Implicit time stepping is often difficult to parallelize. The recently proposed Minimal Residual Approximate Implicit (MRAI) schemes [2] are specially designed as a cheaper and parallelizable alternative for implicit time stepping. A several GMRES iterations are performed to solve approximately the implicit scheme of interest, and the step size is adjusted to guarantee stability. A natural way ...

In this paper we study finite element method for three-dimensional incompressible resistive magnetohydrodynamic equations, in which the velocity, current density, and magnetic induction are divergence-free. It is desirable that discrete solutions should also satisfy divergence-free conditions exactly especially momentum equations. Inspired by constrained transport method, devise a new stable mi...

We have developed boundary integral equation formulas and a corresponding fast 3-D Stokes flow simulation program named FastStokes to accurately simulate viscous drag forces on geometrically complicated MEMS (microelectromechanical systems) devices. Unlike the 3-D finite element or finite difference solvers which often take days to run to completion or fail when geometry gets complicated, the F...

This paper presents flexible inner-outer Krylov subspace methods, which are implemented using the fast multipole method (FMM) for solving scattering problems with mixed dielectric and conducting object. The flexible Krylov subspace methods refer to a class of methods that accept variable preconditioning. To obtain the maximum efficiency of the inner-outer methods, it is desirable to compute the...

Control systems have always been a vital part of the novel technological advancements of human being in any industry, especially transportation. With the introduction of the idea of autonomous driving, classical control systems are not effective anymore and the need for intelligent control systems is inevitable. Advanced Driver Assistance Systems (ADASs), which are systems proposed to help driv...

In this paper, we describe the accuracy control and performance enhancement of linear solvers for the Integrated Water Flow Model (IWFM). This model is used by the State of California Department of Water Resources to assess the impact of climate change on water resources and the analysis of different conjunctive use scenarios across California. IWFM simulates groundwater, surface water and surf...

This paper presents our work on designing a platform for large-scale reservoir simulations. Detailed components, such as grid and linear solver, and data structures are introduced, which can serve as a guide to parallel reservoir simulations and other parallel applications. The main objective of platform is to support implementation of various parallel reservoir simulators on distributed-memory...