[petsc-users] Local Discontinuous Galerkin with PETSc TS

[Salazar De Troya, Miguel]

Hello

I am interested in implementing the LDG method in “A local discontinuous Galerkin method for directly solving Hamilton–Jacobi equations” https://www.sciencedirect.com/science/article/pii/S0021999110005255. The equation is more or less of the form (for 1D case):
                p1 = f(u_x)
                p2 = g(u_x)
                u_t  = H(p1, p2)

where typically one solves for p1 and p2 using the previous time step solution “u” and then plugs them into the third equation to obtain the next step solution. I am wondering if the TS infrastructure could be used to implement this solution scheme. Looking at the manual, I think one could set G(t, U) to the right-hand side in the above equations and F(t, u, u’) = 0 to the left-hand side, although the first two equations would not have time derivative. In that case, how could one take advantage of the operator split scheme I mentioned? Maybe using some block preconditioners?

I am trying to solve the Hamilton-Jacobi equation u_t – H(u_x) = 0. I welcome any suggestion for better methods.

Thanks
Miguel

Miguel A. Salazar de Troya
Postdoctoral Researcher, Lawrence Livermore National Laboratory
B141
Rm: 1085-5
Ph: 1(925) 422-6411
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