Matrix-equation-based strategies for convection-diffusion equations
For researchers solving convection-diffusion PDEs numerically, this work offers a new preconditioning strategy that may improve efficiency, though results are preliminary and incremental.
The paper proposes preconditioners based on matrix equation formulations for solving nonsymmetric linear systems from convection-diffusion PDEs with dominant convection, showing that explicit matrix equation solutions can replace linear system solutions for certain convection coefficients, with numerical experiments in 2D and 3D demonstrating potential.
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.