## Numerics

I will put here the links to posts related to numerical analysis. If you are interested in learning/developing Numerical Analysis skills please visit and support the site Scientific Computing at Stackexchange.com.

Laplace equation in 1D with finite differences

Laplace equation in 2D with finite differences

Numerical Results – Optimal Shapes – Dirichlet Laplacian – Volume Constraint

Numerical Results – Optimal Shapes – Dirichlet Laplacian – Perimeter Constraint

If you are interested in finding some good optimization packages for Matlab, you can find two of them in the following links:

1. LBFGS package – can be found on Liam Stewart‘s page
2. Optimization package (multiple methods including lbfgs) – by Mark Schmidt.

For numerical computations for Helmholtz equations, scattering problems and eigenvalue problems, you can check out MpsPack.

How to find the distance from a point to an ellipsoid? Check this post. This can be useful in handling quadratic constraints in optimization.

Here is a way to find the eigenvalues of the Laplace operator corresponding to a certain figure using the method of fundamental solutions. In this post you can find a method to optimize the $k$-th eigenvalue of a polygon.