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A finite element algorithm for elliptical equations over unstructured domains on a data parallel computer
Author(s) -
Hutchinson Scott A.,
Ng Kwong T.,
Shadid John N.
Publication year - 1994
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.1620371809
Subject(s) - finite element method , conjugate gradient method , preconditioner , computer science , algorithm , polynomial , convergence (economics) , matrix (chemical analysis) , jacobi method , mathematics , iterative method , mathematical analysis , physics , materials science , economics , composite material , thermodynamics , economic growth
In the past, most finite element algorithms on data‐parallel computers have been limited to structured problem domains. Here, we consider methods to generalize the finite element method on data‐parallel architectures to unstructured domains. A nodal assembly algorithm is described which effectively allows for both the generation of the sparse interaction matrix (coefficient matrix) and its solution via a preconditioned conjugate‐gradient type routine utilizing several polynomial preconditioners on the Connection Machine 200 (CM‐200). Jacobi preconditioning along with Neumann series and least‐squares polynomial preconditioners are presented and implemented are presented and implemented. Only the Jacobi preconditioner produces an improvement in the convergence time for the problems examined. Several irregular interprocessor communication protocols available on the CM‐200 are investigated in the solution portion of the algorithm, yielding differing performance characteristics. For one such protocol, sustained performance of over two‐hundred MFlops/s, is demonstrated for a test problem on a 512 processing element CM‐200 in slicewise mode. The results are discussed and conclusions are drawn concerning this finite element algorithm.