Efficient implementation of a finite-difference/galerkin method for simulation of large aspect ratio convection
The efficiency of a mixed finite-difference / Galerkin method is examined for simulation of steady two-dimensional Rayleigh-Bénard convection of large aspect ratio. It is found that computation time is reduced by an order of magnitude for large-aspect-ratio systems if the summations resulting from the formation of inner products are expanded prior to code compilation. The expansion of the summations is carried out by a source code utility, which writes the expanded and simplified source. This eliminates the need to store and multiply sparse tensors. The method extends to large-aspect-ratio problems that would previously be computationally impractical using the finite-difference/Galerkin technique. © 1994 Taylor & Francis Group, LLC.
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