Results 1 
1 of
1
Adaptive Time Discretization for Retarded Potentials
"... We consider retarded boundary integral formulations of the threedimensional wave equation in unbounded domains. Our goal is to apply a Galerkin method in space and time in order to solve these problems numerically. In this approach the computation of the system matrix entries is the major bottlenec ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
(Show Context)
We consider retarded boundary integral formulations of the threedimensional wave equation in unbounded domains. Our goal is to apply a Galerkin method in space and time in order to solve these problems numerically. In this approach the computation of the system matrix entries is the major bottleneck. We will propose new types of finitedimensional spaces for the time discretization. They allow variable timestepping, variable order of approximation and simplify the quadrature problem arising in the generation of the system matrix substantially. The reason is that the basis functions of these spaces are globally smooth and compactly supported. In order to perform numerical tests concerning our new basis functions we consider the special case that the boundary of the scattering problem is the unit sphere. In this case explicit solutions of the problem are available which will serve as reference solutions for the numerical experiments. AMS subject classifications. 35L05, 65N38, 65R20 1.