A time and space parallel algorithm for the heat equation: The implicit collocation method
A collocation method used as a parallel method across time is proposed for solving parabolic partial differential equations. With this method, the solution of the heat equation is approximated by polynomials, the coefficients of which are computed from a block-tridiagonal linear system. Once the polynomials have been determined for a given time interval, the solution can be computed in parallel at any point of this interval. If the number of points where the solution is computed in the considered time interval is sufficient, it appears that the performances of the implicit collocation method on a parallel machine are better than those of finite difference methods. Numerical experiments on a SIMD architecture are reported.
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