Perfectly Matched absorbing Layers
for wave propagation problems

Participants

Numerical simulation of propagating waves in unbounded spatial domains is a challenge common to many branches of engineering and applied sciences. Relevant application areas are electromagnetism, seismology, acoustics, aerodynamics, oceanography, quantum mechanics. In numerical simulations unbounded domains must be replaced by smaller computational domains. An efficient and reliable domain truncation therefore becomes a vital tool in a numerical wave simulator.
The perfectly matched layer (PML) has proved to be flexible and accurate, for simulating the absorption of waves and provides an alternative to absorbing or non-reflecting boundary conditions (ABC). The PML consists of extending the computational domain to a layer (buffer zone), where the underlying equations are modified such that waves decay rapidly in the layer. The modified equations are perfectly matched to the original equations in the interior. That is, there are no reflections as waves propagate across the interface, into the PML. This approach is analogous to the physical treatment of the walls of the anechoic chambers.

The project

The goal of this project is to construct and analysis PML models for various wave propagation problems.

Applications

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Ongoing work

The PML is usually derived by assuming a homogeneous medium and an infinite domain in all directions. In a domain with physical boundaries, in order to avoid unwanted reflection from the interface, the underlying boundary conditions must be accurately extended from the interior into the PML. These type of problems are important in many applications areas, including seismic, optical and gravitational waves. Examples include glancing waves and surface waves in electromagnetic and elastic wave propagation problems. We are currently extending the PML to these problems and our preliminary results are quite promising.

Future or recently started work includes developing the PML technique for:
Non-linear flow problems modeled by the Euler equations and the Navier-Stokes equations,
underwater acoustics, where we aim at designing absorbing layers that model the open boundary below the seafloor. We are also considering quantum molecular dynamics, where we solve the time dependent Schrödinger equation. This is part of an effort of developing efficient methods for simulating chemical reactions.

Articles

Theses

Contact: , Gunilla Kreiss