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The parallel computation of solutions to electrostatic problems using multigrid techniques
Author(s) -
Waring L. C.,
Rooney N.,
Stewart A.,
Fusco V. F.
Publication year - 1994
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.1660070107
Subject(s) - multigrid method , quasistatic process , computation , convergence (economics) , grid , mathematics , relaxation (psychology) , laplace transform , computer science , mathematical optimization , domain decomposition methods , algorithm , computational science , mathematical analysis , geometry , partial differential equation , finite element method , physics , psychology , social psychology , quantum mechanics , economics , thermodynamics , economic growth
The application of multigrid techniques to the computation of the static solutions of electromagnetic field problems governed by Laplace's equation is described. This technique is compared with the conventional successive over‐relaxation (SOR) method for solving finite difference problems. In contrast to SOR, the number of iterations of multigrid needed to achieve convergence is largely independent of the grid size. It is shown that the relative performance of multigrid is excellent on large grids where the number of iterations of SOR needed to achieve convergence becomes prohibitively large. The technique is illustrated by applying a parallel implementation of multigrid to find a quasistatic solution of a boxed microstrip problem.