KRYLOV SUBSPACE SOLVERS IN PARALLEL NUMERICAL COMPUTATIONS OF PARTIAL DIFFERENTIAL EQUATIONS MODELING HEAT TRANSFER APPLICATIONS - Rathish Kumar, B. V.; Kumar, Bipin; Shalini; Mehra, Mani; Chandra, Peeyush; Raghvendra, V.; Singh, R. K.; Mahindra, A. K. (Numerical heat transfer. Part A, Applications, 2004)
In this study, parallel numerical algorithms for Krylov methods such as GMRES(k), Bi-CGM, Bi-CGSTAB, etc., for handling large-scale linear systems resulting from finite-difference analysis (FDA) and finite-element analysis (FEA) of coupled nonlinear partial differential equations (PDEs) describing problems in heat transfer applications are discussed. Parallel code has been successfully implemented on an eight-noded cluster under ANULIB message-passing library environment. Bi-CGM and ILU-GMRES(k) are found to give good performance for linear systems resulting from FEA, whereas Bi-CGSTAB is seen to give good performance with linear systems resulting from FDA.