured meshes while considering both advection and diffusion aspects in a holistic manner. A vertex-centered structured and unstructured finite volume scheme is used, and only data available on either side of the volume face is employed. This includes the addition of a so-called mesh stretching metric. Additionally, non-linear blending with the existing NVSF scheme was performed in the interest of robustness and stability, particularly on equispaced meshes. The developed scheme is assessed in terms of accuracy - this is done analytically and numerically, via comparison to upwind methods which include the popular QUICK and CUI techniques. Numerical tests involved the 1D scalar advection-diffusion equation, a 2D lid driven cavity and turbulent flow case. Significant improvements in accuracy were achieved, with L2 error reductions of up to 75%.

Parallel 3D Mortar Element Method for Adaptive Nonconforming Meshes

Science.gov (United States)

Feng, Huiyu; Mavriplis, Catherine; VanderWijngaart, Rob; Biswas, Rupak

2004-01-01

High order methods are frequently used in computational simulation for their high accuracy. An efficient way to avoid unnecessary computation in smooth regions of the solution is to use adaptive meshes which employ fine grids only in areas where they are needed. Nonconforming spectral elements allow the grid to be flexibly adjusted to satisfy the computational accuracy requirements. The method is suitable for computational simulations of unsteady problems with very disparate length scales or unsteady moving features, such as heat transfer, fluid dynamics or flame combustion. In this work, we select the Mark Element Method (MEM) to handle the non-conforming interfaces between elements. A new technique is introduced to efficiently implement MEM in 3-D nonconforming meshes. By introducing an "intermediate mortar", the proposed method decomposes the projection between 3-D elements and mortars into two steps. In each step, projection matrices derived in 2-D are used. The two-step method avoids explicitly forming/deriving large projection matrices for 3-D meshes, and also helps to simplify the implementation. This new technique can be used for both h- and p-type adaptation. This method is applied to an unsteady 3-D moving heat source problem. With our new MEM implementation, mesh adaptation is able to efficiently refine the grid near the heat source and coarsen the grid once the heat source passes. The savings in computational work resulting from the dynamic mesh adaptation is demonstrated by the reduction of the the number of elements used and CPU time spent. MEM and mesh adaptation, respectively, bring irregularity and dynamics to the computer memory access pattern. Hence, they provide a good way to gauge the performance of computer systems when running scientific applications whose memory access patterns are irregular and unpredictable. We select a 3-D moving heat source problem as the Unstructured Adaptive (UA) grid benchmark, a new component of the NAS Parallel

Finite element modeling of the human kidney for probabilistic occupant models: Statistical shape analysis and mesh morphing.

Science.gov (United States)

Yates, Keegan M; Untaroiu, Costin D

2018-04-16

Statistical shape analysis was conducted on 15 pairs (left and right) of human kidneys. It was shown that the left and right kidney were significantly different in size and shape. In addition, several common modes of kidney variation were identified using statistical shape analysis. Semi-automatic mesh morphing techniques have been developed to efficiently create subject specific meshes from a template mesh with a similar geometry. Subject specific meshes as well as probabilistic kidney meshes were created from a template mesh. Mesh quality remained about the same as the template mesh while only taking a fraction of the time to create the mesh from scratch or morph with manually identified landmarks. This technique can help enhance the quality of information gathered from experimental testing with subject specific meshes as well as help to more efficiently predict injury by creating models with the mean shape as well as models at the extremes for each principal component. Copyright © 2018 Elsevier Ltd. All rights reserved.

A 3D finite element simulation model for TBM tunnelling in soft ground

Science.gov (United States)

Kasper, Thomas; Meschke, Günther

2004-12-01

A three-dimensional finite element simulation model for shield-driven tunnel excavation is presented. The model takes into account all relevant components of the construction process (the soil and the ground water, the tunnel boring machine with frictional contact to the soil, the hydraulic jacks, the tunnel lining and the tail void grouting). The paper gives a detailed description of the model components and the stepwise procedure to simulate the construction process. The soil and the grout material are modelled as saturated porous media using a two-field finite element formulation. This allows to take into account the groundwater, the grouting pressure and the fluid interaction between the soil and slurry at the cutting face and between the soil and grout around the tail void. A Cam-Clay plasticity model is used to describe the material behaviour of cohesive soils. The cementitious grouting material in the tail void is modelled as an ageing elastic material with time-dependent stiffness and permeability. To allow for an automated computation of arbitrarily long and also curvilinear driving paths with suitable finite element meshes, the simulation procedure has been fully automated. The simulation of a tunnel advance in soft cohesive soil below the ground water table is presented and the results are compared with measurements taken from the literature. Copyright

FINITE ELEMENT MODEL FOR PREDICTING RESIDUAL ...

African Journals Online (AJOL)

FINITE ELEMENT MODEL FOR PREDICTING RESIDUAL STRESSES IN ... the transverse residual stress in the x-direction (σx) had a maximum value of 375MPa ... the finite element method are in fair agreement with the experimental results.

Numerical modeling of two-phase binary fluid mixing using mixed finite elements

KAUST Repository

Sun, Shuyu

2012-07-27

Diffusion coefficients of dense gases in liquids can be measured by considering two-phase binary nonequilibrium fluid mixing in a closed cell with a fixed volume. This process is based on convection and diffusion in each phase. Numerical simulation of the mixing often requires accurate algorithms. In this paper, we design two efficient numerical methods for simulating the mixing of two-phase binary fluids in one-dimensional, highly permeable media. Mathematical model for isothermal compositional two-phase flow in porous media is established based on Darcy\\'s law, material balance, local thermodynamic equilibrium for the phases, and diffusion across the phases. The time-lag and operator-splitting techniques are used to decompose each convection-diffusion equation into two steps: diffusion step and convection step. The Mixed finite element (MFE) method is used for diffusion equation because it can achieve a high-order and stable approximation of both the scalar variable and the diffusive fluxes across grid-cell interfaces. We employ the characteristic finite element method with moving mesh to track the liquid-gas interface. Based on the above schemes, we propose two methods: single-domain and two-domain methods. The main difference between two methods is that the two-domain method utilizes the assumption of sharp interface between two fluid phases, while the single-domain method allows fractional saturation level. Two-domain method treats the gas domain and the liquid domain separately. Because liquid-gas interface moves with time, the two-domain method needs work with a moving mesh. On the other hand, the single-domain method allows the use of a fixed mesh. We derive the formulas to compute the diffusive flux for MFE in both methods. The single-domain method is extended to multiple dimensions. Numerical results indicate that both methods can accurately describe the evolution of the pressure and liquid level. © 2012 Springer Science+Business Media B.V.

