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Periodic standing-wave approximation: Nonlinear scalar fields, adapted coordinates, and the eigenspectral method

Bromley, Benjamin and Owen, Robert and Price, Richard (2005) Periodic standing-wave approximation: Nonlinear scalar fields, adapted coordinates, and the eigenspectral method. Physical Review D, 71 (10). Art. No. 104017. ISSN 1550-7998. https://resolver.caltech.edu/CaltechAUTHORS:20170408-160556005

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Abstract

The periodic standing wave (PSW) method for the binary inspiral of black holes and neutron stars computes exact numerical solutions for periodic standing-wave spacetimes and then extracts approximate solutions of the physical problem, with outgoing waves. The method requires solution of a boundary-value problem with a mixed (hyperbolic and elliptic) character. We present here a new numerical method for such problems, based on three innovations: (i) a coordinate system adapted to the geometry of the problem, (ii) an expansion in multipole moments of these coordinates and a filtering out of higher moments, and (iii) the replacement of the continuum multipole moments with their analogs for a discrete grid. We illustrate the efficiency and accuracy of this method with nonlinear scalar model problems. Finally, we take advantage of the ability of this method to handle highly nonlinear models to demonstrate that the outgoing approximations extracted from the standing-wave solutions are highly accurate even in the presence of strong nonlinearities.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevD.71.104017DOIArticle
http://arxiv.org/abs/gr-qc/0502034arXivDiscussion Paper
Additional Information:© 2005 American Physical Society. (Received 9 February 2005; published 13 May 2005) We gratefully acknowledge the support of NSF Grant No. PHY0244605 and NASA Grant No. ATP03-0001-0027, to UTB and of NSF Grant No. PHY-0099568 and NASA Grant No. NAG5-12834 to Caltech. We thank Chris Beetle and Lior Burko for useful discussions and suggestions. We also thank Alexey Blinov and Maria Cranor for help with figures, and with checking calculations.
Group:TAPIR
Funders:
Funding AgencyGrant Number
NSFPHY-0244605
NASAATP03-0001-0027
NSFPHY-0099568
NASANAG5-12834
Issue or Number:10
Classification Code:PACS numbers: 04.25.Dm, 02.60.Lj, 04.25.Nx, 04.30.Db
Record Number:CaltechAUTHORS:20170408-160556005
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170408-160556005
Official Citation:Periodic standing-wave approximation: Nonlinear scalar fields, adapted coordinates, and the eigenspectral method Benjamin Bromley, Robert Owen, and Richard H. Price Phys. Rev. D 71, 104017
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76126
Collection:CaltechAUTHORS
Deposited By: 1Science Import
Deposited On:21 Jun 2017 22:00
Last Modified:03 Oct 2019 16:57

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