Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Professor Olaf Steinbach,Technische Universit?t Graz, Austria
Inviter:	Associate Professor Tao Yin
Title:	Space-time finite and boundary element methods for the wave equation
Language:	Chinese
Time & Venue:	2023.04.20 15:00-16:00 Zoom Meeting: 946 1498 5764, Password: 437247
Abstract:	In this talk we will review some recent results on space-time finite and boundary element methods for the wave equation. As a first model problem we consider the inhomogeneous wave equation with zero Dirichlet boundary and initial conditions. The related space-time variational formulation follows the standard approach when applying integration by parts in space and time simultaneously. Note that a space-time tensor-product based finite element discretization requires a CFL condition to ensure stability. While the ansatz and test spaces are both subspaces of functions whose space-time gradient is square integrable, they differ in zero initial and terminal conditions to be satisfied. When introducing a modified Hilbert transformation we end up with a Galerkin variational formulation which is unconditionally stable. This modified Hilbert transformation is also an essential tool in the formulation of coercive boundary integral equations for the wave equation. Finally we also consider distributed optimal control problems subject to the wave equation, and related space-time least-squares finite and boundary element methods. The talk is based on joint work with Marco Zank (Vienna), Richard L?scher (Graz), Carolina Urzua-Torres (Delft), and Daniel Hoonhout (Delft).