Finite element analysis of piezoelectric materials

International Nuclear Information System (INIS)

Lowrie, F.; Stewart, M.; Cain, M.; Gee, M.

1999-01-01

This guide is intended to help people wanting to do finite element analysis of piezoelectric materials by answering some of the questions that are peculiar to piezoelectric materials. The document is not intended as a complete beginners guide for finite element analysis in general as this is better dealt with by the individual software producers. The guide is based around the commercial package ANSYS as this is a popular package amongst piezoelectric material users, however much of the information will still be useful to users of other finite element codes. (author)

Multigrid for refined triangle meshes

Energy Technology Data Exchange (ETDEWEB)

Shapira, Yair

1997-02-01

A two-level preconditioning method for the solution of (locally) refined finite element schemes using triangle meshes is introduced. In the isotropic SPD case, it is shown that the condition number of the preconditioned stiffness matrix is bounded uniformly for all sufficiently regular triangulations. This is also verified numerically for an isotropic diffusion problem with highly discontinuous coefficients.

Non-conforming finite-element formulation for cardiac electrophysiology: an effective approach to reduce the computation time of heart simulations without compromising accuracy

Science.gov (United States)

Hurtado, Daniel E.; Rojas, Guillermo

2018-04-01

Computer simulations constitute a powerful tool for studying the electrical activity of the human heart, but computational effort remains prohibitively high. In order to recover accurate conduction velocities and wavefront shapes, the mesh size in linear element (Q1) formulations cannot exceed 0.1 mm. Here we propose a novel non-conforming finite-element formulation for the non-linear cardiac electrophysiology problem that results in accurate wavefront shapes and lower mesh-dependance in the conduction velocity, while retaining the same number of global degrees of freedom as Q1 formulations. As a result, coarser discretizations of cardiac domains can be employed in simulations without significant loss of accuracy, thus reducing the overall computational effort. We demonstrate the applicability of our formulation in biventricular simulations using a coarse mesh size of ˜ 1 mm, and show that the activation wave pattern closely follows that obtained in fine-mesh simulations at a fraction of the computation time, thus improving the accuracy-efficiency trade-off of cardiac simulations.

Finite rotation shells basic equations and finite elements for Reissner kinematics

CERN Document Server

Wisniewski, K

2010-01-01

This book covers theoretical and computational aspects of non-linear shells. Several advanced topics of shell equations and finite elements - not included in standard textbooks on finite elements - are addressed, and the book includes an extensive bibliography.

Finite Element Study of Three Different Treatment Designs of a Mandibular Three Implant-Retained Overdenture

Directory of Open Access Journals (Sweden)

M. Shishesaz

Full Text Available Abstract This study compares ball, bar-clip and bar-ball attachment systems for implant-retained mandibular overdentures with three implants. The first implant is placed in the middle of the mandible and the other two are imbedded in the first premolar regions. Linear elastic finite element analysis is used for design analysis. Three dimensional geometry of the mandible is generated from computed tomography. Other parts are modeled using SolidWorks software. The foodstuff is positioned at the right first molar, representing the most frequent masticating situation. To obtain accurate mesh-independent results, finite element models are solved using several mesh grids. They are then validated by means of a detailed convergence analysis. The results demonstrate that the highest von-Mises stress in the bone is always located around the neck of the implant, at its upper threads. Ball and bar-ball attachments transfer the highest and lowest stresses to the bone surrounding the implants, respectively. The lowest stresses in the cortical and cancellous bones are due to bar-ball attachment. Yet, the overdenture gets its maximum movement for this arrangement. Consequently, the use of bar-ball attachment is only recommended for the cases in which stress transferred to peri-implant bone is more important than overdenture stability. Among the three treatment designs, ball attachment seems to exhibit the lowest lateral and overall displacements and hence, better overdenture stability.

Finite element prediction of elastic strains in beryllium compact tension specimens

International Nuclear Information System (INIS)

Guerra, F.; Varma, R.; Bourke, M.

1997-01-01

Three-dimensional finite element (FE) calculations using ABAQUS version 5.5.9 were compared to neutron diffraction measurements of a loaded, pre-cracked beryllium compact tension (CT) specimens. The objective was to validate the FE results with the experimental open-quotes elastic strainclose quotes measurements. Then the FE calculations could be used to study residual stress and other aspects of these problems in the unloaded state and the crack tip stress in the loaded state which is hard to measure experimentally. A graded FE mesh was focused on the regions containing high strain gradients, the smallest elements were approximately 0.5 mm x 0.5 mm x 0.4 mm. A standard 20-node brick element model was complemented by a model with 1/4-point elements at the crack tip. Since the neutron diffraction measurements provided a volume average of approximately a cube of edge 3.0 mm, various averaging (or integrating) techniques were used on the FE results. Several integration schemes showed good agreement with the experimental results

Influence of parafunctional loading and prosthetic connection on stress distribution: a 3D finite element analysis.

Science.gov (United States)

Torcato, Leonardo Bueno; Pellizzer, Eduardo Piza; Verri, Fellippo Ramos; Falcón-Antenucci, Rosse Mary; Santiago Júnior, Joel Ferreira; de Faria Almeida, Daniel Augusto

2015-11-01

Clinicians should consider parafunctional occlusal load when planning treatment. Prosthetic connections can reduce the stress distribution on an implant-supported prosthesis. The purpose of this 3-dimensional finite element study was to assess the influence of parafunctional loading and prosthetic connections on stress distribution. Computer-aided design software was used to construct 3 models. Each model was composed of a bone and an implant (external hexagon, internal hexagon, or Morse taper) with a crown. Finite element analysis software was used to generate the finite element mesh and establish the loading and boundary conditions. A normal force (200-N axial load and 100-N oblique load) and parafunctional force (1000-N axial and 500-N oblique load) were applied. Results were visualized as the maximum principal stress. Three-way analysis of variance and Tukey test were performed, and the percentage of contribution of each variable to the stress concentration was calculated from sum-of squares-analysis. Stress was concentrated around the implant at the cortical bone, and models with the external hexagonal implant showed the highest stresses (PProsthetic Dentistry. Published by Elsevier Inc. All rights reserved.

