Stabilizing block diagonal preconditioners for complex dense matrices in electromagnetics |
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Authors: | Xinyu Geng |
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Affiliation: | a School of Computer Science, Southwest Petroleum University, Chengdu, Sichuan 610500, China b Laboratory for High Performance Scientific Computing and Computer Simulation, Department of Computer Science, University of Kentucky, Lexington, KY 40506-0046, USA c Department of Computer Science, Shippensburg University, Shippensburg, PA 17257, USA |
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Abstract: | Preconditioning techniques are widely used to speed up the convergence of iterative methods for solving large linear systems with sparse or dense coefficient matrices. For certain application problems, however, the standard block diagonal preconditioner makes the Krylov iterative methods converge more slowly or even diverge. To handle this problem, we apply diagonal shifting and stabilized singular value decomposition (SVD) to each diagonal block, which is generated from the multilevel fast multiple algorithm (MLFMA), to improve the stability and efficiency of the block diagonal preconditioner. Our experimental results show that the improved block diagonal preconditioner maintains the computational complexity of MLFMA, converges faster and also reduces the CPU cost. |
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Keywords: | Preconditioning Singular value decomposition (SVD) Iterative method MLFMA |
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