Limited Memory Block Preconditioners for Fast Solution of Fractional Partial Differential Equations

Abstract

An innovative block structured with sparse blocks multi iterative preconditioner for linear multistep formulas used in boundary value form is proposed here to accelerate GMRES, FGMRES and BiCGstab(l). The preconditioner is based on block ω-circulant matrices and a short-memory approximation of the underlying Jacobian matrix of the fractional partial differential equations. Convergence results, numerical tests and comparisons with other techniques confirm the effectiveness of the approach.