Solving the wave equation: acoustic scattering in the time domain
Prof. Paul Martin, Department of Applied Mathematics and Statistics, Colorado School of Mines
Transient acoustic waves are generated or scattered by an obstacle. This leads to initial-boundary value problems for the wave equation. Recent studies usually assume that the solution is smooth. However, many interesting physical problems lead to non-smooth solutions: there are moving wavefronts. These situations are usually handled by seeking weak solutions, but care is needed to ensure that constraints imposed by the underlying continuum mechanics are respected. We investigate some of the consequences, with a focus on the benchmark problem of scattering by a sphere.