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Implementation and performance of the time integration of a 3D numerical transport model
Author(s) -
Sommeijer B. P.,
Kok J.
Publication year - 1995
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650210407
Subject(s) - vectorization (mathematics) , computer science , integrator , stability (learning theory) , tridiagonal matrix , parallel computing , computational science , focus (optics) , scale (ratio) , implementation , mathematics , algorithm , basis (linear algebra) , numerical stability , mathematical optimization , numerical analysis , geometry , physics , computer network , mathematical analysis , eigenvalues and eigenvectors , bandwidth (computing) , quantum mechanics , machine learning , optics , programming language
The total solution of a three‐dimensional model for computing the transport of salinity, pollutants, suspended material (such as sediment or mud), etc. in shallow seas involves many aspects, each of which has to be treated in an optimal way in order to cope with the tremendous computational task involved. In this paper we focus on one of these aspects, i.e. on the time integration, and discuss two numerical solution methods. The emphasis in this paper is on the performance of the methods when implemented on a vector/parallel, shared memory computer such as a Cray‐type machine. The first method is an explicit time integrator and can straightforwardly be vectorized and parallelized. Although a stabilizing technique has been applied to this method, it still suffers from a severe time step restriction. The second method is partly implicit, resulting in much beter stability characteristics; however, as a consequence of the implicitness, it requires in each step the solution of a large number of tridiagonal systems. When implemented in a standard way, the recursive nature would prevent vectorization, resulting in a very long solution time. Following a suggestion of Golub and Van Loan, this part of the algorithm has been tuned for use on the Cray C98/4256. On the basis of a large‐scale test problem, performance results will be presented for various implementations.