A WKB based preconditioner for the 1D helmholtz wave equation

D. L. Green; E. D’Azevedo; D. B. Batchelor; N. Bertelli; C. Lau; R. L. Barnett; J. F. Caneses Marin

doi:10.1063/5.0018579

A WKB based preconditioner for the 1D helmholtz wave equation

D. L. Green, E. D’Azevedo, D. B. Batchelor, N. Bertelli, C. Lau, R. L. Barnett, J. F. Caneses Marin

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

Frequency-domain full-wave solutions to the cold-plasma problem have become ubiquitous in the study of radio frequency power in fusion plasmas. However, recent efforts at extreme levels of geometric fidelity have revealed fundamental limits in the problem size that can be solved by typical sparse direct solver based methods. These limits are of particular importance in the 3D study of RF launchers, where the number of degrees of freedom required can exceed 100 million. In such cases, it would be advantageous to solve the system via iterative means, but due to the large null space of the curl-curl operator, the convergence properties of algorithms like GMRES are poor. Here we present a physics-based preconditioner in the form of a WKB solution and demonstrate the iterative solution to the frequency-domain Helmholtz problem in 1D for several cases ranging from satisfying the WKB approximation to strongly violating it.

Original language	English
Title of host publication	23rd Topical Conference on Radiofrequency Power in Plasmas
Editors	Paul T. Bonoli, Robert I. Pinsker, Xiaojie Wang
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735420137
DOIs	https://doi.org/10.1063/5.0018579
State	Published - Sep 16 2020
Event	23rd Topical Conference on Radiofrequency Power in Plasmas - Hefei, China Duration: May 14 2019 → May 17 2019

Publication series

Name	AIP Conference Proceedings
Volume	2254
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	23rd Topical Conference on Radiofrequency Power in Plasmas
Country/Territory	China
City	Hefei
Period	05/14/19 → 05/17/19

Funding

∗This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).

Funders	Funder number
U.S. Department of Energy

Access to Document

10.1063/5.0018579

Cite this

Green, D. L., D’Azevedo, E., Batchelor, D. B., Bertelli, N., Lau, C., Barnett, R. L., & Caneses Marin, J. F. (2020). A WKB based preconditioner for the 1D helmholtz wave equation. In P. T. Bonoli, R. I. Pinsker, & X. Wang (Eds.), 23rd Topical Conference on Radiofrequency Power in Plasmas Article 60008 (AIP Conference Proceedings; Vol. 2254). American Institute of Physics Inc.. https://doi.org/10.1063/5.0018579

@inproceedings{2236a794c87c45c58625ec2ac404d223,

title = "A WKB based preconditioner for the 1D helmholtz wave equation",

abstract = "Frequency-domain full-wave solutions to the cold-plasma problem have become ubiquitous in the study of radio frequency power in fusion plasmas. However, recent efforts at extreme levels of geometric fidelity have revealed fundamental limits in the problem size that can be solved by typical sparse direct solver based methods. These limits are of particular importance in the 3D study of RF launchers, where the number of degrees of freedom required can exceed 100 million. In such cases, it would be advantageous to solve the system via iterative means, but due to the large null space of the curl-curl operator, the convergence properties of algorithms like GMRES are poor. Here we present a physics-based preconditioner in the form of a WKB solution and demonstrate the iterative solution to the frequency-domain Helmholtz problem in 1D for several cases ranging from satisfying the WKB approximation to strongly violating it.",

author = "Green, {D. L.} and E. D{\textquoteright}Azevedo and Batchelor, {D. B.} and N. Bertelli and C. Lau and Barnett, {R. L.} and {Caneses Marin}, {J. F.}",

note = "Publisher Copyright: {\textcopyright} 2020 American Institute of Physics Inc.. All rights reserved.; 23rd Topical Conference on Radiofrequency Power in Plasmas ; Conference date: 14-05-2019 Through 17-05-2019",

