Scalability of a parallel Schur complement method given the limitations for memory

Abstract

In decomposition methods, the memory costs for solving the interface problem are increasing significantly with the number of subdomains increasing. Using of the Schur complement method allows you to reduce the number of iterations when the system is being solved. At the same time, the Schur complement matrix takes up more memory in comparison with global stiffness matrix. This imposes restrictions on the maximum size of the problem for which you can apply this method. Different approaches to reduce the costs and limitations of memory on stage of the construction and solving of the interface system exist. Parallel algorithm of the construction S with distributed storage of the matrix are considered when implementing using OpenMP and MPI technologies. This approach allows not only to reduce the limits on the maximum size of the solved problem, but also to resolve conflicts of shared memory access by increasing the number of independent parallel tasks.