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- W2012593516 abstract "Hierarchical (<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi mathvariant=script>H</mml:mi></mml:math>-) matrices method is a general mathematical framework providing a highly compact representation and efficient numerical arithmetic. When applied in integral-equation- (IE-) based computational electromagnetics,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi mathvariant=script>H</mml:mi></mml:math>-matrices can be regarded as a fast algorithm; therefore, both the CPU time and memory requirement are reduced significantly. Its kernel independent feature also makes it suitable for any kind of integral equation. To solve<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi mathvariant=script>H</mml:mi></mml:math>-matrices system, Krylov iteration methods can be employed with appropriate preconditioners, and direct solvers based on the hierarchical structure of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi mathvariant=script>H</mml:mi></mml:math>-matrices are also available along with high efficiency and accuracy, which is a unique advantage compared to other fast algorithms. In this paper, a novel sparse approximate inverse (SAI) preconditioner in multilevel fashion is proposed to accelerate the convergence rate of Krylov iterations for solving<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi mathvariant=script>H</mml:mi></mml:math>-matrices system in electromagnetic applications, and a group of parallel fast direct solvers are developed for dealing with multiple right-hand-side cases. Finally, numerical experiments are given to demonstrate the advantages of the proposed multilevel preconditioner compared to conventional “single level” preconditioners and the practicability of the fast direct solvers for arbitrary complex structures." @default.
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- W2012593516 date "2012-01-01" @default.
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- W2012593516 title "Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations" @default.
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- W2012593516 doi "https://doi.org/10.1155/2012/756259" @default.
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