Adaptive quadrature rules for Galerkin BEM

Eecient Automatic Quadrature in 3{d Galerkin Bem

We present cubature methods approximating the surface integrals arising by Galerkin discretization of boundary integral equations on surfaces in R 3. This numerical integrator does not depend on the explicit form of the kernel function, the trial and test space, or the surface parametrization. Thus, it is possible to generate the system matrix for a broad class of integral equations just by rep...

Quadrature Rules for Fuzzy Integrals

Numerical solution of exterior Maxwell problems by Galerkin BEM and Runge-Kutta convolution quadrature

In this paper we consider time-dependent electromagnetic scattering problems from conducting objects. We discretize the time-domain electric field integral equation using RungeKutta convolution quadrature in time and a Galerkin method in space. We analyze the involved operators in the Laplace domain and obtain convergence results for the fully discrete scheme. Numerical experiments indicate the...

Cubature techniques for 3 - D Galerkin BEM

We present cubature methods for the approximation of surface integrals arising from Galerkin discretizations of 3-D boundary integral equations. This numerical integrator is fully implicit in the sense that the form of the kernel function, the surface parametrization, the trial and test space, and the order of the singularity of the kernel functions are not used explicitly. Different kernels ca...

Accelerated Galerkin BEM for 3D Potential Theory

This paper is concerned with the development of a fast spectral method for solving boundary integral equations in three-dimensional potential theory. Upon discretizing the underlying boundary integrals via a Galerkin approximation, the proposed method overlays the problem domain with a regular Cartesian grid that serves as an auxiliary platform for computation. With the aid of the Fast Fourier ...