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THE HP-VERSION OF BEM – FAST CONVERGENCE, ADAPTIVITY AND EFFICIENT PRECONDITIONING

Ernst P. Stephan
Journal of Computational Mathematics
Vol. 27, No. 2/3 (March 2009), pp. 348-359
Stable URL: http://www.jstor.org/stable/43693511
Page Count: 12
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THE HP-VERSION OF BEM – FAST CONVERGENCE, ADAPTIVITY AND EFFICIENT PRECONDITIONING
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Abstract

In this survey paper we report on recent developments of the hp-version of the boundary element method (BEM). As model problems we consider weakly singular and hypersingular integral equations of the first kind on a planar, open surface. We show that the Galerkin solutions (computed with the hp-version on geometric meshes) converge exponentially fast towards the exact solutions of the integral equations. An Zip-adaptive algorithm is given and the implementation of the hp-version BEM is discussed together with the choice of efficient preconditioners for the ill-conditioned boundary element stiffness matrices. We also comment on the use of the hp-version BEM for solving Signorini contact problems in linear elasticity where the contact conditions are enforced only on the discrete set of Gauss-Lobatto points. Numerical results are presented which underline the theoretical results.

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