Incomplete factorization for preconditioning shifted linear systems arising in wind modelling

Abstract

The efficiency of a mass-consistent model for wind field adjustment depends on the stability parameter α. Each simulation with the wind model leads to the resolution of a linear system of equations, the matrix of which depends on a function ε(α), i.e., (M + εN) x ε = b ε , where M and N are constant, symmetric and positive definite. Since each value of ε (α) yields a different linear system, we have to solve a set of them. So we could either construct a different preconditioner for each of them and improve the convergence of PCG at the expense of a high computational cost. On the other hand, a single preconditioner constructed with the first value of ε may be used for all the systems. Here, an intermediate solution is proposed by using a preconditioner, which is constructed once at first and updated for each " at a low computational cost based on incomplete Cholesky factorization of A ε .