Dear Firedrakers, I discussed yesterday with Andrew if Firedrake can be (ab)used to solve PDEs with a non-traditional time stepping method (we call it REXI) and he suggested me to drop an Email to this mailing list. (@David/Colin: It's related to our parallelization-in-time work). Let L be the linear operator of the SWE on the sphere in advective form including the average height (by putting the perturbation into the non-linear part). L also contains the longitude-varying Coriolis term, but this shouldn't make a big difference here. As one building block of the new time stepping method we like to solve the SoEs given by (\alpha - L) U = U0 with \alpha a complex shifted pole creating a non-singular SoE and U0 the DoFs to solve for. I don't see any problem to write this in weak formulation as it is required in Firedrake. Now the following questions arise: * Is Firedrake able to assemble and solve these system of equations with the complex value \alpha? It's only important to keep the real values of "U". The imaginary values of U are not important if that's of any help. * If not, is Firedrake still able to solve a reformulation which would have a 6x6 linear operator instead of a 3x3 and 6 DoFs (3 pseudo DoFs) per cell? (Basically reformulating the SoE with real values instead of complex ones). * Is there any Firedrake code publicly available with the GungHo FEM dyn-core on the sphere with a C-grid? * A question related to possible future work: Is Firedrake supporting Semi-Lagrangian methods efficiently? Cheers, Martin -- Dr. rer.-nat. Martin Schreiber Lecturer, proleptic Scientific and High-Performance Computing University of Exeter College of Engineering, Mathematics and Physical Sciences Harrison Building, Room 319, North Park Road, Exeter, EX4 4QF