Application of preconditioned transpose-free quasi-minimal residual method for two-group reactor kinetics

Two preconditioned transpose-free quasi-minimal residual methods (TFQMR) and quasi-minimal residual variant of the biconjugate gradient stabilized algorithm (QMRCGSTAB) are applied to solve the non-symmetric linear systems of equations which are derived from the time-dependent two-dimensional two-energy-group neutron diffusion equations by finite difference approximation. We compare the TFQMR and QMRCGSTAB methods with the other popular method such as the generalized minimal residual method (GMRES), the conjugate gradient square method (CGS), and biconjugate gradient stabilized algorithm (Bi-CGSTAB). (author)