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A New Sparse Matrix Vector Multiplication GPU Algorithm Designed for Finite Element Problems
Mathematical Software · Submitted 1 Jan 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim GPU finite element simulation results demonstrate the benefit of using GPUs for finite element analysis, and also show that the proposed algorithms can yield speedup factors up to 12-fold for real finite element applications.
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The abstract, sentence by sentence
Recently, graphics processors (GPUs) have been increasingly leveraged in a variety of scientific computing applications. However, architectural differences between CPUs and GPUs necessitate the development of algorithms that take advantage of GPU hardware. As sparse matrix vector multiplication (SPMV) operations are commonly used in finite element analysis, a new SPMV algorithm and several variations are developed for unstructured finite element meshes on GPUs. The effective bandwidth of current GPU algorithms and the newly proposed algorithms are measured and analyzed for 15 sparse matrices of varying sizes and varying sparsity structures. The effects of optimization and differences between the new GPU algorithm and its variants are then subsequently studied. Lastly, both new and current SPMV GPU algorithms are utilized in the GPU CG Solver in GPU finite element simulations of the heart. These results are then compared against parallel PETSc finite element implementation results. The effective bandwidth tests indicate that the new algorithms compare very favorably with current algorithms for a wide variety of sparse matrices and can yield very notable benefits. GPU finite element simulation results demonstrate the benefit of using GPUs for finite element analysis, and also show that the proposed algorithms can yield speedup factors up to 12-fold for real finite element applications.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Recently, graphics processors (GPUs) have been increasingly leveraged in a variety of scientific computing applications. | background 1.00 | 0.05 | 0.02 | asserted 0.99 |
| s1 | However, architectural differences between CPUs and GPUs necessitate the development of algorithms that take advantage of GPU hardware. | background 0.80 | 0.05 | 0.02 | asserted 0.99 |
| s2 | As sparse matrix vector multiplication (SPMV) operations are commonly used in finite element analysis, a new SPMV algorithm and several variations are developed for unstructured finite element meshes on GPUs. | contribution 0.99 | 0.94 | 0.05 | asserted 1.00 |
| s3 | The effective bandwidth of current GPU algorithms and the newly proposed algorithms are measured and analyzed for 15 sparse matrices of varying sizes and varying sparsity structures. | method 0.93 | 0.94 | 0.04 | asserted 0.99 |
| s4 | The effects of optimization and differences between the new GPU algorithm and its variants are then subsequently studied. | method 0.66 | 0.91 | 0.03 | asserted 0.55 |
| s5 | Lastly, both new and current SPMV GPU algorithms are utilized in the GPU CG Solver in GPU finite element simulations of the heart. | method 0.83 | 0.91 | 0.04 | asserted 0.95 |
| s6 | These results are then compared against parallel PETSc finite element implementation results. | method 0.89 | 0.86 | 0.04 | asserted 0.76 |
| s7 | The effective bandwidth tests indicate that the new algorithms compare very favorably with current algorithms for a wide variety of sparse matrices and can yield very notable benefits. | result 0.86 | 0.95 | 0.56 | hedged possibility 0.53 |
| s8 | GPU finite element simulation results demonstrate the benefit of using GPUs for finite element analysis, and also show that the proposed algorithms can yield speedup factors up to 12-fold for real finite element applications. | result 0.97 | 0.95 | 0.77 | asserted 1.00 |
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The paper
Original abstract
Recently, graphics processors (GPUs) have been increasingly leveraged in a variety of scientific computing applications. However, architectural differences between CPUs and GPUs necessitate the development of algorithms that take advantage of GPU hardware. As sparse matrix vector multiplication (SPMV) operations are commonly used in finite element analysis, a new SPMV algorithm and several variations are developed for unstructured finite element meshes on GPUs. The effective bandwidth of current GPU algorithms and the newly proposed algorithms are measured and analyzed for 15 sparse matrices of varying sizes and varying sparsity structures. The effects of optimization and differences between the new GPU algorithm and its variants are then subsequently studied. Lastly, both new and current SPMV GPU algorithms are utilized in the GPU CG Solver in GPU finite element simulations of the heart. These results are then compared against parallel PETSc finite element implementation results. The effective bandwidth tests indicate that the new algorithms compare very favorably with current algorithms for a wide variety of sparse matrices and can yield very notable benefits. GPU finite element simulation results demonstrate the benefit of using GPUs for finite element analysis, and also show that the proposed algorithms can yield speedup factors up to 12-fold for real finite element applications.
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