A multigrid solution method for mixed hybrid finite elements

Energy Technology Data Exchange (ETDEWEB)

Schmid, W. [Universitaet Augsburg (Germany)

1996-12-31

We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.

Comparative study on triangular and quadrilateral meshes by a finite-volume method with a central difference scheme

KAUST Repository

Yu, Guojun

2012-10-01

In this article, comparative studies on computational accuracies and convergence rates of triangular and quadrilateral meshes are carried out in the frame work of the finite-volume method. By theoretical analysis, we conclude that the number of triangular cells needs to be 4/3 times that of quadrilateral cells to obtain similar accuracy. The conclusion is verified by a number of numerical examples. In addition, the convergence rates of the triangular meshes are found to be slower than those of the quadrilateral meshes when the same accuracy is obtained with these two mesh types. © 2012 Taylor and Francis Group, LLC.

Comparative study on triangular and quadrilateral meshes by a finite-volume method with a central difference scheme

KAUST Repository

Yu, Guojun; Yu, Bo; Sun, Shuyu; Tao, Wenquan

2012-01-01

In this article, comparative studies on computational accuracies and convergence rates of triangular and quadrilateral meshes are carried out in the frame work of the finite-volume method. By theoretical analysis, we conclude that the number of triangular cells needs to be 4/3 times that of quadrilateral cells to obtain similar accuracy. The conclusion is verified by a number of numerical examples. In addition, the convergence rates of the triangular meshes are found to be slower than those of the quadrilateral meshes when the same accuracy is obtained with these two mesh types. © 2012 Taylor and Francis Group, LLC.

Finite-element blunt-crack propagation: a modified J-integral approach

International Nuclear Information System (INIS)

Pan, Y.C.; Marchertas, A.H.; Kennedy, J.M.

1983-01-01

In assessing the safety of a liquid metal fast breeder reactor (LMFBR), a major concern is the behavior of concrete structures subjected to high temperatures. The potential of concrete cracking is an important parameter which could significantly influence the safety assessment of thermally attacked concrete. A new modified J-integral approach for the blunt crack model has been derived to provide a general procedure to accurately predict the direction of crack growth. This formulation has been incorporated into the coupled heat transfer-stress analysis finite element code TEMP-STRESS. A description of the formulation is presented in this paper. Results for the problems of a Mode I and mixed mode crack in a plate using regular and slanted meshes subjected to uniaxial and shear loading are presented

Finite element modelling of ionized field quantities around a monopolar HVDC transmission line

International Nuclear Information System (INIS)

Jaiswal, Vinay; Thomas, M Joy

2003-01-01

In this paper, the Poisson's equation describing the ionized field around an HVDC line is solved using an improved finite element based technique. First order isoparametric quadrilateral elements, together with a modified updating criterion for the space charge distribution, are implemented in the iterative procedure. A novel technique is presented for mesh generation in the presence of space charges. Electric field lines and equipotential lines have been computed using the proposed technique. Total corona current at different applied voltages above corona onset voltage, electric field at the ground plane with and without the presence of space charges and current density at the ground plane have also been computed. The results are in agreement with the experimental values available in the published literature

Multi-phase Volume Segmentation with Tetrahedral Mesh

DEFF Research Database (Denmark)

Nguyen Trung, Tuan; Dahl, Vedrana Andersen; Bærentzen, Jakob Andreas

Volume segmentation is efficient for reconstructing material structure, which is important for several analyses, e.g. simulation with finite element method, measurement of quantitative information like surface area, surface curvature, volume, etc. We are concerned about the representations of the 3......D volumes, which can be categorized into two groups: fixed voxel grids [1] and unstructured meshes [2]. Among these two representations, the voxel grids are more popular since manipulating a fixed grid is easier than an unstructured mesh, but they are less efficient for quantitative measurements....... In many cases, the voxel grids are converted to explicit meshes, however the conversion may reduce the accuracy of the segmentations, and the effort for meshing is also not trivial. On the other side, methods using unstructured meshes have difficulty in handling topology changes. To reduce the complexity...

Finite element analysis of elasto-plastic tee joints

International Nuclear Information System (INIS)

Powell, G.H.

1974-09-01

The theory and computational procedures used in the computer program B169TJ/EP for the analysis of elasto-plastic tee joints are described, and detailed user's guide is presented. The program is particularly applicable to joints conforming to the ANSI B16.9 Manufacturing Standard, but can also be applied to other joint geometries. The joint may be loaded by internal pressure and by arbitrary combinations of applied forces and moments at the ends of the branch and run pipes, and the loading sequence may be arbitrary. The joint material is assumed to yield according to the von Mises criterion, and to exhibit either linear kinematic hardening or nonlinear isotropic hardening after yield. The program makes use of the finite element and mesh generation procedures previously applied in the elastic stress analysis program B16.9TJ/ SA, with minor modifications. (U.S.)

Domain decomposition methods for mortar finite elements

Energy Technology Data Exchange (ETDEWEB)

Widlund, O.

1996-12-31

In the last few years, domain decomposition methods, previously developed and tested for standard finite element methods and elliptic problems, have been extended and modified to work for mortar and other nonconforming finite element methods. A survey will be given of work carried out jointly with Yves Achdou, Mario Casarin, Maksymilian Dryja and Yvon Maday. Results on the p- and h-p-version finite elements will also be discussed.

Why do probabilistic finite element analysis ?

CERN Document Server

Thacker, Ben H

2008-01-01

The intention of this book is to provide an introduction to performing probabilistic finite element analysis. As a short guideline, the objective is to inform the reader of the use, benefits and issues associated with performing probabilistic finite element analysis without excessive theory or mathematical detail.

User's manual for DYNA2D: an explicit two-dimensional hydrodynamic finite-element code with interactive rezoning

Energy Technology Data Exchange (ETDEWEB)

Hallquist, J.O.

1982-02-01

This revised report provides an updated user's manual for DYNA2D, an explicit two-dimensional axisymmetric and plane strain finite element code for analyzing the large deformation dynamic and hydrodynamic response of inelastic solids. A contact-impact algorithm permits gaps and sliding along material interfaces. By a specialization of this algorithm, such interfaces can be rigidly tied to admit variable zoning without the need of transition regions. Spatial discretization is achieved by the use of 4-node solid elements, and the equations-of motion are integrated by the central difference method. An interactive rezoner eliminates the need to terminate the calculation when the mesh becomes too distorted. Rather, the mesh can be rezoned and the calculation continued. The command structure for the rezoner is described and illustrated by an example.

