Numerical Analysis and Scientific Computing Seminar | Kenneth Duru, On the stability of the perfectly matched layer (PML) for propagating waves in SBP and DG methods

For Zoom Link please contact ddelreyfernandez@uwaterloo.ca  

Speaker

Kenneth Duru, MSI Fellow at the Mathematical Sciences Institute, Australian National University

Title

On the stability of the perfectly matched layer (PML) for propagating waves in SBP and DG methods

Abstract

It is well-known that reliable and efficient domain truncation is crucial to accurate numerical solution of most wave propagation problems. The perfectly matched layer (PML) is a method which, when stable, can provide a domain truncation scheme which is convergent with increasing layer width/damping. The difficulties in using the PML are primarily associated with stability, which can be present at the continuous level or be triggered by numerical approximations.  The mathematical and numerical analysis of the PML for hyperbolic wave propagation problems has been an area of active research. It is now possible to construct stable and high order accurate numerical wave solvers by augmenting wave equations with the PML and approximating the equations using summation-by-parts finite difference methods, continuous and discontinuous Galerkin finite element methods. In this presentation we will summarise the progress made, from mathematical, numerical, and practical perspectives, point out some open problems and set the stage for future work. We will also present numerical experiments of model problems corroborating the theoretical analysis, and numerical simulations of real-world wave propagation demonstrating impact. Stable and parallel implementations of the PML in the high-performance computing software packages WaveQLab3D and ExaHyPE  allow  to sufficiently limit the computational domain of seismological problems with only a few grid points/elements around the computational boundaries where the PML is active, thus saving as much as 96% of the required computational resources for a three-space dimensional seismological benchmark problem.