Mathematical problems of black-box computational technologies for continuum mechanics.

This paper discusses possible ways of computational technology development for segregated/coupled solving the systems of nonlinear partial differential equations in black-box software. These systems describe physical and chemical processes in the continuum mechanics approximation (multiphysics). The following requirements for the black-box numerical methods are formulated: – robustness (the least number of problem-dependent components); – efficiency (close-to-optimal algorithmic complexity); – parallelism (faster than the best sequential algorithm). Robust Multigrid Technique is used to compute the coarse grid correction. If the initial computational grid is structured, the developed approach has single additional problem-dependent component (the number of smoothing iterations) compared to the traditional single-grid Gauss-Seidel iterative method. If the initial computational grid is unstructured, the developed approach has three additional problem-dependent component (the number of smoothing iterations and intergrid transfer operators). [ABSTRACT FROM AUTHOR]