CONSTRUCTION OF AN ELECTRICAL GENERATOR USING THE FINITE ELEMENT ANALYSIS IN ELECTROMAGNETISM, ANSOFT MAXWELL

Directory of Open Access Journals (Sweden)

SAVULESCU Adrian

2014-11-01

Full Text Available This paper attempts to present the necessary steps in designing a electrical generator represented in 2D, 3D, finite element analysis software of Ansoft Maxwell magnetic fields. This work includes modeling form of generator, boundaries, excitations, parameterization, the analysis of the mesh, optimization, performance and representation fields: A (Flux Vector Lines and A, H (Mag_H and H Vector, B (Mag_B and B vector J (Jz and J vector and the energy and other analyzes as CoreLoss, Ohmic_Loss and Total_Loss.

Element Partition Trees For H-Refined Meshes to Optimize Direct Solver Performance. Part I: Dynamic Programming

KAUST Repository

AbouEisha, Hassan M.

2017-07-13

We consider a class of two-and three-dimensional h-refined meshes generated by an adaptive finite element method. We introduce an element partition tree, which controls the execution of the multi-frontal solver algorithm over these refined grids. We propose and study algorithms with polynomial computational cost for the optimization of these element partition trees. The trees provide an ordering for the elimination of unknowns. The algorithms automatically optimize the element partition trees using extensions of dynamic programming. The construction of the trees by the dynamic programming approach is expensive. These generated trees cannot be used in practice, but rather utilized as a learning tool to propose fast heuristic algorithms. In this first part of our paper we focus on the dynamic programming approach, and draw a sketch of the heuristic algorithm. The second part will be devoted to a more detailed analysis of the heuristic algorithm extended for the case of hp-adaptive

Element Partition Trees For H-Refined Meshes to Optimize Direct Solver Performance. Part I: Dynamic Programming

KAUST Repository

AbouEisha, Hassan M.; Calo, Victor Manuel; Jopek, Konrad; Moshkov, Mikhail; Paszyńka, Anna; Paszyński, Maciej; Skotniczny, Marcin

2017-01-01

We consider a class of two-and three-dimensional h-refined meshes generated by an adaptive finite element method. We introduce an element partition tree, which controls the execution of the multi-frontal solver algorithm over these refined grids. We propose and study algorithms with polynomial computational cost for the optimization of these element partition trees. The trees provide an ordering for the elimination of unknowns. The algorithms automatically optimize the element partition trees using extensions of dynamic programming. The construction of the trees by the dynamic programming approach is expensive. These generated trees cannot be used in practice, but rather utilized as a learning tool to propose fast heuristic algorithms. In this first part of our paper we focus on the dynamic programming approach, and draw a sketch of the heuristic algorithm. The second part will be devoted to a more detailed analysis of the heuristic algorithm extended for the case of hp-adaptive

Computational complexity and memory usage for multi-frontal direct solvers used in p finite element analysis

KAUST Repository

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.

Computational complexity and memory usage for multi-frontal direct solvers used in p finite element analysis

KAUST Repository

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.

Finite element analysis theory and application with ANSYS

CERN Document Server

Moaveni, Saeed

2015-01-01

For courses in Finite Element Analysis, offered in departments of Mechanical or Civil and Environmental Engineering. While many good textbooks cover the theory of finite element modeling, Finite Element Analysis: Theory and Application with ANSYS is the only text available that incorporates ANSYS as an integral part of its content. Moaveni presents the theory of finite element analysis, explores its application as a design/modeling tool, and explains in detail how to use ANSYS intelligently and effectively. Teaching and Learning Experience This program will provide a better teaching and learning experience-for you and your students. It will help: *Present the Theory of Finite Element Analysis: The presentation of theoretical aspects of finite element analysis is carefully designed not to overwhelm students. *Explain How to Use ANSYS Effectively: ANSYS is incorporated as an integral part of the content throughout the book. *Explore How to Use FEA as a Design/Modeling Tool: Open-ended design problems help stude...

Finite-Element Software for Conceptual Design

DEFF Research Database (Denmark)

Lindemann, J.; Sandberg, G.; Damkilde, Lars

2010-01-01

and research. Forcepad is an effort to provide a conceptual design and teaching tool in a finite-element software package. Forcepad is a two-dimensional finite-element application based on the same conceptual model as image editing applications such as Adobe Photoshop or Microsoft Paint. Instead of using...

Adaptive finite element analysis of incompressible viscous flow using posteriori error estimation and control of node density distribution

International Nuclear Information System (INIS)

Yashiki, Taturou; Yagawa, Genki; Okuda, Hiroshi

1995-01-01

The adaptive finite element method based on an 'a posteriori error estimation' is known to be a powerful technique for analyzing the engineering practical problems, since it excludes the instinctive aspect of the mesh subdivision and gives high accuracy with relatively low computational cost. In the adaptive procedure, both the error estimation and the mesh generation according to the error estimator are essential. In this paper, the adaptive procedure is realized by the automatic mesh generation based on the control of node density distribution, which is decided according to the error estimator. The global percentage error, CPU time, the degrees of freedom and the accuracy of the solution of the adaptive procedure are compared with those of the conventional method using regular meshes. Such numerical examples as the driven cavity flows of various Reynolds numbers and the flows around a cylinder have shown the very high performance of the proposed adaptive procedure. (author)

Books and monographs on finite element technology

Science.gov (United States)

Noor, A. K.

1985-01-01

The present paper proviees a listing of all of the English books and some of the foreign books on finite element technology, taking into account also a list of the conference proceedings devoted solely to finite elements. The references are divided into categories. Attention is given to fundamentals, mathematical foundations, structural and solid mechanics applications, fluid mechanics applications, other applied science and engineering applications, computer implementation and software systems, computational and modeling aspects, special topics, boundary element methods, proceedings of symmposia and conferences on finite element technology, bibliographies, handbooks, and historical accounts.

A study of the consistent and the lumped source approximations in finite element neutron diffusion calculations

International Nuclear Information System (INIS)

Ozgener, B.; Azgener, H.A.

