Algebraic multilevel preconditioning methods, II
SIAM Journal on Numerical Analysis
On a MIC(0) preconditioning of non-conforming mixed FEM elliptic problems
Mathematics and Computers in Simulation
Numerical Analysis and Its Applications
| Hi-index | 0.00 |
We consider a second-order elliptic problem in mixed form that has to be solved as a part of a projection algorithm for unsteady Navier-Stokes equations The use of Crouzeix-Raviart non-conforming elements for the velocities and piece-wise constants for the pressure provides a locally mass-conservative approximation Since the mass matrix corresponding to the velocities is diagonal, these unknowns can be eliminated exactly We address the design of efficient solution methods for the reduced weighted graph-Laplacian system. Construction of preconditioners based on algebraic multilevel iterations (AMLI) is considered AMLI is a stabilized recursive generalization of two-level methods We define hierarchical two-level transformations and corresponding block 2x2 splittings locally for macroelements associated with the edges of the coarse triangulation Numerical results for two sets of hierarchical partitioning parameters are presented for the cases of two-level and AMLI methods The observed behavior complies with the theoretical expectations and the constructed AMLI preconditioners are optimal.