Title / Abstract
Time Domain Boundary Element MethodsI propose to contribute with 3 lectures on time domain BEM with full space-time Galerkin approach and one lecture about some examples of industrial applications of BEM in both time and frequency domains. I would begin with a recall of principal mathematical basis for the study of BEM and wave problems, if you juge that it may be interesting and if it is not already planned.
Outline
Lecture 1 (optional) : Mathematical background- a rapid recall of surface differential operators, Fourier transform, convolution, single/double layer distributions, jump formula...
- the wave equation, causality and radiation condition + elementary solutions for acoustic and electromagnetic waves
- Integral representation
- Frequency dependent Sobolev norms
- Integral equations in the frequency domain
- Optimal estimates
- A Paley-Wiener theorem
- Space-time functional framework
- Space-time variational fomulation
- Space-time Galerkin discretization
- Boundary value and transmission conditions
- Dispersive relations
- Fluid-structure coupling (vibro-acoustics)
- FEM/BEM and DGM/BEM coupling
- Fast-algorithms
- applications in acoustics
- applications in electromagnetics (EMC and lighting indirect effects)
