Department of Geophysics
A new look at well-posedness, stability and accurate numerical approximations of perfectly matched layers for wave equations Many important engineering problems and fundamental physical processes can be described by time-dependent partial differential equations whose solutions are composed of waves. Typical examples are in nondestructive testing, seismology, earthquake engineering, ultrasonics, and ground penetrating radar technologies. Efficient numerical simulators for time-dependent wave propagation problems must include two important components: 1. Reliable and accurate domain truncation schemes which provide arbitrary accuracy at small cost. 2. High order accurate and time-stable volume discretizations applicable to complicated media on grids that can be generated efficiently. To this end, my presentation has two parts. In the first part, I will discuss my recent results on the development of stable perfectly matched layers to effectively truncate unbounded computational domains. The general theory can be applied either to first order or second order hyperbolic systems. The second part of the presentation will consider the development of novel and efficient numerical methods for second order hyperbolic systems using summation-by-parts finite difference operators. I will present a number of examples focusing on the Maxwell's equations and equations of linear elastodynamics.
Sponsored by the Department of Mathematical Sciences
Host: Susan Minkoff and John Zweck