Development of efficient Krylov preconditioning techniques for multi-dimensional method of characteristics

Abstract

Two techniques are proposed in the preconditioning for the Krylov sub-space method called the Generalized Minimal RESidual (GMRES) method to accelerate inner iterations based on the method of characteristics (MOC). The GMRES method is an iterative method to solve a linear algebraic system byminimizing the norm of the residual vector. The proposed preconditioning technique is based on the first flight collision probability which is efficiently made by the multi-dimensional MOC code. To simplify the preconditioner, slight couplings among regions are ignored by considering the mean free path. And another proposed technique makes simplified preconditioner by the scaling matrix which can homogenize and de-homogenize the fuel region and the cladding region. The scaling technique reduces the size of the matrix and also reduces the calculation time of inverse matrix. Numerical results show that the preconditioner simplified by the mean free path efficiently reduces the number of iterations for the GMRES algorithm. And the scaling technique keeps the efficiency of preconditioner even in the multi-dimensional geometry. The total calculation time is found to be reduced when these techniques are employed.