New variants of the global Krylov type methods for linear systems with multiple right-hand sides arising in elliptic PDEs

	New variants of the global Krylov type methods for linear systems with multiple right-hand sides arising in elliptic PDEs
Computational Methods for Differential Equations
مقاله 1، دوره 6، شماره 2، تیر 2018، صفحه 111-127 اصل مقاله (237.95 K)
نوع مقاله: Research Paper
نویسندگان
Ghodrat Ebadi^* ؛ Somaiyeh Rashedi
Faculty of Mathematical Sciences, University of Tabriz, 51666-14766 Tabriz, Iran
چکیده
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.
کلیدواژه‌ها
Matrix Krylov subspaces؛ Elliptic Partial differential equation؛ Non symmetric linear systems؛ Global iterative methods؛ Multiple right-hand sides

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