Diffusion problems arise in many branches of science and engineering. The onedimensional diffusion equation is solved using a multirate numerical algorithm. The algorithm divides the system into different parts or blocks, allowing each block to take different time steps.
For each of the three initial profiles studied in tandem with three representative diffusion coefficient dependences, there is a very significant speedup over a CrankNicholson timestepping scheme without blocking. The greatest speedup (by a factor of 5 in certain cases) is obtained for a linear diffusion with relatively small diffusion coefficient. Diffusion speed and block size are found to be major factors affecting the performance of this algorithm. Implementation of this algorithm for a twodimensional diffusion is possible, and even greater speedups are expected in that case, since the second dimension allows for the inactive block(s) to occupy larger fractions of the overall domain.

This project was supported by a SMART grant.
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