StiffMa

版本 1.6 (27.7 MB) 作者: Francisco Ramírez
StiffMa: Fast finite element STIFFness MAtrix generation in MATLAB by using GPU computing.
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150.0 次下载
更新时间 2020/6/15
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The finite element method (FEM) is a well established numerical technique for solving partial differential equations (PDEs) in a wide range of complex science and engineering applications. This method has two costly operation that are the construction of global matrices and vectors to form the system of linear or nonlinear equations (assemblage), and their solution (solver). Many efforts have been directed to accelerate the solver. However, the assembly stage has been less investigated although it may represent a serious bottleneck in iterative processes such as non-linear and time-dependent phenomena, and in optimization procedures involving FEM with unstructured meshes. Thus, a fast technique for the global FEM matrices construction is proposed herein by using parallel computing on graphics processing units (GPUs). This work focuses on matrices that arise by solving elliptic PDEs, what is commonly known as stiffness matrix. For performance tests, a scalar problem typically represented by the thermal conduction phenomenon and a vector problem represented by the structural elasticity are considered in a three-dimensional (3D) domain. Unstructured meshes with 8-node hexahedral elements are used to discretize the domain. The MATLAB Parallel Computing Toolbox (PCT) is used to program the CUDA code. The stiffness matrix are built with three GPU kernels that are the indices computation, the numerical integration and the global assembly. Symmetry and adequate data precision are used to save memory and runtime. This proposed methodology allows generating global stiffness matrices from meshes with more than 16.3 millions elements in less than 3 seconds for the scalar problem and up to 3.1 millions for the vector one in 6 seconds using an Nvidia Tesla V100 GPU with 16 GB of memory. Large speedups are obtained compared with a non-optimized CPU code.

引用格式

Francisco Ramírez (2024). StiffMa (https://github.com/fjramireg/StiffMa/releases/tag/v1.6), GitHub. 检索来源 .

MATLAB 版本兼容性
创建方式 R2020a
与 R2015b 及更高版本兼容
平台兼容性
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Utils

libs/mutils-0.4-2

libs/mutils-0.4-2/SuiteSparse

libs/mutils-0.4-2/examples

libs/mutils-0.4-2/mutils

libs/mutils-0.4-2/mutils/interp

libs/mutils-0.4-2/mutils/libmatlab

libs/mutils-0.4-2/mutils/libutils

libs/mutils-0.4-2/mutils/quadtree

libs/mutils-0.4-2/mutils/reorder

libs/mutils-0.4-2/mutils/sparse

libs/mutils-0.4-2/mutils/sparse/spmvbench

libs/mutils-0.4-2/triangle

tbx/StiffMa

tbx/StiffMa/Common

tbx/StiffMa/Scalar

tbx/StiffMa/Vector

tests/Comparison_fsparse

tests/Comparison_fsparse/Old

tests/Comparison_fsparse/Old/StiffMa_CPUvsGPU

tests/Comparison_fsparse/Old/StiffMa_CPUvsGPU_R2020a

tests/Comparison_fsparse/StiffMa_CPUvsGPU_scalar

tests/Comparison_fsparse/StiffMa_CPUvsGPU_vector

tests/Performance

tests/Performance/AssemblyPerfTestRst

tests/Performance/EStiffPerfTestRst

tests/Performance/EStiffPerfTestRst/secondrun_EStiffPerfTestRst

tests/Performance/IndexPerfTestRst

tests/Performance/StiffMa2_PerfTestRst

tests/Performance/StiffMaPerfTestRst

tests/Verification

tbx/StiffMa

tbx/doc

tbx/doc/examples

版本 已发布 发行说明
1.6

See release notes for this release on GitHub: https://github.com/fjramireg/StiffMa/releases/tag/v1.6
1.5

1.4.0.0

See release notes for this release on GitHub: https://github.com/fjramireg/StiffMa/releases/tag/v1.4
1.3.0.0

See release notes for this release on GitHub: https://github.com/fjramireg/StiffMa/releases/tag/v1.3
1.2.0.0

See release notes for this release on GitHub: https://github.com/fjramireg/StiffMa/releases/tag/v1.2
1.1.0.0

See release notes for this release on GitHub: https://github.com/fjramireg/StiffMa/releases/tag/v1.1
1.0.0.0

See release notes for this release on GitHub: https://github.com/fjramireg/StiffMa/releases/tag/v1.0
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要查看或报告此来自 GitHub 的附加功能中的问题，请访问其 GitHub 仓库。