Papers Published

1. Howle, L.E., Efficient implementation of a finite-difference/Galerkin method for simulation of large aspect ratio convection, Numerical Heat Transfer, Part B: Fundamentals, vol. 26 no. 1 (1994), pp. 105 - 114 .
   (last updated on 2007/04/06)

   Abstract:
   The efficiency of a mixed finite-difference/Galerkin method is examined for simulation of steady two-dimensional Rayleigh-Benard 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.

   Keywords:
   Finite difference method;Tensors;Mathematical models;Boundary layers;Approximation theory;Function evaluation;Computational methods;