A preconditioned Richardson method for solving three‐dimensional thin film problems with first order derivatives and variable coefficients

A preconditioned Richardson method for solving three‐dimensional thin film elliptic problems with first order derivatives and variable coefficients has been developed based on the idea of the modified upwind difference scheme and the fact that the thickness of the thin domain is small. This method is simple because only a tridiagonal linear system is needed to solve for each iteration. The computation speed is fast since the spectral radius of the iterative operator is small. Numerical example shows the method to be efficient.