An incomplete factorization preconditioning method based on modification of element matrices
The paper concerns the problem of stability of incomplete factorization (IC) and modified incomplete factorization (MIC) of matrices arising from the finite element solution of selfadjoint boundary value problems. For the purpose of construction of a stable incomplete factorization, it introduces an auxiliary matrix arising from the assembly of modified element matrices. This matrix is a weakly diagonally dominant \(M\)-matrix and can therefore be exploited for the construction of IC or MIC preconditioners. Moreover, this auxiliary matrix is spectrally equivalent to the original finite element matrix so that the asymptotic effect of preconditioning is preserved. The author applies the above idea to several cases of higher-order elements, hierarchical elements and anisotropy problems and shows favourable behaviour of the introduced technique.
incomplete factorization preconditioning method
scientific article; zbMATH DE number 881185