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...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 hp-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.展开更多
文摘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 hp-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.
