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JuliaApproximation / MultivariateOrthogonalPolynomials.jl

Supports approximating functions and solving differential equations on various higher dimensional domains such as disks and triangles
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Generalized eigenvalue problems on a disc #121

Open ioannisPApapadopoulos opened 2 years ago

ioannisPApapadopoulos commented 2 years ago

Timon @TSGut has done the heavy lifting and has implemented Jacobi matrices for Zernike polynomials on a disc.

Alberto @APaganini could you remind us what exactly you required? If I remember correctly, as a first step you wanted to solve

-Laplace(u)(x,y) = q(x,y) u(x,y)

on a disc with zero Dirichlet bcs. What should we pick for q(x,y)? (@dlfivefifty)

APaganini commented 2 years ago

Amazing, many thanks for your help! The function q I'm interested in is

q(x,y) = (1 + |g(x+iy)|^2)^2

where g(z) is a polynomial with real coefficients in the complex variable z.

dlfivefifty commented 2 years ago

So it’s actually polynomial in x and y? Should be easy to get working…

APaganini commented 2 years ago

Yes, we don't need anything more complicated than that. In a next step we may be brave and even try rational functions (but I first have to think about what having poles in the disc would mean for the specific application).