Author
Babb, T
Gillman, A
Hao, S
Martinsson, P-G
Journal title
BIT NUMERICAL MATHEMATICS
DOI
10.1007/s10543-018-0714-0
Issue
4
Volume
58
Last updated
2018-12-31T08:00:45.61+00:00
Page
851-879
Abstract
© 2018 The Author(s) This paper presents a numerical method for variable coefficient elliptic PDEs with mostly smooth solutions on two dimensional domains. The method works best for domains that can readily be mapped onto a rectangle, or a collection of nonoverlapping rectangles. The PDE is discretized via a multi-domain spectral collocation method of high local order (order 30 and higher have been tested and work well). Local mesh refinement results in highly accurate solutions even in the presence of local irregular behavior due to corner singularities, localized loads, etc. The system of linear equations attained upon discretization is solved using a direct (as opposed to iterative) solver with (Formula presented.) complexity for the factorization stage and (Formula presented.) complexity for the solve. The scheme is ideally suited for executing the elliptic solve required when parabolic problems are discretized via time-implicit techniques. In situations where the geometry remains unchanged between time-steps, very fast execution speeds are obtained since the solution operator for each implicit solve can be pre-computed.
Symplectic ID
856222
Download URL
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000451967100002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=4fd6f7d59a501f9b8bac2be37914c43e
Publication type
14
Publication date
December 2018
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