A parallel alternating direction implicit preconditioning method *

An Alternating Direction Implicit Method for Modeling of Fluid Flow

This research includes of the numerical modeling of fluids in two-dimensional cavity. The cavity flow is an important theoretical problem. In this research, modeling was carried out based on an alternating direction implicit via Vorticity-Stream function formulation. It evaluates different Reynolds numbers and grid sizes. Therefore, for the flow field analysis and prove of the ability of the sc...

High-accuracy alternating segment explicit-implicit method for the fourth-order heat equation

Based on a group of new Saul’yev type asymmetric difference schemes constructed by author, a high-order, unconditionally stable and parallel alternating segment explicit-implicit method for the numerical solution of the fourth-order heat equation is derived in this paper. The truncation error is fourth-order in space, which is much more accurate than the known alternating segment explicit-impli...

Solving Two-Dimensional Fuzzy Partial Dierential Equation by the Alternating Direction Implicit Method

Parallelizing Alternating Direction Implicit Solver on GPUs

We present a parallel Alternating Direction Implicit (ADI) solver on GPUs. Our implementation significantly improves existing implementations in two aspects. First, we address the scalability issue of existing Parallel Cyclic Reduction (PCR) implementations by eliminating their hardware resource constraints. As a result, our parallel ADI, which is based on PCR, no longer has the maximum domain ...

Parallel ADI Preconditioners for All-Scale Atmospheric Models

Effective preconditioning lies at the heart of multiscale flow simulation, including a broad range of geoscientific applications that rely on semi-implicit integrations of the governing PDEs. For such problems, conditioning of the resulting sparse linear operator directly responds to the squared ratio of largest and smallest spatial scales represented in the model. For thin-spherical-shell geom...