A multilevel Cartesian non-uniform grid time domain algorithm

  • Authors:

  • Jun Meng;Amir Boag;Vitaliy Lomakin;Eric Michielssen

  • Affiliations:

  • Cadence Research Center Beijing, 15/F Metropolis Tower, No. 2, Haidian Dongsanjie Street, Haidian District, Beijing 100080, PR China and University of Illinois at Urbana Champaign, Urbana, IL 6180 ...;School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel;Department of Electrical and Computer Engineering, University of California, San Diego, La Jolla, CA 92093, USA;Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2010

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Abstract

A multilevel Cartesian non-uniform grid time domain algorithm (CNGTDA) is introduced to rapidly compute transient wave fields radiated by time dependent three-dimensional source constellations. CNGTDA leverages the observation that transient wave fields generated by temporally bandlimited and spatially confined source constellations can be recovered via interpolation from appropriately delay- and amplitude-compensated field samples. This property is used in conjunction with a multilevel scheme, in which the computational domain is hierarchically decomposed into subdomains with sparse non-uniform grids used to obtain the fields. For both surface and volumetric source distributions, the computational cost of CNGTDA to compute the transient field at N"s observation locations from N"s collocated sources for N"t discrete time instances scales as O(N"tN"slogN"s) and O(N"tN"slog^2N"s) in the low- and high-frequency regimes, respectively. Coupled with marching-on-in-time (MOT) time domain integral equations, CNGTDA can facilitate efficient analysis of large scale time domain electromagnetic and acoustic problems.