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Alternating direction collocation for irregular regions
Author(s) -
Cooper K. D.,
McArthur K. M.,
Prenter P. M.
Publication year - 1996
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199603)12:2<147::aid-num1>3.0.co;2-q
Subject(s) - mathematics , collocation method , collocation (remote sensing) , rectangle , mathematical analysis , boundary (topology) , separable space , boundary value problem , grid , convergence (economics) , norm (philosophy) , geometry , differential equation , ordinary differential equation , remote sensing , geology , economic growth , political science , law , economics
Several methods are presented for solving separable elliptic partial differential equations over an irregular region B using alternating direction collocation on a rectangular grid over an embedding rectangle R . The methods are geometric predictor‐corrector schemes. At each iterative step, the numerical solution is predicted on R via a full ADI sweep. The forcing term is then updated (corrected) on collocation points interior to B . By this means, the geometry of B and boundary conditions on ∂ B are approximated implicitly using rectangular grids on R . The methods are O ( h 4 ) in the L 2 ( R ) norm and are boundary exact, in that the computed solution converges exactly to the given boundary conditions on ∂ B for appropriate choices of a pair of acceleration parameters. A number of examples are presented. Proof of convergence is established elsewhere. © 1996 John Wiley & Sons, Inc.