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The "Interpolated Factored Green Function" Method.

Record Type:	Electronic resources : Monograph/item
Title/Author:	The "Interpolated Factored Green Function" Method./
Author:	Bauinger, Christoph.
Description:	1 online resource (148 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-01, Section: B.
Contained By:	Dissertations Abstracts International85-01B.
Subject:	Aircraft. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30554151click for full text (PQDT)
ISBN:	9798379855161

The "Interpolated Factored Green Function" Method.
Bauinger, Christoph.

The "Interpolated Factored Green Function" Method. - 1 online resource (148 pages)

Source: Dissertations Abstracts International, Volume: 85-01, Section: B.

Thesis (Ph.D.)--California Institute of Technology, 2023.

Includes bibliographical references

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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798379855161Subjects--Topical Terms:

832698
Aircraft.
Index Terms--Genre/Form:

542853
Electronic books.

The "Interpolated Factored Green Function" Method.
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245 1 4 $a The "Interpolated Factored Green Function" Method.
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300 $a 1 online resource (148 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 85-01, Section: B.
500 $a Advisor: Bruno, Oscar P.
502 $a Thesis (Ph.D.)--California Institute of Technology, 2023.
504 $a Includes bibliographical references
520 $a 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.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
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650 4 $a Propagation. $3 3680519
650 4 $a Boxes. $3 3564918
650 4 $a Partial differential equations. $3 2180177
650 4 $a Helmholtz equations. $3 3704765
650 4 $a Integral equations. $3 589037
650 4 $a Fourier transforms. $3 3545926
650 4 $a Interpolation. $3 620349
650 4 $a Geometry. $3 517251
650 4 $a Mathematics. $3 515831
655 7 $a Electronic books. $2 lcsh $3 542853
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710 2 $a California Institute of Technology. $b Engineering and Applied Science. $3 2093123
773 0 $t Dissertations Abstracts International $g 85-01B.
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