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A GPU Solver for Sparse Generalized Eigenvalue Problems with Symmetric Complex-Valued Matrices Obtained Using Higher-Order FEM
Abstract
The paper discusses a fast implementation of the stabilized locally optimal block preconditioned conjugate gradient (sLOBPCG) method, using a hierarchical multilevel preconditioner to solve nonHermitian sparse generalized eigenvalue problems with large symmetric complex-valued matrices obtained using the higher-order finite-element method (FEM), applied to the analysis of a microwave resonator. The resonant frequencies of the low-order modes are the eigenvalues of the smallest real part of a complex symmetric (though non-Hermitian) matrix pencil. These type of pencils arise in the FEM analysis of resonant cavities loaded with a lossy material. To accelerate the computations, graphics processing units (GPU, NVIDIA Pascal P100) were used. Single and dual-GPU variants are considered and a GPU-memorysaving implementation is proposed. An efficient sliced ELLR-T sparse matrix storage format was used and operations were performed on blocks of vectors for best performance on a GPU. As a result, significant speedups (exceeding a factor of six in some computational scenarios) were achieved over the reference parallel implementation using a multicore central processing unit (CPU, Intel Xeon E5-2680 v3, twelve cores). These results indicate that the solution of generalized eigenproblems needs much more GPU memory than iterative techniques when solving a sparse system of equations, and also requires a second GPU to store some data structures in order to reduce the footprint, even for a moderately large systems
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- Copyright (2018 IEEE)
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Details
- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
IEEE Access
no. 6,
pages 69826 - 69834,
ISSN: 2169-3536 - Language:
- English
- Publication year:
- 2018
- Bibliographic description:
- Dziekoński A., Mrozowski M.: A GPU Solver for Sparse Generalized Eigenvalue Problems with Symmetric Complex-Valued Matrices Obtained Using Higher-Order FEM// IEEE Access. -Vol. 6, (2018), s.69826-69834
- DOI:
- Digital Object Identifier (open in new tab) 10.1109/access.2018.2871219
- Verified by:
- Gdańsk University of Technology
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