Solution of Helmholtz equation in the exterior domain by elementary boundary integral methods
Journal of Computational Physics
GMRES with Deflated Restarting
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Regularized Combined Field Integral Equations
Numerische Mathematik
SIAM Journal on Scientific Computing
A stable well-conditioned integral equation for electromagnetism scattering
Journal of Computational and Applied Mathematics
Improving the Accuracy of GMRes with Deflated Restarting
SIAM Journal on Scientific Computing
Numerical Estimation of Coercivity Constants for Boundary Integral Operators in Acoustic Scattering
SIAM Journal on Numerical Analysis
| Hi-index | 31.45 |
The paper presents a detailed numerical study of an iterative solution to 3-D sound-hard acoustic scattering problems at high frequency considering the Combined Field Integral Equation (CFIE). We propose a combination of an OSRC preconditioning technique and a Fast Multipole Method which leads to a fast and efficient algorithm independently of both a frequency increase and a mesh refinement. The OSRC-preconditioned CFIE exhibits very interesting spectral properties even for trapping domains. Moreover, this analytic preconditioner shows highly-desirable advantages: sparse structure, ease of implementation and low additional computational cost. We first investigate the numerical behavior of the eigenvalues of the related integral operators, CFIE and OSRC-preconditioned CFIE, in order to illustrate the influence of the proposed preconditioner. We then apply the resolution algorithm to various and significant test-cases using a GMRES solver. The OSRC-preconditioning technique is combined to a Fast Multipole Method in order to deal with high-frequency 3-D cases. This variety of tests validates the effectiveness of the method and fully justifies the interest of such a combination.