Parallel algorithms for solving diffusion equations

The operation of a sequential electrochemical microscope is described using partial differential equations to model diffusion processes. Since there is no analytical solution to these equations, we approximate them to the equations of numerical methods. Achieving an accurate result requires a lot of calculations that can take a long time, so it makes sense to look for ways to speed up the calculations. This paper will look at ways to speed up the computation of the model using parallel algorithms. Parallel algorithms were written using the MPI implementation: mpi4py in the Python programming language. The main goal of the work is to find an optimal parallel algorithm to model the oxygen concentration generated by experiments with a scanning electrochemical microscope (SECM). The experiments used the VU MIF Distributed Computing Network and the author's local resources. Two parallel algorithms were implemented: one-dimentional and two-dimentional Up to 5 cores were used for computations in the local environment, and up to 50 cores in the MIF cluster. The calculations were successfully accelerated using the algorithms described in the literature. The one-dimensional algorithm has been found to be the most optimal way to parallelize the calculations. The one-dimensiona algorithm was the fastest in both the local and MIF cluster environments