The main subject of this contribution is to present some recent methods, specially designed to be implemented on parallel platforms, to deal with acoustic scattering problems involving a bounded zone filled by a heterogeneous medium. The main approach is to couple a Finite Element Method, for handling this zone, with a Boundary Integral Equation, specially adapted to treat the unbounded part of...

Domain decomposition methods are designed to deal with coupled or transmission problems for partial differential equations. Since the original boundary value problem is replaced by local problems in substructures, domain decomposition methods are well suited for both parallelization and coupling of different discretization schemes. In general, the coupled problem is reduced to the Schur complem...

Isogeometric analysis is applied to boundary integral equations corresponding to boundary-value problems governed by Laplace’s equation. It is shown that the smoothness of geometric parametrizations central to computer-aided design can be exploited for regularizing integral operators. As a result, one obtains high-order collocation methods based on superior approximation and numerical integrati...

The potential of sparse grid discretizations for solving boundary integral equations is studied for the screen problem on a square in IR 3. Theoretical and numerical results on approximation rates, preconditioning, adaptivity and compression for piecewise constant and linear sparse grid spaces are obtained.

This paper considers the numerical solution of boundary integral equations of the second kind for Laplace s equation u on connected regions D in R with boundary S The boundary S is allowed to be smooth or piecewise smooth and we let f K j K Ng be a triangulation of S The numerical method is collocation with approximations which are piecewise quadratic in the parametrization variables leading to...

When an mtemally heated body IS cooled along Its boundary by a penpherally flowmg flmd that IS contmually replemshed from an external source, a dlfferentml energy balance on the boundary leads to unfamiliar boundary condltlons Such boundary condltlons Involve mued second denuatrues with respect to spatial vmables, which under addltlonal assumptions (such as an mhmte heat transfer coefficient) l...

The weak-form of Helmholtz differential equation, in conjunction with vector test-functions (which are gradients of the fundamental solutions to the Helmholtz differential equation in free space) is utilized as the basis in order to directly derive non-hyper-singular boundary integral equations for the velocity potential, as well as its gradients. Thereby, the presently proposed boundary integr...

In this paper, the four integral identities satisfied by the fundamental solution for elastostatic problems are reviewed and slightly different forms of the third and fourth identities are presented. Two new identities, namely the fifth and sixth identities, are derived. These integral identities can be used to develop weakly singular and nonsingular forms of the boundary integral equations (BI...

and objectives In tutorial 2, we demonstrated the basic steps for deriving the direct boundary integral equation. In this tutorial we will explain, with more examples, the derivation of the direct boundary integral equation for systems of partial differential equations. We will consider two examples: elasticity problems and shear-deformable plate bending problems. 1 Elasticity equations In this...

Abstract. Starting from a recently developed energetic space-time weak formulation of boundary integral equations related to wave propagation problems defined on single and multidomains, a coupling algorithm is presented, which allows a flexible use of finite and boundary element methods as local discretization techniques, in order to efficiently treat unbounded multilayered media. Partial diff...