year = "2020",

month = sep,

day = "16",

doi = "10.1063/5.0018579",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "Bonoli, {Paul T.} and Pinsker, {Robert I.} and Xiaojie Wang",

booktitle = "23rd Topical Conference on Radiofrequency Power in Plasmas",

}

Green, DL, D’Azevedo, E, Batchelor, DB, Bertelli, N, Lau, C , Barnett, RL & Caneses Marin, JF 2020, A WKB based preconditioner for the 1D helmholtz wave equation. in PT Bonoli, RI Pinsker & X Wang (eds), 23rd Topical Conference on Radiofrequency Power in Plasmas., 60008, AIP Conference Proceedings, vol. 2254, American Institute of Physics Inc., 23rd Topical Conference on Radiofrequency Power in Plasmas, Hefei, China, 05/14/19. https://doi.org/10.1063/5.0018579

A WKB based preconditioner for the 1D helmholtz wave equation. / Green, D. L.; D’Azevedo, E.; Batchelor, D. B. et al.
23rd Topical Conference on Radiofrequency Power in Plasmas. ed. / Paul T. Bonoli; Robert I. Pinsker; Xiaojie Wang. American Institute of Physics Inc., 2020. 60008 (AIP Conference Proceedings; Vol. 2254).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - A WKB based preconditioner for the 1D helmholtz wave equation

AU - Green, D. L.

AU - D’Azevedo, E.

AU - Batchelor, D. B.

AU - Bertelli, N.

AU - Lau, C.

AU - Barnett, R. L.

AU - Caneses Marin, J. F.

PY - 2020/9/16

Y1 - 2020/9/16

N2 - Frequency-domain full-wave solutions to the cold-plasma problem have become ubiquitous in the study of radio frequency power in fusion plasmas. However, recent efforts at extreme levels of geometric fidelity have revealed fundamental limits in the problem size that can be solved by typical sparse direct solver based methods. These limits are of particular importance in the 3D study of RF launchers, where the number of degrees of freedom required can exceed 100 million. In such cases, it would be advantageous to solve the system via iterative means, but due to the large null space of the curl-curl operator, the convergence properties of algorithms like GMRES are poor. Here we present a physics-based preconditioner in the form of a WKB solution and demonstrate the iterative solution to the frequency-domain Helmholtz problem in 1D for several cases ranging from satisfying the WKB approximation to strongly violating it.

AB - Frequency-domain full-wave solutions to the cold-plasma problem have become ubiquitous in the study of radio frequency power in fusion plasmas. However, recent efforts at extreme levels of geometric fidelity have revealed fundamental limits in the problem size that can be solved by typical sparse direct solver based methods. These limits are of particular importance in the 3D study of RF launchers, where the number of degrees of freedom required can exceed 100 million. In such cases, it would be advantageous to solve the system via iterative means, but due to the large null space of the curl-curl operator, the convergence properties of algorithms like GMRES are poor. Here we present a physics-based preconditioner in the form of a WKB solution and demonstrate the iterative solution to the frequency-domain Helmholtz problem in 1D for several cases ranging from satisfying the WKB approximation to strongly violating it.

UR - http://www.scopus.com/inward/record.url?scp=85092048239&partnerID=8YFLogxK

U2 - 10.1063/5.0018579

DO - 10.1063/5.0018579

M3 - Conference contribution

AN - SCOPUS:85092048239

T3 - AIP Conference Proceedings

BT - 23rd Topical Conference on Radiofrequency Power in Plasmas

A2 - Bonoli, Paul T.

A2 - Pinsker, Robert I.

A2 - Wang, Xiaojie

PB - American Institute of Physics Inc.

T2 - 23rd Topical Conference on Radiofrequency Power in Plasmas

Y2 - 14 May 2019 through 17 May 2019

ER -

A WKB based preconditioner for the 1D helmholtz wave equation

Abstract

Publication series

Conference

Funding

Access to Document

Other files and links

Fingerprint

Cite this