Numerical methods for space-time variational formulations of retarded potential boundary integral equations [Elektronische Ressource] / Elke Ostermann

Numerical Methods for Space-Time VariationalFormulations of Retarded Potential BoundaryIntegral EquationsVon der Fakulta¨t fu¨r Mathematik und Physikder Gottfried Wilhelm Leibniz Universita¨t Hannoverzur Erlangung des Grades einerDoktorin der NaturwissenschaftenDr. rer. nat.genehmigte DissertationvonDipl.-Math. Elke Ostermanngeboren am 02. Dezember 1980, in Barßel2010Referent: Prof. Dr. E. P. Stephan, Gottfried Wilhelm Leibniz Universita¨t HannoverKoreferent: PD Dr. M. Maischak, Brunel University, Uxbridge, United KingdomKoreferent: Prof. S. Sauter, Universita¨t Zu¨rich, SchweizTag der Promotion: 21.12.2009vAbstractThis thesis discusses the numerical solution of time dependent scattering phenomena in unbounded domains usingretarded potential boundary integral equations, also known as time domain boundary integral equations. We employ anunconditionally stable space-time variational formulation whose fully discrete formulation results in a marching-on-in-time (MOT) scheme through a history of sparse matrices and solution vectors.The main focus of this work lies on the efficient computation of the matrix entries. We study the discrete retardedpotentials evaluated on one element of a surface triangulation. We show that besides the classical corner-edge singu-larities on the boundary of the element additional singularities of geometrical nature exist, which we call geometricallight cone singularities.