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An approximate factorization scheme for elliptic grid generation with control functions
Author(s) -
Mathur J. S.,
Chakrabartty S. K.
Publication year - 1994
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/num.1690100606
Subject(s) - mathematics , convergence (economics) , scheme (mathematics) , factorization , grid , relaxation (psychology) , partial differential equation , rate of convergence , acceleration , mathematical analysis , algorithm , geometry , computer science , psychology , social psychology , economics , economic growth , channel (broadcasting) , computer network , physics , classical mechanics
An Alternating Direction Implicit (ADI), Approximate Factorization (AF) scheme is presented here for the solution of the two‐dimensional elliptic partial differential equations, with control functions as source terms, used for grid generation. This scheme requires significantly less computational effort than a Successive Over Relaxation (SOR) scheme. The dependence of the choice of the acceleration parameter on the rate of convergence of the AF scheme has been studied. As an example, grids generated by this method are shown, along with a comparison of the convergence history for the present AF and SOR schemes. © 1994 John Wiley & Sons, Inc.