AILU: a preconditioner based on the analytic factorization of the elliptic operator

AILU for Helmholtz problems: A new Preconditioner Based on the Analytic Parabolic Factorization.∗

On the Relation between Optimized Schwarz Methods and Source Transfer

Optimized Schwarz methods (OS) use Robin or higher order transmission conditions instead of the classical Dirichlet ones. An optimal Schwarz method for a general second-order elliptic problem and a decomposition into strips was presented in [13]. Here optimality means that the method converges in a finite number of steps, and this was achieved by replacing in the transmission conditions the hig...

Complete pivoting strategy for the $IUL$ preconditioner obtained from Backward Factored APproximate INVerse process

‎In this paper‎, ‎we use a complete pivoting strategy to compute the IUL preconditioner obtained as the by-product of the Backward Factored APproximate INVerse process‎. ‎This pivoting is based on the complete pivoting strategy of the Backward IJK version of Gaussian Elimination process‎. ‎There is a parameter $alpha$ to control the complete pivoting process‎. ‎We have studied the effect of dif...

The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...

Computing a block incomplete LU preconditioner as the by-product of block left-looking A-biconjugation process

In this paper, we present a block version of incomplete LU preconditioner which is computed as the by-product of block A-biconjugation process. The pivot entries of this block preconditioner are one by one or two by two blocks. The L and U factors of this block preconditioner are computed separately. The block pivot selection of this preconditioner is inherited from one of the block versions of...