1991-01-01

In finite element formulations for the solution of the within-group neutron diffusion equation, two different treatments are possible for the group source term: the consistent source approximation (CSA) and the lumped source approximation (LSA). CSA results in intra-group scattering and fission matrices which have the same nondiagonal structure as the global coefficient matrix. This situation might be regarded as a disadvantage, compared to the conventional (i.e. finite difference) methods where the intra-group scattering and fission matrices are diagonal. To overcome this disadvantage, LSA could be used to diagonalize these matrices. LSA is akin to the lumped mass approximation of continuum mechanics. We concentrate on two different aspects of the source approximations. Although it has been reported that LSA does not modify the asymptotic h 2 convergence behaviour for linear elements, the effect of LSA on convergence of higher degree elements has not been investigated. Thus, we would be interested in determining, p, the asymptotic order of convergence, in: Δk |k eff (analytical) -k eff (finite element)| = Ch p (1) for finite element approximations of varying degree (N) with both of the source approximations. Since (1) is valid in the asymptotic limit, we must use ultra-fine meshes and quadruple precision arithmetic. For our order of convergence study, we used infinite cylindrical geometry with azimuthal symmetry. Hence, the effects of singularities remain uninvestigated. The second aspect we dwell on is the performance of LSA in bilinear 3-D finite element calculations, compared to CSA. LSA has been used quite extensively in 1- and 2-D even-parity transport and diffusion calculations. In this work, we will try to assess the relative merits of LSA and CSA in 3-D problems. (author)

TSAAS: finite-element thermal and stress analysis of plane and axisymmetric solids with orthotropic temperature-dependent material properties

Energy Technology Data Exchange (ETDEWEB)

Browning, R.V.; Anderson, C.A.

1982-02-01

The finite element method is used to determine the temperatures, displacements, stresses, and strains in axisymmetric solids with orthotropic, temperature-dependent material properties under axisymmetric thermal and mechanical loads. The mechanical loads can be surface pressures, surface shears, and nodal point forces as well as an axial or centripetal acceleration. The continuous solid is replaced by a system of ring elements with triangular or quadrilateral cross sections. Accordingly, the method is valid for solids that are composed of many different materials and that have complex geometry. Nonlinear mechanical behavior as typified by plastic, locking, or creeping materials can be approximated. Two dimensional mesh generation, plotting, and editing features allow the computer program to be readily used. In addition to a stress analysis program that is based on a modified version of the SAAS code, TSAAS can carry out a transient thermal analysis with the finite element mesh used in stress analysis. An implicit time differencing scheme allows the use of arbitrary time steps with consequent fast running times. At specified times, the program will return to SAAS for thermal stress analysis. Nonlinear thermal properties and Arrhenius reaction kinetics are also incorporated into TSAAS. Several versions of TSAAS are in use at Los Alamos, running on CDC-7600, CRAY-1 and VAX 11/780 computers. This report describes the nominal TSAAS; other versions may have some unique features.

A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins

Science.gov (United States)

Xu, Jingjie; Lu, Benzhuo

2018-01-01

Membrane channel proteins control the diffusion of ions across biological membranes. They are closely related to the processes of various organizational mechanisms, such as: cardiac impulse, muscle contraction and hormone secretion. Introducing a membrane region into implicit solvation models extends the ability of the Poisson–Boltzmann (PB) equation to handle membrane proteins. The use of lateral periodic boundary conditions can properly simulate the discrete distribution of membrane proteins on the membrane plane and avoid boundary effects, which are caused by the finite box size in the traditional PB calculations. In this work, we: (1) develop a first finite element solver (FEPB) to solve the PB equation with a two-dimensional periodicity for membrane channel proteins, with different numerical treatments of the singular charges distributions in the channel protein; (2) add the membrane as a dielectric slab in the PB model, and use an improved mesh construction method to automatically identify the membrane channel/pore region even with a tilt angle relative to the z-axis; and (3) add a non-polar solvation energy term to complete the estimation of the total solvation energy of a membrane protein. A mesh resolution of about 0.25 Å (cubic grid space)/0.36 Å (tetrahedron edge length) is found to be most accurate in linear finite element calculation of the PB solvation energy. Computational studies are performed on a few exemplary molecules. The results indicate that all factors, the membrane thickness, the length of periodic box, membrane dielectric constant, pore region dielectric constant, and ionic strength, have individually considerable influence on the solvation energy of a channel protein. This demonstrates the necessity to treat all of those effects in the PB model for membrane protein simulations. PMID:29495644

Probabilistic finite elements for fracture mechanics

Science.gov (United States)

Besterfield, Glen

1988-01-01

The probabilistic finite element method (PFEM) is developed for probabilistic fracture mechanics (PFM). A finite element which has the near crack-tip singular strain embedded in the element is used. Probabilistic distributions, such as expectation, covariance and correlation stress intensity factors, are calculated for random load, random material and random crack length. The method is computationally quite efficient and can be expected to determine the probability of fracture or reliability.

Comparison of finite-element stress analysis with experimental copper sphere impacts

International Nuclear Information System (INIS)

Frantz, C.E.; Hecker, S.S.; Stout, M.G.; Browning, R.V.

1980-07-01

Three copper spheres were impacted on targets of varying surface finishes at 100 m/s. Impact face friction was varied for each test and the impact was photographed with a high-speed camera. Postimpact strains and deformation were measured. A finite-element computer code, NONSAP, was used to model the impact. The best agreement between computer prediction and experiment was obtained using isoparametric elements, a graded mesh, and actual high-strain-rate copper stress-strain data. Frictional conditions at the impact face were also modeled by altering the standard NONSAP code. The most critical test of NONSAP was accurate prediction of experimental impact strains. The best agreement we could obtain had a maximum point-to-point error of 20%, although in general, the comparison was much better. Results of this research indicate that we must know more about material and impact interface friction in order to obtain reliable numerical predictions

Numerical modeling of the dynamic behavior of structures under impact with a discrete elements / finite elements coupling

International Nuclear Information System (INIS)

Rousseau, J.

