Imaging and Computing Seminar
Thomas Hagstrom , Department of Mathematics, SMU
Title:
Towards the Ultimate Solver for Wave Equations in the Time Domain
Abstract:
Efficient time-domain solvers for wave propagation problems must include
three crucial components:
i. Radiation boundary conditions which provide arbitrary accuracy at
small cost (spectral convergence, weak dependence on the simulation time
and wavelength)
ii. Algorithms for using the information at or near the boundary to
directly propagate the solution to remote locations - avoid sampling
the wave whenever possible.
iii. Reliable high-resolution volume discretizations applicable in
complex geometry (i.e. on grids that can be generated efficiently) -
we believe that high-resolution methods enabling accurate simulations
with minimal dofs-per-wavelength are necessary to solve difficult
3+1-dimensional problems with the possibility of error control.
In this talk we will discuss recent developments in all three areas,
including our own work on the construction of complete radiation
boundary conditions (CRBCs), which are optimal local radiation
conditions, as well as novel spectral elements based on Hermite
interpolation.