Parallel algorithms for deformation-diffusion problems

V. P. Fedotov ; A. S. Nefedov

Matematičeskoe modelirovanie, Tome 14 (2002) no. 8, pp. 16-22

Résumé

The modern software packages for the solution of the problems of mathematical physics (heat transport, diffusion, elastic-plastic deformation, hydrodynamics etc.) are based on algorithms that were developed for implementation of consecutive calculations (finite element method, finite difference method, boundary element method). The possibilities of numerical implementation on multiprocessor computer complexes were not included in the structure of these algorithms. Searching methods of the solution of connected problems which algorithms initially contain principles of a parallelization is topical. Boundary variational methods are offered for the problems of the deformation and the diffusion, based on the combination of the variational method and boundary element method. Such statement has allowed considering the problem with unknowns by functions on a surface (surface velocities and surface stresses for problems of a deformation, concentration of an admixture and streams for diffusion problems). The dimension of the problem is reduced per unit; the calculation of coordinate functions and stress-strain states in the field is carried out in a parallel way with use of results of the solution on boundary. The problem of the diffusion of hydrogen and deformation in the zone of spherical defect was considered here.