Two sides tangential filtering decomposition

In this paper we study a class of preconditioners that satisfy the so-called left and/or right filtering conditions. For practical applications, we use a multiplicative combination of filtering based preconditioners with the classical ILU(0)ILU(0) preconditioner, which is known to be efficient. Although the left filtering condition has a more sound theoretical motivation than the right one, extensive tests on convection–diffusion equations with heterogeneous and anisotropic diffusion tensors reveal that satisfying left or right filtering conditions lead to comparable results. On the filtering vector, these numerical tests reveal that e=[1,…,1]T is a reasonable choice, which is effective and can avoid the preprocessing needed in other methods to build the filtering vector. Numerical tests show that the composite preconditioners are rather robust and efficient for these problems with strongly varying coefficients.