TY - JOUR

T1 - Iterative schemes for high order compact discretizations to the exterior Helmholtz equation

AU - Erlangga, Yogi

AU - Turkel, Eli

PY - 2012/5

Y1 - 2012/5

N2 - We consider high order finite difference approximations to the Helmholtz equation in an exterior domain. We include a simplified absorbing boundary condition to approximate the Sommerfeld radiation condition. This yields a large, but sparse, complex system, which is not self-adjoint and not positive definite. We discretize the equation with a compact fourth or sixth order accurate scheme. We solve this large system of linear equations with a Krylov subspace iterative method. Since the method converges slowly, a preconditioner is introduced, which is a Helmholtz equation but with a modified complex wavenumber. This is discretized by a second or fourth order compact scheme. The system is solved by BICGSTAB with multigrid used for the preconditioner. We study, both by Fourier analysis and computations this preconditioned system especially for the effects of high order discretizations.

AB - We consider high order finite difference approximations to the Helmholtz equation in an exterior domain. We include a simplified absorbing boundary condition to approximate the Sommerfeld radiation condition. This yields a large, but sparse, complex system, which is not self-adjoint and not positive definite. We discretize the equation with a compact fourth or sixth order accurate scheme. We solve this large system of linear equations with a Krylov subspace iterative method. Since the method converges slowly, a preconditioner is introduced, which is a Helmholtz equation but with a modified complex wavenumber. This is discretized by a second or fourth order compact scheme. The system is solved by BICGSTAB with multigrid used for the preconditioner. We study, both by Fourier analysis and computations this preconditioned system especially for the effects of high order discretizations.

KW - Helmholtz equation

KW - High order compact schemes

UR - http://www.scopus.com/inward/record.url?scp=84855846901&partnerID=8YFLogxK

U2 - 10.1051/m2an/2011063

DO - 10.1051/m2an/2011063

M3 - מאמר

AN - SCOPUS:84855846901

VL - 46

SP - 647

EP - 660

JO - ESAIM: Mathematical Modelling and Numerical Analysis

JF - ESAIM: Mathematical Modelling and Numerical Analysis

SN - 0764-583X

IS - 3

ER -