These html pages are based on the PhD thesis "Cluster-Based Parallelization of Simulations on Dynamically Adaptive Grids and Dynamic Resource Management" by Martin Schreiber.

There is also more information and a PDF version available.

There is also more information and a PDF version available.

Discretizing the time step term from Eq. (2.9). We can factor out U by considering that φ are functions only depending on spatial parameters. This yields

| (2.10) |

The integrals on the right-hand side of Eq. (2.10) can then be precomputed and their values stored to the mass matrix . Using vector notation , we get a matrix-vector formulation

| (2.11) |

with also a matrix in case of several conserved quantities.

See Appendix A.1 for examples of matrices derived in this section and used in our simulations. Those matrices are
computed with Maple^{1} ,
a computer algebra system for symbolic computations.

Applying the explicit Euler time-stepping method, this can then be rearranged to