31
views
0
recommends
+1 Recommend
0 collections
    16
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

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

      Preprint

      ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          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 use frequency independent perfectly matched layers to simulate the extension to infinity. Pure imaginary stretching functions based on Zolotarev's optimal rational approximation of the square root are implemented leading to perfectly matched layers with a controlled accuracy over a complete spectral interval of interest. A new Krylov-based solution method via stability-corrected operator exponents is presented which 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. 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 intervals.

          Related collections

          Most cited references 16

          • Record: found
          • Abstract: not found
          • Article: not found

          A perfectly matched layer for the absorption of electromagnetic waves

            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            Spectral properties of many-body Schrödinger operators with dilatation-analytic interactions

              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              A class of analytic perturbations for one-body Schrödinger Hamiltonians

                Bookmark

                Author and article information

                Journal
                02 February 2012
                2012-04-13
                Article
                1202.0424

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                35L05, 35B34, 65F60
                24 pages, 8 figures
                math-ph math.MP math.NA

                Comments

                Comment on this article