Details

Autor(en) / Beteiligte

• Darbas, M.
• Darrigrand, E.
• Lafranche, Y.

Titel

Combining analytic preconditioner and Fast Multipole Method for the 3-D Helmholtz equation

Ist Teil von

• Journal of computational physics, 2013-03, Vol.236, p.289-316

Ort / Verlag

Elsevier Inc

Erscheinungsjahr

2013

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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.