A Krylov subspace projection method for simultaneous solution of Helmholtz problems at multiple frequencies

Marcus M. Wagner; Peter M. Pinsky; Assad A. Oberai; Manish Malhotra

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A Krylov subspace projection method for simultaneous solution of Helmholtz problems at multiple frequencies

机译：用于同时求解亥姆霍兹问题的Krylov子空间投影方法

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摘要

A Krylov subspace projection method which provides simultaneous solutions of the Helmholtz equation at multiple frequencies in one solution step is presented. The projector is obtained with an unsymmetric block Lanczos algorithm applied to a transfer function derived from a finite element discretization. This approach is equivalent to a matrix-valued Pade approximation of the transfer function. The proposed method is an extension of the formulation presented in [J. Comput. Acoust. 8 (2000) 223] to unsymmetric systems and allows the treatment of a much wider range of practical problems, including near-field and fluid-structure interaction computations.

机译：提出了一种Krylov子空间投影方法，该方法可以在一个求解步骤中同时提供多个频率的Helmholtz方程的求解。通过将非对称块Lanczos算法应用于从有限元离散化得出的传递函数中获得了投影机。这种方法等效于传递函数的矩阵值Pade近似。所提出的方法是对[J.Am.Sci。计算co 8（2000）223]提出了非对称系统，并允许处理更广泛的实际问题，包括近场和流体-结构相互作用计算。

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来源
《Computer Methods in Applied Mechanics and Engineering》 |2003年第42期|p.4609-4640|共32页
作者
Marcus M. Wagner; Peter M. Pinsky; Assad A. Oberai; Manish Malhotra;
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作者单位

Division of Mechanics and Computation, Stanford University, Stanford, CA 94305-4040, USA;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类自动化基础理论;工程基础科学;
关键词
multiple-frequency solution; krylov subspace; lanczos algorithm; pade approximation; helmholtz equation; dirichlet-to-neumann map; acoustics;

机译：多频解Krylov子空间Lanczos算法帕德逼近Helmholtz方程Dirichlet到Neumann图声学;

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2. Preconditioned krylov subspace methods for boundary element solution of the Helmholtz equation [J] . S. Amini, N. D. Maines International Journal for Numerical Methods in Engineering . 1998,第5期

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3. A multigrid-based preconditioned Krylov subspace method for the Helmholtz equation with PML [J] . Chen Z., Cheng D., Feng W., Journal of Mathematical Analysis and Applications . 2011,第2期

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4. Accelerated Solution of Helmholtz Equation with Iterative Krylov Methods on GPU [C] . Cheik Ahamed Abal-Kassim, Magoules Frederic 2014 IEEE Intl Conf on High Performance Computing and Communications, 2014 IEEE 6th Intl Symp on Cyberspace Safety and Security, 2014 IEEE 11th Intl Conf on Embedded Software and Syst . 2014

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5. On the Krylov subspace solutions of matrix equations in control theory. [D] . Peng, Wujian. 2005

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7. Preconditioned Krylov subspace methods for sixth order compact approximations of the Helmholtz equation [O] . Gryazin, Yury 2012

机译：六阶紧致的预条件Krylov子空间方法亥姆霍兹方程的近似

A Krylov subspace projection method for simultaneous solution of Helmholtz problems at multiple frequencies

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