I was wondering if anyone use this approach to solve free boundary problems?

what does it involve ? how is it implemented ?

Sorry, the topic might be a bit confusing as this approach is called "Phase Field" in the Computational Material Sciences and the "Set Level Method" in CFD.Well, you need to reformulate your problem in terms of scalar level set functions where a free boundary is treated as an intersection of these functions. Basically, the equations you need to discretisize are Hamilton-Jacobi equations where the velocity is defined by the physics and the geometry of your problem. Just wondering if this approach has been used in finance or not.

dude, you don't seem to have had a lot of success on this one. I d be interested in the answer myself. from what I know about this method is that it is more suitable for strong advection problems, problems with hyperbolic character, such as in gas dynamics, combustion, but also in computer vision and image processing. to me most pdes in finance are more of the diffusive type, but I must admit that my scope of understanding is a little limited here. anyway, there have some very highly successful mixed particle-field methods in fluid dynamics lately, such as SPH and lot of other shit like LBE, for high reynolds number flows, but again I am not sure that this is so useful when dealing with diffusion problems a la black and scholes.

Thanks for your reply. It looks like this approach has not been used in finance.