Modeling of wave propagation in open domains

Abstract

Simulating electromagnetic or acoustic wave propagation in complex open structures is extremely important in many areas of science and engineering. In a wide range of applications, ranging from photonics and plasmonics to seismic exploration, efficient wave field solvers are required in various design and optimization frameworks. In this thesis, a Krylov subspace projection methodology is presented to efficiently solve wave propagation problems on unbounded domains. To model the extension of the computational domain to infinity, an optimal complex scaling method is introduced. Traditionally, complex scaling has been used to simulate open quantum systems. Here, an optimized complex scaling method is implemented that allows us to simulate wave propagation on unbounded domains provided we compute the propagating waves via a stability-corrected wave function. In our Krylov subspace framework, this wave function is approximated by polynomial or rational functions, which are obtained via Krylov subspace projection. We show that the field approximations are actually expansions in terms of approximate open resonance modes of the system and we present a novel and highly efficient Krylov subspace implementation for media exhibiting second-order relaxation effects. Numerical examples for one-, two-, and three-dimensional problems illustrate the performance of the method and show that our Krylov resonance expansions significantly outperform conventional solution methods.