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The finite element solution of elliptical systems on a data parallel computer
Author(s) -
Hutchinson Scott,
Hensel Edward,
Castillo Steven,
Dalton Kim
Publication year - 1991
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.1620320208
Subject(s) - finite element method , massively parallel , scalar (mathematics) , conjugate gradient method , partial differential equation , helmholtz equation , airfoil , computer science , mathematics , mathematical analysis , parallel computing , algorithm , geometry , engineering , structural engineering , boundary value problem
A study is conducted of the finite element solution of elliptic partial differential equations on a data parallel computer. A nodal assembly technique is introduced which maps a single node to a single processor. The system of equations is first assembled and then solved in parallel using a conjugate gradient algorithm for unsymmetric, non‐positive definite systems. Using this technique and a massively parallel machine, problems in excess of 100k nodes are solved. Results of electromagnetic scattering, governed by the 2‐d scalar Helmholtz equation, are presented for both an infinite cylinder and an airfoil cross‐section. Solutions are demonstrated for a wide range of object sizes. A summary of performance data is given for a set of test problems.