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A Schwarz alternating procedure using spline collocation methods
Author(s) -
Yanik Elizabeth Greenwell
Publication year - 1989
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620280310
Subject(s) - rectangle , collocation (remote sensing) , collocation method , mathematics , schwarz alternating method , convergence (economics) , additive schwarz method , spline (mechanical) , mathematical analysis , geometry , computer science , finite element method , differential equation , domain decomposition methods , ordinary differential equation , physics , economics , thermodynamics , machine learning , economic growth
A collocation method is described which obtains an approximate solution to Poisson's equation, δ u = f , on an L shaped region. The L shaped region is viewed as the union of two overlapping rectangles. The Schwarz alternating procedure may be employed to reduce the problem to one in which collocation techniques are used on each rectangle. The convergence of the alternating scheme depends upon a discrete maximum principle for collocation methods. Several sample problems are presented to illustrate the order of convergence of this method and to compare it with several existing numerical methods for the L shaped region.