A Preconditioning Method Based on Strongly Implicit Procedure for the Multi- Diagonal Equation

Abstract Ellipsoidal partial differential equation is usually discretized into a multi-diagonal equation when using the finite-difference or finite-volume numerical method. The neutron diffusion equation in reactor physics and the thermal conduction convection equation in thermal fluid calculations are elliptical partial differential equations. Therefore, the efficient solution of multi-diagonal equation is of great significance to nuclear engineering calculations. GMRES algorithm has been widely used to solve multi-diagonal equations, but the computational efficiency of this method depends on the effect of preconditioning method. This paper combines the SIP preconditioning method with GMRES to solve steady-state thermal conductivity problems for flat cartesian and cylinder. The calculation results show that the SIP preconditioning method can reduce the iterations of multi-diagonal equations, without increasing the additional preconditioner’s memory compared with the traditional ILU(0) preconditioning method.