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We study numerical methods for solving a non-stationary mixed Stokes-Darcy problem that models coupled fluid flow and porous media flow. A decoupling approach based on interface approximation via temporal extrap-olation is proposed for devising decoupled marching algorithms for the mixed model. Error estimates are derived and numerical experiments are… (More)

This paper deals with a solution approach suitable for (:omposite PDEs with interface conditions. We present a general framework based on interface relaxation which provides a uniform platform for building problem solving environmen\.s t1lrough efficient softwaIe integration and for implementing various relaxation schemes. Mathematically, this framework… (More)

- Mo Mu, John R Rice, Rice, John R, John R Momu, Rice +1 other
- 2013

We consider the problem of modeling very complex physical systems by a network of collaborating PDE solvers. Various aspects of this problem are examined from the points of view of real applications, modern computer science technologies, and their impact on numerical methods. The related methodologies include network 0/ collaborating software modules,… (More)

A new approach was presented in [11] for construcling preconditioners through a function approximation for the domain decomposi~ion-based preconditioned conjugate gradient method. This work extends the approach to more general cases where grids may be nonuniform; elliptic op-eratoI'B may have variable coefficients (but are separable and self-adjoint); and… (More)