GPU‐based Polynomial Finite Element Matrix Assembly for Simplex Meshes

The aim of this paper is to evaluate efficiency of different approaches to parallelization ofstiffness matrix assembly operations, that can be found in any finite element software. OpenMP [1, 2]and POSIX Threads (Pthreads) programming models are two considered in this paper. The OpenMPmodel consist of an Application Program Interface (API) for multi-platform shared-memory parallelprogramming in C/C++. POSIX is an acronym for Portable Operating System Interface and Pthreadsstandards [3] defined as a set of C/C++ language [4] programming types and procedure calls forshared-memory parallel programming. The paper shows that parallelization can efficiently exploit thepower of modern available hardware, significantly reducing the needed computation time. Differentapproaches of each programming model are used for parallelization of stiffness matrix assemblycompared and their efficiency is evaluated in this paper.The different parallelization strategies were implemented in OOFEM [5] which is a free finiteelement code with object oriented architecture for solving mechanical, transport and fluid mechanicsproblems that operates on various platforms. The finite element method leads to set of algebraic equa-tions which components are assembled from contributions of individual elements. In this paper wefocus on assembly of sparse matrix contributions, such as stiffness as mass matrices. Domain decom-position paradigm, where the whole domain is decomposed into sub domain, which contributions areevaluated and assembled by individual threads is hard.The paper discuss the differences between approaches based on OpenMP and Pthreads, datascoping specification for correct parallel programming and memory allocation synchronization andscheduling.

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GPU-Accelerated Finite-Element Matrix Generation for Lossless, Lossy, and Tensor Media [EM Programmer's Notebook]

IEEE Antennas and Propagation Magazine ◽

10.1109/map.2014.6971943 ◽

2014 ◽

Vol 56 (5) ◽

pp. 186-197 ◽

Cited By ~ 4

Author(s):

Adam Dziekonski ◽

Piotr Sypek ◽

Adam Lamecki ◽

Michal Mrozowski

Keyword(s):

Finite Element ◽

Element Matrix

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Analytical finite element matrix elements and global matrix assembly for hierarchical 3-D vector basis functions within the hybrid finite element boundary integral method

Advances in Radio Science ◽

10.5194/ars-12-1-2014 ◽

2014 ◽

Vol 12 ◽

pp. 1-11

Author(s):

L. Li ◽

K. Wang ◽

H. Li ◽

T. F. Eibert

Keyword(s):

Finite Element ◽

Large Scale ◽

Higher Order ◽

Boundary Integral ◽

Basis Functions ◽

Boundary Integral Method ◽

Matrix Elements ◽

Matrix Assembly ◽

Time Accuracy ◽

Element Boundary

Abstract. A hybrid higher-order finite element boundary integral (FE-BI) technique is discussed where the higher-order FE matrix elements are computed by a fully analytical procedure and where the gobal matrix assembly is organized by a self-identifying procedure of the local to global transformation. This assembly procedure applys to both, the FE part as well as the BI part of the algorithm. The geometry is meshed into three-dimensional tetrahedra as finite elements and nearly orthogonal hierarchical basis functions are employed. The boundary conditions are implemented in a strong sense such that the boundary values of the volume basis functions are directly utilized within the BI, either for the tangential electric and magnetic fields or for the asssociated equivalent surface current densities by applying a cross product with the unit surface normals. The self-identified method for the global matrix assembly automatically discerns the global order of the basis functions for generating the matrix elements. Higher order basis functions do need more unknowns for each single FE, however, fewer FEs are needed to achieve the same satisfiable accuracy. This improvement provides a lot more flexibility for meshing and allows the mesh size to raise up to λ/3. The performance of the implemented system is evaluated in terms of computation time, accuracy and memory occupation, where excellent results with respect to precision and computation times of large scale simulations are found.

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Large Geometrically Nonlinear Responses of Discretized Plate Structures Under Nonstationary Random Excitations

Volume 2: 19th Computers and Information in Engineering Conference ◽

10.1115/detc99/cie-9061 ◽

1999 ◽

Author(s):

C. W. S. To ◽

M. L. Liu

Keyword(s):

Finite Element ◽

Difference Method ◽

Large Scale ◽

Hybrid Strain ◽

Central Difference ◽

Nonstationary Random Process ◽

Highly Nonlinear ◽

Strain Formulation ◽

Central Difference Method ◽

Element Matrix

Abstract In the investigation reported here novel techniques for the computation of highly nonlinear response statistics, such as mean square and covariance of generalized displacements of large scale discretized plate and shell structures have been developed. The techniques combine the versatile finite element method and the stochastic central difference method as well as derivatives of the latter such that complex aerospace and naval structures under intensive transient disturbances represented as nonstationary random processes can be considered. The flat triangular plate finite element is of the Mindlin type and is based on the hybrid strain formulation. The updated Lagrangiah hybrid strain based formulation is capable of dealing with deformations of finite rotations and finite strains. Explicit expressions for the consistent element mass and stiff matrices were previously obtained, and therefore no numerical matrix inversion and integration is necessary in the element matrix derivation. Several additional features are novel. First, the so-called averaged deterministic central difference scheme is employed in the co-ordinate updating process for large deformations. Second, application of the time co-ordinate transformation in conjunction with the stochastic central difference method enables one to deal with highly stiff discretized structures. Third, application of the adaptive time schemes makes it convenient to solve a wide variety of highly nonlinear systems. Finally, the recursive nature of the stochastic central difference method makes it possible to deal with a wide class of nonstationary random process.

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Tetrahedral finite element matrix primitives

Computer Physics Communications ◽

10.1016/s0010-4655(84)82886-6 ◽

1984 ◽

Vol 35 ◽

pp. C-756

Author(s):

Peter P. Silvester ◽

F.U. Minhas ◽

Z.J. Csendes

Keyword(s):

Finite Element ◽

Element Matrix

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