Nonlinear Preconditioning for Diffuse Interfaces

A method of transforming problems with diffuse interfaces is presented which leads to equations that are easier to compute accurately. Information obtained by internal layer asymptotic analysis is utilized to motivate transformations of the dependent variables. The new evolution equations which result from this change of variables can be solved numerically in a straightforward manner. Numerical experiments indicate that truncation errors can be significantly reduced in such problems, allowing a coarser grid to be used. Applications to several well-known models are presented.