Stencil Interface

[xtalax]

Start work on using the stencil interfaces, the result will be scalarized for now until MTK supports array equations. Since this will not give much advantage for now, the changes will be pushed to the stencils branch.

fixes #196
fixes #40
fixes #93

• Check that this fixes Discretizing a PDE below a certain dx dy threshold fails #196

[codecov]

Codecov Report

Merging #187 (eca3e0b) into stencils (0e3eccc) will decrease coverage by 1.90%.
The diff coverage is 75.06%.

❗ Current head eca3e0b differs from pull request most recent head 97dab43. Consider uploading reports for the commit 97dab43 to get more accurate results

@@             Coverage Diff              @@
##           stencils     #187      +/-   ##
============================================
- Coverage     80.48%   78.58%   -1.91%     
============================================
  Files            35       37       +2     
  Lines          1681     1840     +159     
============================================
+ Hits           1353     1446      +93     
- Misses          328      394      +66     

Impacted Files	Coverage Δ
src/MOL_utils.jl	63.63% <ø> (-3.04%)	⬇️
src/interface/solution/plot_utils.jl	0.00% <0.00%> (ø)
src/system_parsing/pde_system_transformation.jl	40.74% <16.66%> (+0.61%)	⬆️
src/discretization/interface_boundary.jl	73.13% <73.13%> (ø)
src/MOL_discretization.jl	76.78% <76.92%> (+0.63%)	⬆️
src/discretization/generate_bc_eqs.jl	79.76% <80.30%> (-3.20%)	⬇️
src/system_parsing/bcs/parse_boundaries.jl	87.69% <83.56%> (-11.23%)	⬇️
...ion/schemes/upwind_difference/upwind_difference.jl	88.40% <86.66%> (+0.17%)	⬆️
src/discretization/discretize_vars.jl	86.51% <87.50%> (-0.39%)	⬇️
...schemes/spherical_laplacian/spherical_laplacian.jl	92.30% <87.50%> (ø)
... and 14 more

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[gladisor]

Is there any estimation on how this change to the discrimination formulation will affect the sizes of domains we can work with? The 2 d domain that i consider takes several minutes to discretize for only 30 x 30. Im curious about what the capabilities of MOL will be after this change goes through.

Thank you all for your work on this package!

[xtalax]

@gladisor The essential idea is that once this is pushed and the infrastructure in MTK is done, discretization and compile time will be O(1), domain size will no longer have an effect.

It will be entirely dependent on the complexity of the PDESystem itself. Early experiments suggest that this method even improves upon discretization time for low N problems

[alicanter]

Is there an estimate of the remaining work or time required to complete this PR?