## Joint domain-decomposition $\cal H$-LU preconditioners for saddle point problems

### Summary

Summary: For saddle point problems in fluid dynamics, several popular preconditioners exploit the block structure of the problem to construct block triangular preconditioners. The performance of such preconditioners depends on whether fast, approximate solvers for the linear systems on the block diagonal (representing convection-diffusion problems) as well as for the Schur complement (in the pressure variables) are available. In this paper, we will introduce a completely different approach in which we ignore this given block structure. We will instead compute an approximate LU-factorization of the complete system matrix using hierarchical matrix techniques. In particular, we will use domain-decomposition clustering with an additional local pivoting strategy to order the complete index set.

### Mathematics Subject Classification

65F05, 65F30, 65F50

### Keywords/Phrases

hierarchical matrices, data-sparse approximation, oseen equations, preconditioning, factorization