2009-07-01

That study focuses on concrete structures submitted to impact loading and is aimed at predicting local damage in the vicinity of an impact zone as well as the global response of the structure. The Discrete Element Method (DEM) seems particularly well suited in this context for modeling fractures. An identification process of DEM material parameters from macroscopic data (Young's modulus, compressive and tensile strength, fracture energy, etc.) will first be presented for the purpose of enhancing reproducibility and reliability of the simulation results with DE samples of various sizes. Then, a particular interaction, between concrete and steel elements, was developed for the simulation of reinforced concrete. The discrete elements method was validated on quasi-static and dynamic tests carried out on small samples of concrete and reinforced concrete. Finally, discrete elements were used to simulate impacts on reinforced concrete slabs in order to confront the results with experimental tests. The modeling of a large structure by means of DEM may lead to prohibitive computation times. A refined discretization becomes required in the vicinity of the impact, while the structure may be modeled using a coarse FE mesh further from the impact area, where the material behaves elastically. A coupled discrete-finite element approach is thus proposed: the impact zone is modeled by means of DE and elastic FE are used on the rest of the structure. An existing method for 3D finite elements was extended to shells. This new method was then validated on many quasi-static and dynamic tests. The proposed approach is then applied to an impact on a concrete structure in order to validate the coupled method and compare computation times. (author)

A comparison of numerical methods used for finite element modelling of soft tissue deformation

KAUST Repository

Pathmanathan, P; Gavaghan, D; Whiteley, J

2009-01-01

Soft tissue deformation is often modelled using incompressible non-linear elasticity, with solutions computed using the finite element method. There are a range of options available when using the finite element method, in particular the polynomial degree of the basis functions used for interpolating position and pressure, and the type of element making up the mesh. The effect of these choices on the accuracy of the computed solution is investigated, using a selection of model problems motivated by typical deformations seen in soft tissue modelling. Model problems are set up with discontinuous material properties (as is the case for the breast), steeply changing gradients in the body force (as found in contracting cardiac tissue), and discontinuous first derivatives in the solution at the boundary, caused by a discontinuous applied force (as in the breast during mammography). It was found that the choice of pressure basis functions is vital in the presence of a material interface, higher-order schemes do not perform as well as may be expected when there are sharp gradients, and in general it is important to take the expected regularity of the solution into account when choosing a numerical scheme. © IMechE 2009.

A comparison of numerical methods used for finite element modelling of soft tissue deformation

KAUST Repository

Pathmanathan, P

2009-05-01

Soft tissue deformation is often modelled using incompressible non-linear elasticity, with solutions computed using the finite element method. There are a range of options available when using the finite element method, in particular the polynomial degree of the basis functions used for interpolating position and pressure, and the type of element making up the mesh. The effect of these choices on the accuracy of the computed solution is investigated, using a selection of model problems motivated by typical deformations seen in soft tissue modelling. Model problems are set up with discontinuous material properties (as is the case for the breast), steeply changing gradients in the body force (as found in contracting cardiac tissue), and discontinuous first derivatives in the solution at the boundary, caused by a discontinuous applied force (as in the breast during mammography). It was found that the choice of pressure basis functions is vital in the presence of a material interface, higher-order schemes do not perform as well as may be expected when there are sharp gradients, and in general it is important to take the expected regularity of the solution into account when choosing a numerical scheme. © IMechE 2009.

Tooth Fracture Detection in Spiral Bevel Gears System by Harmonic Response Based on Finite Element Method

Directory of Open Access Journals (Sweden)

Yuan Chen

2017-01-01

Full Text Available Spiral bevel gears occupy several advantages such as high contact ratio, strong carrying capacity, and smooth operation, which become one of the most widely used components in high-speed stage of the aeronautical transmission system. Its dynamic characteristics are addressed by many scholars. However, spiral bevel gears, especially tooth fracture occurrence and monitoring, are not to be investigated, according to the limited published issues. Therefore, this paper establishes a three-dimensional model and finite element model of the Gleason spiral bevel gear pair. The model considers the effect of tooth root fracture on the system due to fatigue. Finite element method is used to compute the mesh generation, set the boundary condition, and carry out the dynamic load. The harmonic response spectra of the base under tooth fracture are calculated and the influence of main parameters on monitoring failure is investigated as well. The results show that the change of torque affects insignificantly the determination of whether or not the system has tooth fracture. The intermediate frequency interval (200 Hz–1000 Hz is the best interval to judge tooth fracture occurrence. The best fault test region is located in the working area where the system is going through meshing. The simulation calculation provides a theoretical reference for spiral bevel gear system test and fault diagnosis.

An open source software tool to assign the material properties of bone for ABAQUS finite element simulations.

Science.gov (United States)

Pegg, Elise C; Gill, Harinderjit S

2016-09-06

A new software tool to assign the material properties of bone to an ABAQUS finite element mesh was created and compared with Bonemat, a similar tool originally designed to work with Ansys finite element models. Our software tool (py_bonemat_abaqus) was written in Python, which is the chosen scripting language for ABAQUS. The purpose of this study was to compare the software packages in terms of the material assignment calculation and processing speed. Three element types were compared (linear hexahedral (C3D8), linear tetrahedral (C3D4) and quadratic tetrahedral elements (C3D10)), both individually and as part of a mesh. Comparisons were made using a CT scan of a hemi-pelvis as a test case. A small difference, of -0.05kPa on average, was found between Bonemat version 3.1 (the current version) and our Python package. Errors were found in the previous release of Bonemat (version 3.0 downloaded from www.biomedtown.org) during calculation of the quadratic tetrahedron Jacobian, and conversion of the apparent density to modulus when integrating over the Young׳s modulus field. These issues caused up to 2GPa error in the modulus assignment. For these reasons, we recommend users upgrade to the most recent release of Bonemat. Processing speeds were assessed for the three different element types. Our Python package took significantly longer (110s on average) to perform the calculations compared with the Bonemat software (10s). Nevertheless, the workflow advantages of the package and added functionality makes 'py_bonemat_abaqus' a useful tool for ABAQUS users. Copyright © 2016 Elsevier Ltd. All rights reserved.

Rib fractures under anterior-posterior dynamic loads: experimental and finite-element study.

