I am trying to work with a simulation of Brain Tumor growth and I was fortunate to get a very great example at http://community.wolfram.com/. However, I need clarifications on some of the code. I want to know what it does and how it works. Here are the piece that I do not understand:
1.
diffcoeff = ListInterpolation[ImageData[img3], InterpolationOrder -> 3]
2.
boundaries = {-y, y - 1, -x, x - 1};
Ω = ImplicitRegion[And @@ (# <= 0 & /@ boundaries), {x, y}];
3.
sols = NDSolveValue[{{Div[
1./500.*(diffcoeff[798.*x, 654*y])^4* Grad[u[t, x, y], {x, y}], {x, y}] - D[u[t, x, y], t] + 0.025*u[t, x, y] == NeumannValue[0., x >= 1. || x <= 0. || y <= 0. || y >= 1.]},
{u[0, x, y] == Exp[-1000. ((x - 0.6)^2 + (y - 0.6)^2)]}},
u,
{x, y}∈ Ω,
{t, 0, 20},
Method -> {"FiniteElement",
"MeshOptions" -> {
"BoundaryMeshGenerator" -> "Continuation",
MaxCellMeasure -> 0.002
}
}
]
I really would like to understand each element of these code pieces (and probably the rationale behind their use). Your kind and expert contributions would be greatly appreciated. Since the web page does not load anymore, I have the pdf copy I earlier saved, here!.