New Numerical Integration Schemes for Applications of Galerkin Bem to 2-D Problems

Abstract

SUMMARYWe consider hypersingular integral formulation of some elasticity and potential boundary value problems on 2-D domains. In particular, we consider all integrals whose evaluation is required when the equations are solved by a Galerkin BEM based on piecewise polynomial approximants of arbitrary local degrees. In order to compute these integrals, we use very e cient formulas recently proposed, which require the user to deÿne a mesh, not necessarily uniform, on the boundary and specify the local degrees of the approximant. These rules are quite suitable for the construction of h-p version of the BEM. Implementation of h−, p− and h-p methods are applied to some classical problems and several numerical results are presented. ? 1997 by John Wiley & Sons, Ltd.

Galerkin BEM with Direct Evaluation of Hypersingular Integrals

“…where E(y, ε) is defined by (19) with E = E. Expression (26) for the distance vector r becomes in this case…”

“…The same is true for the limit to the boundary method [16,17,18]. On the other hand, techniques based on the finite part idea [19,20,21] completely overlook the free term evaluation, as the 'bump' associated to the vanishing neighbourhood is never taken into account.…”

“…SGBEM formulations based on the so called finite part integrals have been also developed. In [19,20] they are evaluated numerically, while in [21] an analytical evaluation is pursued.…”

Analytical integrations in 2D BEM elasticity

“…There is nowadays an extensive literature on this subject (see, among others [38][39][40][41][42][43][44]). A huge amount of literature concerns the numerical evaluation of hypersingular integrals: among others [15; 18; 19; 38; 45-47].…”

“…Furthermore, a multizone problem with rigid interface is proposed and solved via the SGBEM. A pure integration test is also conducted, comparing analytical integration with recently proposed numerical integration schemes [42].…”