A Frozen Jacobian Multiscale Mortar Preconditioner for Nonlinear Interface Operators

We present an efficient approach for preconditioning systems arising in multiphase flow in a parallel domain decomposition framework known as the mortar mixed finite element method. Subdomains are coupled together with appropriate interface conditions using mortar finite elements. These conditions are enforced using an inexact Newton--Krylov method, which traditionally required the solution of nonlinear subdomain problems on each interface iteration. A new preconditioner is formed by constructing a multiscale basis on each subdomain for a fixed Jacobian and time step. This basis contains the solutions of nonlinear subdomain problems for each degree of freedom in the mortar space and is applied using an efficient linear combination. Numerical experiments demonstrate the relative computational savings of recomputing the multiscale preconditioner sparingly throughout the simulation versus the traditional approach.