On Tue, Feb 28, 2012 at 14:20, Dmitry Karpeev <[email protected]> wrote:

Just out of curiosity: how many transient problems have we seen where the transient residual doesn't split like R(U,U_t) = R_0(U_t) + R_1(U)? There is the issue of explicit dependence on time, but if that could be addressed, the problem would naturally split and, as a side benefit, there would be a natural "mass" matrix coming out of the linearization of R_0.

Moving mesh problems often have terms involving both U_t and U. The IMEX interface is g(t,X,X_t) = f(t,X) which lets us split the implicit and explicit parts. Having a separate mass matrix is normally quite wasteful and it's confusing for people doing matrix-free methods where it is natural to keep both together.