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Stabilizing block diagonal preconditioners for complex dense matrices in electromagnetics. (English) Zbl 1202.65040
Summary: 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 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.
65F08 Preconditioners for iterative methods
65F10 Iterative numerical methods for linear systems
65F50 Computational methods for sparse matrices
65Y20 Complexity and performance of numerical algorithms
65F20 Numerical solutions to overdetermined systems, pseudoinverses
78A55 Technical applications of optics and electromagnetic theory
78M15 Boundary element methods applied to problems in optics and electromagnetic theory
BILUTM; Scaleme
Full Text: DOI
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