Improvement of Locality of Parallel Algorithms of the Numerical Solutions of the Two-Dimensional Quasilinear Parabolic Equations

The equations of parabolic type describe processes of nonlinear heat conductivity, diffusions of the loaded particles in plasma, diffusion and drift of impurity atoms in semiconductor structures, in chemical kinetics. At the numerical solution of practical tasks such there are the difficulties caused by the insufficient capacity and volume of memory of the personal computer. There is a problem of creation of parallel methods and algorithms for the numerical decision the parabolic equations on supercomputers. One of methods of the numerical solution of the multidimensional parabolic equations the locally one dimensional method is. Parallel realization of a locally one method for numerical solutions of the linear and quasi-linear two-dimensional parabolic equations on supercomputers with the distributed memory is offered. The parallel algorithm is constructed taking into account locality of data - the operations and data are distributed between processes in such a way that the considerable part of data is privatized by processes and doesn’t need communication operations. Results of numerical experiments are given.

parallel computation, data locality, data alignment, parabolic equations, locally one dimensional method