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LEAST‐SQUARES SOLUTIONS OF A GENERAL NUMERICAL METHOD FOR ARBITRARY IRREGULAR GRIDS
Author(s) -
BATY ROY S.,
WOLFE WALTER P.
Publication year - 1997
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/(sici)1097-0207(19970515)40:9<1701::aid-nme135>3.0.co;2-o
Subject(s) - mathematics , least squares function approximation , computer science , calculus (dental) , mathematical optimization , algorithm , statistics , medicine , dentistry , estimator
Abstract This article describes a computational method to calculate solutions of elliptic boundary value problems using arbitrary irregular grids. The main feature of the numerical method is its ability to approximate solutions of differential equations without co‐ordinate mapping or metric tensor information. For linear differential equations, the numerical method yields coupled linear systems on local computational cells. Optimal least‐squares solutions of coupled linear systems are discussed and applied to the scheme. The numerical method is used to simulate potential flow for two model problems. The computational results are in very good agreement with analytical solutions. © 1997 by John Wiley & Sons, Ltd.