APPLICATION OF KRYLOV SUBSPACE METHODS TO BOUNDARY ELEMENT SOUND FIELD ANALYSIS : Numerical analysis of large-scale sound fields using iterative solvers Part 1

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  • 境界要素音場解析へのKrylov部分空間法の適用 : 反復解法を利用した大規模音場数値解析 その1
  • キョウカイ ヨウソ オンジョウ カイセキ エ ノ Krylov ブブン クウカンホウ ノ テキヨウ ハンプクカイホウ オ リヨウ シタ ダイキボ オンジョウ スウチ カイセキ ソノ 1

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Abstract

Iterative solvers are widely used for solving large systems of linear equations, and applied to the systems obtained with the acoustical FEM and BEM. In the present paper, the convergence behavior of the Krylov subspace iterative solvers towards the systems with the 3-D acoustical fast muftipole BEM, an efficient BEM based on the fast multipole algorithm, is investigated through numerical experiments. The convergence behavior of solvers is much affected by the formulation of the BEM (basic form (BF), normal derivative form (NDF) and Burton-Miller formulation), the complexity of the shape of the problem, and the sound absorption property of the boundaries. In BiCG-like solvers, GPBiCG and BiCGStab2 converge more stable than others, and these solvers are useful when solving interior problems using BF. When solving exterior problems with greatly complex shape using Burton-Miller formulation, all solvers hardly converge without preconditioning, whereas the convergence behavior is much improved with ILU-type preconditioning. In these cases GMRes is the fastest, whereas CGS is one of the good choices, when taken into account the difficulty of determining the timing of restart for GMRes. As for calculation for thin objects using NDF, much more rapid convergence is observed than ordinary interior/exterior problems, especially using BiCG-like solvers.

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