Abstract
Frontal routines are used for the solution of large, sparse and generally unsymmetric systems of linear equations arising in certain applications of the Galerkin/finite element approach to the iterative solution of nonlinear boundary value problems. Based on Gauss elimination, these methods have advantages over banded matrix methods in that core requirements and computation time can be considerably reduced. We present an explicitly vectorized frontal routine for in-core solution of the equation set with the CYBER 205 vector processor; the routine exploits the large central memory, high execution speed and pipelined functional units of this supercomputer. Nodal arrays of the original algorithm of Hood are replaced by long vectors of node labels to get the benefit of contiguity in memory; the CYBER 200 FORTRAN vector syntax is used to reduce the number of non-vectorizable loops; the elimination procedure is modified to take advantage of longer vectors and the associated large iteration counts. The algorithm is enhanced by efficient threshold pivoting and determinant evaluation for stability and bifurcation analysis. The assembly procedure is designed with the flexibility to accommodate extra equations and unknowns for continuation in parameters and eigenanalysis. A listing of the code is provided.
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© 1985 Plenum Press, New York
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Boudouvis, A.G., Scriven, L.E. (1985). Explicitly Vectorized Frontal Routine for Hydrodynamic Stability and Bifurcation Analysis by Galerkin/Finite Element Methods. In: Numrich, R.W. (eds) Supercomputer Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2503-1_15
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DOI: https://doi.org/10.1007/978-1-4613-2503-1_15
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-9514-3
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