Numerical solution for domain decomposed, heterogeneously modeled seepage problems

摘要

A new domain decomposition technique for free boundary problems is considered. A parallel iterative scheme is used that reduces the original free boundary problem to a sequence of problems on two subdomains, one of which includes the free boundary and is described by a variational inequality and the other includes the remainder of the problem and is described by a second order partial differential equation. At each step of the iteration, two subproblems are solved simultaneously either by using a Dirichlet condition on the interface and alternatively using a Neumann condition on the interface. Since these two subproblems can be solved simultaneously in this parallel scheme, the convergence speed is faster than solving one subproblem at one time. Furthermore, this parallel scheme can be extended to multi-subdomain problems very easily.