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The "Interpolated Factored Green Function" Method


Bauinger, Christoph (2023) The "Interpolated Factored Green Function" Method. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1cnc-s558.


This thesis presents a novel Interpolated Factored Green Function (IFGF) method for the accelerated evaluation of the integral operators in scattering theory and other areas. Like existing acceleration methods in these fields, the IFGF algorithm evaluates the action of Green function-based integral operators at a cost of O(N log N) operations for an N-point surface mesh. The IFGF strategy capitalizes on slow variations inherent in a certain Green function analytic factor, which is analytic up to and including infinity, and which therefore allows for accelerated evaluation of fields produced by groups of sources on the basis of a recursive application of classical interpolation methods. Unlike other approaches, the IFGF method does not utilize the Fast Fourier Transform (FFT), and it is thus better suited than other methods for efficient parallelization in distributed-memory computer systems. In fact, a (hybrid MPI-OpenMP) parallel implementation of the IFGF algorithm is proposed in this thesis which results in highly efficient data communication, and which exhibits in practice excellent parallel scaling up to large numbers of cores -- without any hard limitations on the number of cores concurrently employed with high efficiency. Moreover, on any given number of cores, the proposed parallel approach preserves the linearithmic (O(N log N)) computing cost inherent in the sequential version of the IFGF algorithm. This thesis additionally introduces a complete acoustic scattering solver that incorporates the IFGF method in conjunction with a suitable singular integration scheme. A variety of numerical results presented in this thesis illustrate the character of the proposed parallel IFGF-accelerated acoustic solver. These results include applications to several highly relevant engineering problems, e.g., problems concerning acoustic scattering by structures such as a submarine and an aircraft-nacelle geometry, thus establishing the suitability of the IFGF method in the context of real-world engineering problems. The theoretical properties of the IFGF method, finally, are demonstrated by means of a variety of numerical experiments which display the method's serial and parallel linearithmic scaling as well as its excellent weak and strong parallel scaling -- for problems of up to 4,096 wavelengths in acoustic size, and scaling tests spanning from 1 compute core to all 1,680 cores available in the High Performance Computing cluster used.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Integral Equations, Scattering, Green Function, Acceleration, Numerical Methods, High Performance Computing, OpenMP, MPI,
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied And Computational Mathematics
Awards:The W.P. Carey and Co. Prize in Applied Mathematics, 2023.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Bruno, Oscar P.
Thesis Committee:
  • Meiron, Daniel I. (chair)
  • Bruno, Oscar P.
  • Schroeder, Peter
  • Owhadi, Houman
Defense Date:15 August 2022
Funding AgencyGrant Number
Defense Advanced Research Projects Agency (DARPA)HR00111720035
Vannevar Bush Faculty Fellowship (VBFF)N00014-16-1-2808
Air Force Office of Scientific Research (AFOSR)FA9550-19-1-0173
Air Force Office of Scientific Research (AFOSR)FA9550-21-1-0373
Record Number:CaltechTHESIS:07072022-003500251
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for Chapters 1, 3, and 5. adapted for Chapters 1, 4 and 5. adapted for Section 5.5.
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14968
Deposited By: Christoph Bauinger
Deposited On:19 Aug 2022 19:09
Last Modified:16 Jun 2023 16:30

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