International audienceIn this paper we consider Dirichlet or Neumann wave propagation problems reformulated in terms of boundary integral equations with retarded potential. Starting from a natural energy identity, a space–time weak formulation for 1D integral problems is briefly introduced, and continuity and coerciveness properties of the related bilinear form are proved. Then, a theoretical analysis of an extension of the introduced formulation for 2D problems is proposed, pointing out the novelty with respect to existing literature results. At last, various numerical simulations will be presented and discussed, showing unconditional stability of the space–time Galerkin boundary element method applied to the energetic weak problem

This paper deals with the discrete counterpart of 2D elliptic model problems rewritten in terms of Boundary Integral Equations. The study is done within the framework of Isogeometric Analysis based on B-splines. In such a context, the problem of constructing appropriate, accurate and efficient quadrature rules for the Symmetric Galerkin Boundary Element Method is here investigated. The new integration schemes, together with row assembly and sum factorization, are used to build a more efficient strategy to derive the final linear system of equations. Key ingredients are weighted quadrature rules tailored for B-splines, that are constructed to be exact in the whole test space, also with respect to the singular kernel. Several simulations are presented and discussed, showing accurate evaluation of the involved integrals and outlining the superiority of the new approach in terms of computational cost and elapsed time with respect to the standard element-by-element assembly.

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.

SUMMARYIn this paper we consider singular and hypersingular integral equations associated with 2D boundary value problems deÿned on domains whose boundaries have piecewise smooth parametric representations. In particular, given any (polynomial) local basis, we show how to compute e ciently all integrals required by the Galerkin method. The proposed numerical schemes require the user to specify only the local polynomial degrees; therefore they are quite suitable for the construction of p-and h-p versions of Galerkin BEM.

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