The convergence analysis of multigrid methods for boundary element equations arising from negative-order pseudo-differential operators is quite different from the usual finite element multigrid analysis for elliptic partial differential equations. In this paper, we study the convergence of geometric multigrid methods for solving large-scale, data-sparse boundary element equations arising from t...

Recently, a refined finite element analysis for highly indefinite Helmholtz problems was introduced by the second author. We generalise the analysis to the Galerkin method applied to an abstract, highly indefinite variational problem. In the refined analysis, the condition for stability and a quasi-optimal error estimate is expressed in terms of approximation properties T (S) ≈ S and T (u + S) ...

An efficient method to solve time harmonic Maxwell’s equations in exterior domain for high frequencies is obtained by using the integral formulation of Després combined with a coupling method (MLFMD) based on the Microlocal Discretization method (MD) and the Multi-Level Fast Multipole Method (MLFMM) [1]. In this paper, we consider curved finite elements of higher order in the MLFMD method. More...

This paper is devoted to the fast solution of interface concentrated finite element equations. The interface concentrated finite element schemes are constructed on the basis of a non-overlapping domain decomposition where a conforming boundary concentrated finite element approximation is used in every subdomain. Similar to data-sparse boundary element domain decomposition methods the total numb...

This paper presents three new coupling methods for interior penalty discontinuous Galerkin finite element methods and boundary element methods. The new methods allow one to use discontinuous basis functions on the interface between the subdomains represented by the finite element and boundary element methods. This feature is particularly important when discontinuous Galerkin finite element meth...

ABSTRACT Fluid-loaded nested cylindrical shells are modelled using a doubled-walled cylindrical shell structure closed at each end by circular end plates and excited by a transverse force at one end. The effects of various influencing factors on the radiated sound power are examined corresponding to non-concentricity of the cylindrical shells, entrained fluid and rib connections in the annular ...

This paper presents a Galerkin boundary element method for solving crack problems governed by potential theory in nonhomogeneous media. In the simple boundary element method, the nonhomogeneous problem is reduced to a homogeneous problem using variable transformation. Cracks in heat conduction problem in functionally graded materials are investigated. The thermal conductivity varies parabolical...

The goal of this paper is to generalize the BEM-based FEM for second order elliptic boundary value problems to three space dimensions with the emphasis on polyhedral meshes with polygonal faces, where even nonconvex elements are allowed. Due to an implicit definition of the trial functions, the strategy yields conforming approximations and is very flexible with respect to the meshes. Thus, it g...

In this paper we propose and analyze some new methods for coupling mixed finite element and boundary element methods for the model problem of the Laplace equation in free space or in the exterior of a bounded domain. As opposed to the existing methods, which use the complete matrix of operators of the Calderón projector to obtain a symmetric coupled system, we propose methods with only one inte...

The purpose of this paper is to test the applicability of a fast boundary element method in the context of geoid computations of the gravity. The fast multipole method is the method of choice due to the its advantageous property of a fast evaluation in the post-processing. Several sets of trianglar meshes for the approximation of the unit sphere and several modifications of the prediscribed dat...