A Parallel Block-Based PDE Solver with Space-Time Adaptivity

Stefan Söderberg

December 2001

Abstract:

A second order space and time adaptive method for parallel solution of hyperbolic PDEs on structured grids is presented. The grid is adapted to the underlying solution by successive refinement in blocks. Therefore, there may be jumps in the cell size at the block faces. Special attention is needed at the block boundaries to maintain second order accuracy and stability. The stability of the method is proven for a model problem.

The step sizes in space and time are selected based on estimates of the local truncation errors and an error tolerance provided by the user. The global error in the solution is also computed by solving an error equation similar to the original problem on a coarser grid.

The performance of the method depends on the number of blocks used in the domain. A method of predicting the optimal number of blocks is presented. The cells are distributed in blocks over the processor set using a number of different partitioning schemes.

The method is used to successfully solve a number of test problems where the method selects the appropriate space and time steps according to the error tolerance.

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