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A multidomain spectral method for solving elliptic equations

Pfeiffer, Harald P. and Kidder, Lawrence E. and Scheel, Mark A. and Teukolsky, Saul A. (2003) A multidomain spectral method for solving elliptic equations. Computer Physics Communications, 152 (3). pp. 253-273. ISSN 0010-4655. https://resolver.caltech.edu/CaltechAUTHORS:20180605-160909307

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Abstract

We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three distinct features. First, the combined problem of solving the PDE, satisfying the boundary conditions, and matching between different subdomains is cast into one set of equations readily accessible to standard linear and nonlinear solvers. Second, touching as well as overlapping subdomains are supported; both rectangular blocks with Chebyshev basis functions as well as spherical shells with an expansion in spherical harmonics are implemented. Third, the code is very flexible: The domain decomposition as well as the distribution of collocation points in each domain can be chosen at run time, and the solver is easily adaptable to new PDEs. The code has been used to solve the equations of the initial value problem of general relativity and should be useful in many other problems. We compare the new method to finite difference codes and find it superior in both runtime and accuracy, at least for the smooth problems considered here.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/S0010-4655(02)00847-0DOIArticle
https://arxiv.org/abs/gr-qc/0202096arXivDiscussion Paper
ORCID:
AuthorORCID
Pfeiffer, Harald P.0000-0001-9288-519X
Kidder, Lawrence E.0000-0001-5392-7342
Teukolsky, Saul A.0000-0001-9765-4526
Additional Information:© 2002 Elsevier. Received 19 July 2002, Accepted 15 October 2002, Available online 30 January 2003. We thank Gregory Cook for helpful discussions. This work was supported in part by NSF grants PHY-9800737 and PHY-9900672 to Cornell University. Computations were performed on the IBM SP2 of the Department of Physics, Wake Forest University, with support from an IBM SUR grant, as well as on the Platinum cluster of NCSA.
Funders:
Funding AgencyGrant Number
NSFPHY-9800737
NSFPHY-9900672
IBMUNSPECIFIED
Subject Keywords:Spectral methods; Domain decomposition; Elliptic partial differential equations; General relativity; Initial value problem
Issue or Number:3
Classification Code:PACS 02.70.Jn; 02.60.L; j04.25.Dm
Record Number:CaltechAUTHORS:20180605-160909307
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180605-160909307
Official Citation:Harald P. Pfeiffer, Lawrence E. Kidder, Mark A. Scheel, Saul A. Teukolsky, A multidomain spectral method for solving elliptic equations, Computer Physics Communications, Volume 152, Issue 3, 2003, Pages 253-273, ISSN 0010-4655, https://doi.org/10.1016/S0010-4655(02)00847-0. (http://www.sciencedirect.com/science/article/pii/S0010465502008470)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86812
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:06 Jun 2018 15:04
Last Modified:09 Mar 2020 13:19

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