Sparse Jacobian Benchmark

There is a benchmark that is included (also written as a pytest test), which compares the time it takes to generate both a sparse and dense Jacobian. The results are as follows:

For N=250,

Method	Time
Dense	20 seconds
Sparse	~0.6 seconds

The benchmark can be executed from the parent folder using the command

python -m pytest -s benchmark

The sparsity pattern of the Jacobian is as follows. Both split parameter and boundary conditions lead to wrap-around and reshuffle of the sparse entries, which are correctly captured and match with the dense Jacobian entries. Note that the image is shown for N=20 for better representation. Also,

Solver Verification

One of the tests in the tests folder is a verification test for the solver. This involves advecting the initial condition of a multi-dimensional problem in a 1D domain with a constant velocity and comparing the solution to the initial condition after one cycle over the domain.