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Direct numerical solution of three‐dimensional equations containing elliptic operators
Author(s) -
Martin E. Dale
Publication year - 1973
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.1620060206
Subject(s) - subroutine , solver , fortran , partial differential equation , reduction (mathematics) , direct methods , mathematics , elliptic partial differential equation , computational science , numerical analysis , algorithm , computer science , mathematical analysis , mathematical optimization , geometry , physics , programming language , nuclear magnetic resonance
A direct three‐dimensional elliptic solver is presented for application in a wide class of numerical methods for solving partial differential equations in physics and engineering. The derived algorithm and FORTRAN code implement Buzbee, Golub and Nielson's proposed extension of Buneman's Cyclic‐Reduction Poisson solver to three dimensions. Both a ‘most direct’ cyclic reduction and a revised method (to eliminate roundoff error difficulties) are derived. Tests on an IBM 360/67 computer, using various optional combinations of subroutines, showed significant differences in accuracy and computing time, with the optimum subroutine combination depending on mesh size.