A MONTE CARLO SYNTHETIC ACCELERATION METHOD FOR THE NON-LINEAR,TIME-DEPENDENT DIFFUSION EQUATION

摘要

We present a Monte Carlo synthetic-acceleration method for solving the time-dependent, nonlinear, equilibrium diffusion equation in three-dimensions. The new scheme uses the adjoint Monte Carlo method as a relaxation step that accelerates standard Jacobi iteration. Results show that this method is 40% faster than regular Jacobi iteration and is competitive with Jacobi-preconditioned Conjugate Gradient methods. Furthermore, the new method is not limited to symmetric, positive-definite systems, and therefore, it can be used for non-symmetric systems. Such systems arise in fully coupled, nonlinear-consistent (Newton) solvers.