Computational and Numerical Analysis of Transient Problems in Acoustics, Elasticity, and Electromagnetism (16w5071)
The primary goal of this conference is to bring together experts in time domain integral equations, time domain volume techniques, linear system solvers and absorbing boundary conditions in order to explore the strengths and weakness of the various approaches in a collaborative environment. Researchers from these groups are very rarely together in one venue.
There has been much exciting progress recently in each of the different areas of wave propagation covered by this workshop. This raises fundamentally important questions about the ``best'' strategy for solving different types of problems. In particular, about the relative merits of the BIE and PDE approaches for time domain problems. For example, should time domain problems be solved by means of Fourier transforming frequency domain solutions, or are time domain strategies always better (i.e. more accurate, efficient, reliable)? Do time domain boundary integral methods have other advantages that allow them to compete with timed domain differential equation formulations that use sophisticated absorbing boundary conditions and overlapping grid techniques? Are there situations when a combination of these approaches is most suitable (for example when dealing with scattering from large bodies with attached wires)?
We expect to exploit better connections between time domain Integral equations and volume techniques. Other specific problems to be discussed include fast solvers for time domain boundary integral equations, and the stabilization of time domain integral equations for Maxwell’s equations (instability, likely due to low frequency degeneration of the integral equations, is sometimes observed for Maxwell’s equations).
An expectation is that we can create a mathematical and computational framework for a new generation of fast and more robust methods capable of handling complex heterogeneous media.