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High-order, Dispersionless, Spatio-Temporally Parallel "Fast-Hybrid" Wave Equation Solver at O(1) Sampling Cost

Anderson, Thomas G. and Bruno, Oscar P. and Lyon, Mark (2018) High-order, Dispersionless, Spatio-Temporally Parallel "Fast-Hybrid" Wave Equation Solver at O(1) Sampling Cost. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20181102-090208948

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Abstract

This paper proposes a frequency/time hybrid integral-equation method for the time dependent wave equation in two and three-dimensional spatial domains. Relying on Fourier Transformation in time, the method utilizes a fixed (time-independent) number of frequency-domain integral equation solutions to evaluate, with superalgebraically-small errors, time domain solutions for arbitrarily long times. The approach relies on two main elements, namely, 1) A smooth time-windowing methodology that enables smooth time partitioning of incident waves, and 2) A novel Fourier transform approach which, in a time-parallel manner and without causing spurious periodicity effects, delivers numerically dispersionless spectrally accurate solutions. A similar hybrid technique can be obtained on the basis of Laplace transforms instead of Fourier transforms, but we do not consider the Laplace-based method in the present contribution. The algorithm can handle dispersive materials, it can tackle complex physical structures and interface conditions (provided a correspondingly capable frequency-domain solver is used), it enables parallelization in time in a straightforward manner, and it allows for time leaping, that is, solution sampling at any given time T at O(1)-bounded sampling cost, for arbitrarily large values of T, and without requirement of evaluation of the solution at intermediate times. The proposed frequency/time hybridization strategy, which generalizes to any linear partial differential equation in the time domain for which frequency-domain solutions can be obtained (including e.g. the time-domain Maxwell equations), and which is applicable in a wide range of scientific and engineering contexts, provides significant advantages over volumetric discretization and convolution-quadrature approaches.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1807.02718arXivDiscussion Paper
ORCID:
AuthorORCID
Bruno, Oscar P.0000-0001-8369-3014
Additional Information:The authors gratefully acknowledge support by NSF, AFOSR and DARPA through contracts DMS-1411876 and FA9550-15-1-0043 and HR00111720035, and the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808. T. G. Anderson acknowledges support from the DOE Computational Sciences Fellowship, DOE grant DE-FG02-97ER25308.
Funders:
Funding AgencyGrant Number
NSFDMS-1411876
Air Force Office of Scientific Research (AFOSR)FA9550-15-1-0043
Defense Advanced Research Projects Agency (DARPA)HR00111720035
National Security Science and Engineering Faculty FellowshipN00014-16-1-2808
Department of Energy (DOE)DE-FG02-97ER25308
Record Number:CaltechAUTHORS:20181102-090208948
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20181102-090208948
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90608
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:02 Nov 2018 16:25
Last Modified:02 Nov 2018 16:25

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