KRYLOV SUBSPACE SOLVERS IN PARALLEL NUMERICAL COMPUTATIONS OF PARTIAL DIFFERENTIAL EQUATIONS MODELING HEAT TRANSFER APPLICATIONS
B. V. Rathish Kumar, Bipin Kumar, Shalini, Mani Mehra, Peeyush Chandra, V. Raghvendra, R. K. Singh, A. K. Mahindra · 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.