CahnHillard Benchmark

[Batmanabcdefg]

Hello! so far it seems that the periodic boundary conditions are not applied for CahnHillard Benchmark?

Best regards!

[lyc102]

Periodic boundary condition requires special treatment. I will add it later on.

[scaomath]

Periodic boundary condition requires special treatment. I will add it later on.

Is it worth adding it maybe for a future student project?

@Batmanabcdefg do you still need this? If not using Long's cryptic sparse matrix manipulation. A simple tweak based on the current data structure would be (let us assume only left and right are periodical the rest is the Dirichlet):

• Use Dirichlet as bc.
• Identify left-right node pairs as an M x 2 array.
• Adding the pair node contributions from unchanged stiffness matrix and the right-hand side together. This can be done using similar tricks here: https://github.com/lyc102/ifem/blob/884a92ad70a3b41582a86bc3b44e7e41510dc04e/equation/Poisson.m#L324-L328
• Adding only the nodes on the left side to the freeNode.
• Solve like usual (if all boundaries are PBC then do not forget to eliminate the constant kernel).
• If you want to visualize the solution, just do an accumarray using the index pair from step 2.

A more ifemish change would be changing the number indicator in the bdFlag tradition, for example, 4 represents the BC are periodical there.