Science.gov (United States)

Li, Zuoping; Kindig, Matthew W; Kerrigan, Jason R; Untaroiu, Costin D; Subit, Damien; Crandall, Jeff R; Kent, Richard W

2010-01-19

The purpose of this study was to investigate whether using a finite-element (FE) mesh composed entirely of hexahedral elements to model cortical and trabecular bone (all-hex model) would provide more accurate simulations than those with variable thickness shell elements for cortical bone and hexahedral elements for trabecular bone (hex-shell model) in the modeling human ribs. First, quasi-static non-injurious and dynamic injurious experiments were performed using the second, fourth, and tenth human thoracic ribs to record the structural behavior and fracture tolerance of individual ribs under anterior-posterior bending loads. Then, all-hex and hex-shell FE models for the three ribs were developed using an octree-based and multi-block hex meshing approach, respectively. Material properties of cortical bone were optimized using dynamic experimental data and the hex-shell model of the fourth rib and trabecular bone properties were taken from the literature. Overall, the reaction force-displacement relationship predicted by both all-hex and hex-shell models with nodes in the offset middle-cortical surfaces compared well with those measured experimentally for all the three ribs. With the exception of fracture locations, the predictions from all-hex and offset hex-shell models of the second and fourth ribs agreed better with experimental data than those from the tenth rib models in terms of reaction force at fracture (difference rib responses and bone fractures for the loading conditions considered, but coarse hex-shell models with constant or variable shell thickness were more computationally efficient and therefore preferred. Copyright 2009 Elsevier Ltd. All rights reserved.

Morphing the feature-based multi-blocks of normative/healthy vertebral geometries to scoliosis vertebral geometries: development of personalized finite element models.

Science.gov (United States)

Hadagali, Prasannaah; Peters, James R; Balasubramanian, Sriram

2018-03-12

Personalized Finite Element (FE) models and hexahedral elements are preferred for biomechanical investigations. Feature-based multi-block methods are used to develop anatomically accurate personalized FE models with hexahedral mesh. It is tedious to manually construct multi-blocks for large number of geometries on an individual basis to develop personalized FE models. Mesh-morphing method mitigates the aforementioned tediousness in meshing personalized geometries every time, but leads to element warping and loss of geometrical data. Such issues increase in magnitude when normative spine FE model is morphed to scoliosis-affected spinal geometry. The only way to bypass the issue of hex-mesh distortion or loss of geometry as a result of morphing is to rely on manually constructing the multi-blocks for scoliosis-affected spine geometry of each individual, which is time intensive. A method to semi-automate the construction of multi-blocks on the geometry of scoliosis vertebrae from the existing multi-blocks of normative vertebrae is demonstrated in this paper. High-quality hexahedral elements were generated on the scoliosis vertebrae from the morphed multi-blocks of normative vertebrae. Time taken was 3 months to construct the multi-blocks for normative spine and less than a day for scoliosis. Efforts taken to construct multi-blocks on personalized scoliosis spinal geometries are significantly reduced by morphing existing multi-blocks.

Introduction to finite and spectral element methods using Matlab

CERN Document Server

Pozrikidis, Constantine

2014-01-01

The Finite Element Method in One Dimension. Further Applications in One Dimension. High-Order and Spectral Elements in One Dimension. The Finite Element Method in Two Dimensions. Quadratic and Spectral Elements in Two Dimensions. Applications in Mechanics. Viscous Flow. Finite and Spectral Element Methods in Three Dimensions. Appendices. References. Index.

A novel upwind stabilized discontinuous finite element angular framework for deterministic dose calculations in magnetic fields.

Science.gov (United States)

Yang, R; Zelyak, O; Fallone, B G; St-Aubin, J

2018-01-30

Angular discretization impacts nearly every aspect of a deterministic solution to the linear Boltzmann transport equation, especially in the presence of magnetic fields, as modeled by a streaming operator in angle. In this work a novel stabilization treatment of the magnetic field term is developed for an angular finite element discretization on the unit sphere, specifically involving piecewise partitioning of path integrals along curved element edges into uninterrupted segments of incoming and outgoing flux, with outgoing components updated iteratively. Correct order-of-accuracy for this angular framework is verified using the method of manufactured solutions for linear, quadratic, and cubic basis functions in angle. Higher order basis functions were found to reduce the error especially in strong magnetic fields and low density media. We combine an angular finite element mesh respecting octant boundaries on the unit sphere to spatial Cartesian voxel elements to guarantee an unambiguous transport sweep ordering in space. Accuracy for a dosimetrically challenging scenario involving bone and air in the presence of a 1.5 T parallel magnetic field is validated against the Monte Carlo package GEANT4. Accuracy and relative computational efficiency were investigated for various angular discretization parameters. 32 angular elements with quadratic basis functions yielded a reasonable compromise, with gamma passing rates of 99.96% (96.22%) for a 2%/2 mm (1%/1 mm) criterion. A rotational transformation of the spatial calculation geometry is performed to orient an arbitrary magnetic field vector to be along the z-axis, a requirement for a constant azimuthal angular sweep ordering. Working on the unit sphere, we apply the same rotational transformation to the angular domain to align its octants with the rotated Cartesian mesh. Simulating an oblique 1.5 T magnetic field against GEANT4 yielded gamma passing rates of 99.42% (95.45%) for a 2%/2 mm (1%/1 mm) criterion.

A novel upwind stabilized discontinuous finite element angular framework for deterministic dose calculations in magnetic fields

Science.gov (United States)

Yang, R.; Zelyak, O.; Fallone, B. G.; St-Aubin, J.

2018-02-01

Angular discretization impacts nearly every aspect of a deterministic solution to the linear Boltzmann transport equation, especially in the presence of magnetic fields, as modeled by a streaming operator in angle. In this work a novel stabilization treatment of the magnetic field term is developed for an angular finite element discretization on the unit sphere, specifically involving piecewise partitioning of path integrals along curved element edges into uninterrupted segments of incoming and outgoing flux, with outgoing components updated iteratively. Correct order-of-accuracy for this angular framework is verified using the method of manufactured solutions for linear, quadratic, and cubic basis functions in angle. Higher order basis functions were found to reduce the error especially in strong magnetic fields and low density media. We combine an angular finite element mesh respecting octant boundaries on the unit sphere to spatial Cartesian voxel elements to guarantee an unambiguous transport sweep ordering in space. Accuracy for a dosimetrically challenging scenario involving bone and air in the presence of a 1.5 T parallel magnetic field is validated against the Monte Carlo package GEANT4. Accuracy and relative computational efficiency were investigated for various angular discretization parameters. 32 angular elements with quadratic basis functions yielded a reasonable compromise, with gamma passing rates of 99.96% (96.22%) for a 2%/2 mm (1%/1 mm) criterion. A rotational transformation of the spatial calculation geometry is performed to orient an arbitrary magnetic field vector to be along the z-axis, a requirement for a constant azimuthal angular sweep ordering. Working on the unit sphere, we apply the same rotational transformation to the angular domain to align its octants with the rotated Cartesian mesh. Simulating an oblique 1.5 T magnetic field against GEANT4 yielded gamma passing rates of 99.42% (95.45%) for a 2%/2 mm (1%/1 mm) criterion.

