Development and verification of MOC code based on Krylov subspace and efficient preconditioning techniques

Derived from the conventional characteristic sweeping operations, the method of characteristics (MOC) with matrix form has more favorable performance compared with its traditional implementation potentially. However, the advantage depends heavily upon the efficiency of the linear algebraic solver. In current study, a simple and efficient preconditioning technique is implemented in the restart version of Generalized Minimal RESidual algorithm (GMRES) to accelerate the resulted linear system. A complete code including geometry processing and algebraic solver has been developed and verified with the reference benchmark problem. Numerical results demonstrate the code can model the reference problem accurately, and the proposed preconditioning techniques based on the typical iterative method can decrease dramatically the number of iterations without introducing additional computation and storage expense.