TIME-DOMAIN BOUNDARY INTEGRAL EQUATIONS: A CONVOLUTION QUADRATURE PERSPECTIVE - LEHEL BANJAI - HERIOT WATT UNIVERSITY

A brief introduction will be given to a background on boundary integral equations for steady state
problems and their numerical discretization.
Focus will however be on time-domain boundary integral equations (TDBIE) for acoustic scattering
problems. After an overview of the Bamberger/Ha Duong analysis of TDBIE, the rest of the course
will centre on their numerical discretization. In particular, close attention will be afforded to the
numerical analysis and efficient implementation of convolution quadrature as a method for time discretization
of TDBIE taking the original Laplace domain approach of Lubich. The course will
end with some more advanced applications such as FEM/BEM coupling and will also cover
implementation in open source software such as delta beam and BEM++.
Program (main topics)
 Applications of boundary integral equations in steady state and transient problems. (1 hour)
 Sobolev spaces and space discretization of boundary integral equations: BEM and collocation (3 hours)
 Bamberger/Ha Duong analysis of time-domain boundary integral equations (2 hours)
 Convolution quadrature. Analysis and implementation of both low order (linear multistep) and high-order (Runge-Kutta) schemes. (6 hours)
 FEM/BEM coupling (3 hours)
 Modified CQ schemes (1 hour)
 Large scale implementation (4 hours)
Schedule of the course
 Monday March 22nd: 10:00-12:00
 Thursday March 25th: 10:00-12:00
 Monday March 29th: 10:00-12:00
 Monday April 19th: 10:00-12:00
 Thursday April 22nd: 10:00-12:00
 Monday April 26th: 10:00-12:00
 Thursday April 29th: 10:00-12:00
 Monday May 3rd: 10:00-12:00
 Thursday May 6th: 10:00-12:00
 Monday May 10th: 10:00-12:00