Friday, February 3, 2012

1202.0424 (Vladimir Druskin et al.)

A Krylov Stability-Corrected Coordinate-Stretching Method to Simulate
Wave Propagation in Unbounded Domains

Vladimir Druskin, Rob Remis
The Krylov subspace projection approach is a well-established tool for the
reduced order modeling of dynamical systems in the time domain. In this paper,
we address the main issues obstructing the application of this powerful
approach to the time-domain solution of exterior wave problems. We design
efficient frequency independent perfectly matched layers with controlled
accuracy and introduce a new Krylov-based solution method via
stability-corrected operator exponents. This approach allows us to construct
reduced-order models (ROMs) that respect the delicate spectral properties of
the original scattering problem. The ROMs are unconditionally stable and are
based on a renormalized bi-Lanczos algorithm, which enables us to efficiently
compute the time-domain solution. We give a theoretical foundation of our
method and illustrate its performance through a number of numerical examples in
which we simulate 2D electromagnetic wave propagation in unbounded domains,
including a photonic waveguide example. The new algorithm outperforms the
conventional finite-difference time domain method for problems on large time
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