A GPU Solver for Sparse Generalized Eigenvalue Problems with Symmetric Complex-Valued Matrices Obtained Using Higher-Order FEM - Publication - MOST Wiedzy

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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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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
Bibliography: test
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  34. ADAM DZIEKONSKI received the M.S.E.E. and Ph.D. degrees (Hons.) in microwave engineering from the Gdańsk University of Technology, Gdańsk, Poland, in 2009 and 2015, respectively. His current research interests include computational electromagnetics (mainly focused on parallelizing computa- tions on graphics processing and central processing units). He was a recipient of the Domestic Grant for Young Scientists from the Foundation for Polish Science in 2012 and 2013. He was also a recipient of the Prime Minister's Award for his Ph.D. thesis in 2016. open in new tab
  35. MICHAL MROZOWSKI (F'08) received the M.Sc. and Ph.D. degrees (Hons.) from the Gdańsk University of Technology in 1983 and 1990, respectively. In 1986, he joined the Faculty of Electronics, Gdańsk University of Technology, where he is currently a Full Professor, the Head of the Department of Microwave and Antenna Engineering, and the Director of the Center of Excellence for Wireless Communication Engineering. open in new tab
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