Matrix-equation-based strategies for convection-diffusion equations

TL;DR

This paper introduces matrix-equation-based preconditioners for efficiently solving nonsymmetric linear systems from convection-diffusion PDE discretizations, especially with dominant convection, demonstrating promising numerical results.

Contribution

It proposes a novel matrix equation formulation as a preconditioning strategy for convection-diffusion problems with separable coefficients and dominant convection.

Findings

Effective preconditioners for certain convection coefficients

Numerical experiments confirm potential of the approach

Applicable to 2D and 3D problems

Abstract

We are interested in the numerical solution of nonsymmetric linear systems arising from the discretization of convection-diffusion partial differential equations with separable coefficients and dominant convection. Preconditioners based on the matrix equation formulation of the problem are proposed, which naturally approximate the original discretized problem. For certain types of convection coefficients, we show that the explicit solution of the matrix equation can effectively replace the linear system solution. Numerical experiments with data stemming from two and three dimensional problems are reported, illustrating the potential of the proposed methodology.