Parallel solution techniques in computational structural mechanics Original Research Article

This paper presents three domain decomposition formulations combined with the Preconditioned Conjugate Gradient (PCG) method for solving large-scale linear problems in mechanics. In the first approach a subdomain-by-subdomain PCG algorithm is implemented on the global level. An approximate inverse of the global stiffness matrix, which stands as the preconditioner, is expressed by a truncated Neumann series of its local contributions. In the second approach the PCG algorithm is applied on the interface problem after eliminating the internal degrees of freedom. For this Schur complement implementation the preconditioner is formulated, as in the previous case, from the contributions of the local Schur complements expressed by a truncated Neumann series. The third approach operates on the global level after partitioning the domain into a set of totally disconnected subdomains using Lagrange multipliers. The local problem at each subdomain is solved by the PCG method while the interface problem is handled by a preconditioned conjugate projected gradient algorithm.