Parallel Implementation of a High-Order Implicit Collocation Method
for the Heat Equation
Jules Kouatchou
We combine a high order compact finite difference approximation and
collocation techniques to numerically solve the two dimensional heat
equation. The resulting method is implicit and can be parallelized with
a strategy that allows parallelization across both time and space.
We compare the parallel implementation of the new method with a classical
implicit method, namely the Crank-Nicolson method, where the
parallelization is done across space only. We find the set of conditions
for which each method is more advantageous than the other. Numerical
experiments are carried out on the SGI Origin 2000.