Scalable Implicit Methods for Reaction-diffusion Equations in Two and Three Space Dimensions
نویسنده
چکیده
This paper describes the implementation of a solver for systems of semi-linear parabolic partial di erential equations in two and three space dimensions. The solver is based on a parallel implementation of a non-linear Alternating Direction Implicit (ADI) scheme which uses a Cartesian grid in space and an implicit time-stepping algorithm. Various reordering strategies for the linearized equations are used to reduce the stride and improve the overall e ectiveness of the parallel implementation. We have successfully used this solver for large-scale reaction-di usion problems in computational biology and medicine in which the desired solution is a traveling wave that may contain rapid transitions. A number of examples that illustrate the e ciency and accuracy of the method are given here; the theoretical analysis will be presented in [7].
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