Parallel and vectorized implementation of analytic evaluation of boundary integral operators

Zapletal, Jan; Merta, Michal

doi:10.1016/j.enganabound.2018.08.015

Cited by 11 publications

(6 citation statements)

References 31 publications

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“…Indeed, in addition to the evaluation of the distance between spatial coordinates x − y , which is the most time consuming part of the BEM assembly for the Laplace equation, one has to evaluate the exponential and error functions in many quadrature points for all blocks of the Toeplitz matrix. The implementation strategy in shared memory thus follows the ideas presented by the authors previously for 3d space and 2d space-time BEM in [20,21,22]. To make use of modern multicore processors with vector arithmetic units we make use of features of modern OpenMP [23], namely threading and SIMD vectorisation.…”

Section: Methodsmentioning

confidence: 99%

“…To exploit the full potential of floating point units we vectorise the code at the level of local contributions to the global matrix. For simplicity we opt for the OpenMP implementation of vector processing similarly as in [20,21,22].…”

Section: Local Contributionsmentioning

confidence: 99%

“…, to ensure unit strided access to data. Earlier work [20,21,22] has shown that this approach is more efficient than an array of vectors.…”

Section: Local Contributionsmentioning

confidence: 99%

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Semi-analytic integration for a parallel space-time boundary element method modeling the heat equation

Zapletal,

Watschinger,

et al. 2021

Preprint

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The presented paper concentrates on the boundary element method (BEM) for the heat equation in three spatial dimensions. In particular, we deal with tensor product space-time meshes allowing for quadrature schemes analytic in time and numerical in space. The spatial integrals can be treated by standard BEM techniques known from three dimensional stationary problems. The contribution of the paper is twofold. First, we provide temporal antiderivatives of the heat kernel necessary for the assembly of BEM matrices and the evaluation of the representation formula. Secondly, the presented approach has been implemented in a publicly available library besthea allowing researchers to reuse the formulae and BEM routines straightaway. The results are validated by numerical experiments in an HPC environment.

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Section: Methodsmentioning

confidence: 99%

Section: Local Contributionsmentioning

confidence: 99%

See 1 more Smart Citation

Semi-analytic integration for a parallel space-time boundary element method modeling the heat equation

Zapletal,

Watschinger,

et al. 2021

Preprint

Self Cite

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show abstract

“…The most popular methods are the message passing interface (MPI) and open multi-processing (OpenMP) (e.g. applied in [21,22]). Another very common method is the application of graphics processing unit (GPU) for numerical calculations (by CUDA or OpenCL) [23,24].…”

Section: Introductionmentioning

confidence: 99%

The FMM accelerated PIES with the modified binary tree in solving potential problems for the domains with curvilinear boundaries

Kużelewski

Zieniuk

2021

Numer Algor

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The paper presents an accelerating of solving potential boundary value problems (BVPs) with curvilinear boundaries by modified parametric integral equations system (PIES). The fast multipole method (FMM) known from the literature was included into modified PIES. To consider complex curvilinear shapes of a boundary, the modification of a binary tree used by the FMM is proposed. The FMM combined with the PIES, called the fast PIES, also allows a significant reduction of random access memory (RAM) utilization. Therefore, it is possible to solve complex engineering problems on a standard personal computer (PC). The proposed algorithm is based on the modified PIES and allows for obtaining accurate solutions of complex BVPs described by the curvilinear boundary at a reasonable time on the PC.

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“…3 we propose a strategy to parallelize the assembly of the MTF matrix blocks and their application in an iterative solver based on the approach presented in [11][12][13] for single domain problems. Except for the distributed parallelism, the method takes full advantage of the BEM4I library [14,20,21] and its assemblers parallelized in shared memory and vectorized by OpenMP. We provide the results of numerical experiments in Sect.…”

Section: Introductionmentioning

confidence: 99%

Parallel Adaptive Cross Approximation for the Multi-trace Formulation of Scattering Problems

Kravčenko

Zapletal

Claeys

et al. 2020

Parallel Processing and Applied Mathematics

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We present a highly parallel version of the boundary element method accelerated by the adaptive cross approximation for the efficient solution of scattering problems with composite scatterers. Individual boundary integral operators are treated independently, i.e. the boundary of every homogeneous subdomain is decomposed into clusters of elements defining a block structure of the local matrix. The blocks are distributed across computational nodes by a graph algorithm providing a load balancing strategy. The intra-node implementation further utilizes threading in shared memory and in-core SIMD vectorization to make use of all features of modern processors. The suggested approach is validated on a series of numerical experiments presented in the paper.

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Parallel and vectorized implementation of analytic evaluation of boundary integral operators

Cited by 11 publications

References 31 publications

Semi-analytic integration for a parallel space-time boundary element method modeling the heat equation

Semi-analytic integration for a parallel space-time boundary element method modeling the heat equation

The FMM accelerated PIES with the modified binary tree in solving potential problems for the domains with curvilinear boundaries

Parallel Adaptive Cross Approximation for the Multi-trace Formulation of Scattering Problems

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