Hello all,
I am a beginner in dealii. I want to solve a linear, transient advection
equation explicitly in two dimensions using DG. The resulting discrete
equation will have a mass matrix as the system matrix and a sum of terms
which depend on previous solution (multiplied by mass, differentiation,
flux and boundary matrix) as the rhs.
[image: linearAdvection2D.png]
Instead of using MeshWorker::loop for every single time step, I think the
following approach would be better. I am using a ghost cell approach to
specify the boundary condition: the boundary condition can be specified by
an appropriately calculated normal numerical flux.
1. Before the any time steps, use a MeshWorker::loop each for each of
the four matrices: mass, differentiation, flux and boundary
2. During each update
1. Again use MeshWorker::loop, but this time only to calculate the
normal numerical flux.
2. Use the normal numerical flux and the previous solution to obtain
the RHS using appropriate matrix-vector products
3. Solve the system
I have few question regarding this approach.
1. Is it feasible
2. Can it give significant improvement in performance over the case when
assembling is done for every time step
3. (Assuming answers to above questions are positive) For higher orders,
the flux and boundary matrices will be very sparse. The normal numerical
flux (which will be a vector) will also be sparse. Can the matrix-vector
product involving these combinations be optimised by using appropriate
sparsity pattern? Can a sparsity pattern be specified for a vector too?
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