Parameterized preconditioning for generalized saddle point problems arising from the Stokes equation
A parameterized preconditioning framework to improve the conditions of the generalized saddle point problems is proposed. This is done by multiplying the submatrices by some parameters to precondition the system of saddle point problems. The authors give the explicit expression of the quasi-optimal preconditioning parameter by minimizing the upper bounds of the spectral condition numbers of the matrices based on the eigenvalue estimates. They apply the proposed techniques to the generalized saddle point problems derived from the mixed finite element discretization of the stationary Stokes equation. More specifically, the proposed parametrized preconditioners are combined with well-known iterative methods, and the numerical results demonstrate that they are efficient.
scientific article; zbMATH DE number 5991214
scientific article