WAVEHOLTZ: ITERATIVE SOLUTION OF THE HELMHOLTZ EQUATION VIA THE WAVE EQUATION

被引：18

作者：

Appelo, Daniel ^{[1
]}

Garcia, Fortino ^{[1
]}

Runborg, Olof ^{[2
]}

机构：

[1] Univ Colorado, Dept Appl Math, Boulder, CO 80309 USA

[2] KTH, Dept Math, S-10044 Stockholm, Sweden

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2020年 / 42卷 / 04期

关键词：

Helmholtz; wave equation; positive definite; POLARIZED TRACES; SWEEPING PRECONDITIONER; CONTROLLABILITY METHODS; DOMAIN DECOMPOSITION; PERIODIC-SOLUTIONS; COMPUTATION; FORMULATION; SCATTERING; LAYER;

D O I：

10.1137/19M1299062

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new iterative method, the WaveHoltz iteration, for solution of the Helmholtz equation is presented. WaveHoltz is a fixed point iteration that filters the solution to the solution of a wave equation with time periodic forcing and boundary data. The WaveHoltz iteration corresponds to a linear and coercive operator which, after discretization, can be recast as a positive definite linear system of equations. The solution to this system of equations approximates the Helmholtz solution and can be accelerated by Krylov subspace techniques. Analysis of the continuous and discrete cases is presented, as are numerical experiments.

引用

页码：A1950 / A1983

页数：34

共 41 条

[1]

[Anonymous], 1997, Electron. Trans. Numer. Anal

[2]

AppelEo D., 2005, THESIS

[3] An energy-based discontinuous Galerkin discretization of the elastic wave equation in second order form [J].

Appelo, Daniel ;

Hagstrom, Thomas .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2018, 338 :362-391

[4] A NEW DISCONTINUOUS GALERKIN FORMULATION FOR WAVE EQUATIONS IN SECOND-ORDER FORM [J].

Appeloe, Daniel ;

Hagstrom, Thomas .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2015, 53 (06) :2705-2726

[5] A high-order super-grid-scale absorbing layer and its application to linear hyperbolic systems [J].

Appeloe, Daniel ;

Colonius, Tim .

JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 228 (11) :4200-4217

[6]

Appelö D, 2009, COMMUN COMPUT PHYS, V5, P84

[7] Efficient implementation of high-order finite elements for Helmholtz problems [J].

Beriot, Hadrien ;

Prinn, Albert ;

Gabard, Gwenael .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2016, 106 (03) :213-240

[8]

Bjorck A., 2015, NUMERICAL METHODS MA, V59

[9] Controllability methods for the computation of time-periodic solutions;: application to scattering [J].

Bristeau, MO ;

Glowinski, R ;

Périaux, J .

JOURNAL OF COMPUTATIONAL PHYSICS, 1998, 147 (02) :265-292

[10] A SOURCE TRANSFER DOMAIN DECOMPOSITION METHOD FOR HELMHOLTZ EQUATIONS IN UNBOUNDED DOMAIN [J].

Chen, Zhiming ;

Xiang, Xueshuang .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2013, 51 (04) :2331-2356

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