Regularized finite element modeling of progressive failure in soils within nonlocal softening plasticity

Science.gov (United States)

Huang, Maosong; Qu, Xie; Lü, Xilin

2017-11-01

By solving a nonlinear complementarity problem for the consistency condition, an improved implicit stress return iterative algorithm for a generalized over-nonlocal strain softening plasticity was proposed, and the consistent tangent matrix was obtained. The proposed algorithm was embodied into existing finite element codes, and it enables the nonlocal regularization of ill-posed boundary value problem caused by the pressure independent and dependent strain softening plasticity. The algorithm was verified by the numerical modeling of strain localization in a plane strain compression test. The results showed that a fast convergence can be achieved and the mesh-dependency caused by strain softening can be effectively eliminated. The influences of hardening modulus and material characteristic length on the simulation were obtained. The proposed algorithm was further used in the simulations of the bearing capacity of a strip footing; the results are mesh-independent, and the progressive failure process of the soil was well captured.

Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations

KAUST Repository

Jin, Bangti

2013-01-01

We consider the initial boundary value problem for a homogeneous time-fractional diffusion equation with an initial condition ν(x) and a homogeneous Dirichlet boundary condition in a bounded convex polygonal domain Ω. We study two semidiscrete approximation schemes, i.e., the Galerkin finite element method (FEM) and lumped mass Galerkin FEM, using piecewise linear functions. We establish almost optimal with respect to the data regularity error estimates, including the cases of smooth and nonsmooth initial data, i.e., ν ∈ H2(Ω) ∩ H0 1(Ω) and ν ∈ L2(Ω). For the lumped mass method, the optimal L2-norm error estimate is valid only under an additional assumption on the mesh, which in two dimensions is known to be satisfied for symmetric meshes. Finally, we present some numerical results that give insight into the reliability of the theoretical study. © 2013 Society for Industrial and Applied Mathematics.

Finite Element Methods and Their Applications

CERN Document Server

Chen, Zhangxin

2005-01-01

This book serves as a text for one- or two-semester courses for upper-level undergraduates and beginning graduate students and as a professional reference for people who want to solve partial differential equations (PDEs) using finite element methods. The author has attempted to introduce every concept in the simplest possible setting and maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Quite a lot of attention is given to discontinuous finite elements, characteristic finite elements, and to the applications in fluid and solid mechanics including applications to porous media flow, and applications to semiconductor modeling. An extensive set of exercises and references in each chapter are provided.

Moving finite element method for ICF target implosion

Science.gov (United States)

Furuta, J.; Kawata, S.; Niu, K.

1985-03-01

One dimensional hydrodynamic codes for the analysis of internal confinement fusion (ICF) target implosion which include various effects were developed, but most of them utilize the artificial viscosity (e.g., Von Neumann's viscosity) which cannot reveal accurately the shock waves. A gain of ICF target implosion is much due to the dissipation at the shock fronts, so it is necessary to express correctly the shock waves which are affected by the viscosity. The width of the shock waves is usually a few times as large as the length of mean free path, therefore the meshes for the shock waves must be set to about 10 to the 4th to 10 to the 5th power. It is a serious problem because of the computational memories or CPU time. In the moving finite element (MPE) method, both nodal amplitudes and nodal positions move continuously with time in such a way as to satisfy simultaneous ordinary differential equations (OPDs) which minimize partial differential equation (PDE) residuals.

Parallel paving: An algorithm for generating distributed, adaptive, all-quadrilateral meshes on parallel computers

Energy Technology Data Exchange (ETDEWEB)

Lober, R.R.; Tautges, T.J.; Vaughan, C.T.

1997-03-01

Paving is an automated mesh generation algorithm which produces all-quadrilateral elements. It can additionally generate these elements in varying sizes such that the resulting mesh adapts to a function distribution, such as an error function. While powerful, conventional paving is a very serial algorithm in its operation. Parallel paving is the extension of serial paving into parallel environments to perform the same meshing functions as conventional paving only on distributed, discretized models. This extension allows large, adaptive, parallel finite element simulations to take advantage of paving`s meshing capabilities for h-remap remeshing. A significantly modified version of the CUBIT mesh generation code has been developed to host the parallel paving algorithm and demonstrate its capabilities on both two dimensional and three dimensional surface geometries and compare the resulting parallel produced meshes to conventionally paved meshes for mesh quality and algorithm performance. Sandia`s {open_quotes}tiling{close_quotes} dynamic load balancing code has also been extended to work with the paving algorithm to retain parallel efficiency as subdomains undergo iterative mesh refinement.

A Study of the Transient Response of Duct Junctions: Measurements and Gas-Dynamic Modeling with a Staggered Mesh Finite Volume Approach

Directory of Open Access Journals (Sweden)

Antonio J. Torregrosa

2017-05-01

Full Text Available Duct junctions play a major role in the operation and design of most piping systems. The objective of this paper is to establish the potential of a staggered mesh finite volume model as a way to improve the description of the effect of simple duct junctions on an otherwise one-dimensional flow system, such as the intake or exhaust of an internal combustion engine. Specific experiments have been performed in which different junctions have been characterized as a multi-port, and that have provided precise and reliable results on the propagation of pressure pulses across junctions. The results obtained have been compared to simulations performed with a staggered mesh finite volume method with different flux limiters and different meshes and, as a reference, have also been compared with the results of a more conventional pressure loss-based model. The results indicate that the staggered mesh finite volume model provides a closer description of wave dynamics, even if further work is needed to establish the optimal calculation settings.

Programming the finite element method

CERN Document Server

Smith, I M; Margetts, L

2013-01-01

Many students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to develop computer programs to solve specific engineering problems using the finite element method. This new fifth edition offers timely revisions that include programs and subroutine libraries fully updated to Fortran 2003, which are freely available online, and provides updated material on advances in parallel computing, thermal stress analysis, plasticity return algorithms, convection boundary c