University of Tabriz Computational Methods for Differential Equations 2345-3982 6 2 2018 04 01 New variants of the global Krylov type methods for linear systems with multiple right-hand sides arising in elliptic PDEs 111 127 7218 EN Ghodrat Ebadi Faculty of Mathematical Sciences, University of Tabriz, 51666-14766 Tabriz, Iran Somaiyeh Rashedi Faculty of Mathematical Sciences, University of Tabriz, 51666-14766 Tabriz, Iran Journal Article 2017 04 20 In this paper, we present new variants of global bi-conjugate gradient (Gl-BiCG) and global bi-conjugate residual (Gl-BiCR) methods for solving nonsymmetric linear systems with multiple right-hand sides. These methods are based on global oblique projections of the initial residual onto a matrix Krylov subspace. It is shown that these new algorithms converge faster and more smoothly than the Gl-BiCG and Gl-BiCR methods. The preconditioned versions of these methods are also explored in this study. Eventually, the efficiency of these approaches are demonstrated through numerical experimental results arising from two and three-dimensional advection dominated elliptic PDE. https://cmde.tabrizu.ac.ir/article_7218_d74a81e5c537c6a78b780d5dd92c2e64.pdf