Approximation of boundary values in the boundary element method

Fast Isogeometric Boundary Element Method based on Independent Field Approximation

An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies, permits an efficient evaluation of geometry related information, a mixed collocation scheme which deals with discontinuous tractions along non-smooth boundaries ...

Approximation of Integrals for Boundary Element Methods

A new method for approximating two-dimensional integrals B f (x) µ(dx) over surfaces B ⊂ R 3 is introduced where µ is the standard measure of surface area. Such integrals typically occur in boundary element methods. The algorithm is based on triangulations T := T i approximating B. Under the assumption that the surface B is given implicitly by an equation H(x) = 0, a retraction P : U ⊃ B → B is...

Evaluation of Fracture Parameters by Coupling the Edge-Based Smoothed Finite Element Method and the Scaled Boundary Finite Element Method

This paper presents a technique to evaluate the fracture parameters by combining the edge based smoothed finite element method (ESFEM) and the scaled boundary finite element method (SBFEM). A semi-analytical solution is sought in the region close to the vicinity of the crack tip using the SBFEM, whilst, the ESFEM is used for the rest of the domain. As both methods satisfy the partition of unity...

Boundary Element Approximation for Maxwell’s Eigenvalue Problem

We introduce a new method for computing eigenvalues of the Maxwell operator with boundary finite elements. On bounded domains with piecewise constant material coefficients, the Maxwell solution for fixed wave number can be represented by boundary integrals, which allows to reduce the eigenvalue problem to a nonlinear problem for determining the wave number along with boundary and interface trac...

A Regular Indirect Boundary Element Method for Thermal Analysis