PDE 12: Helmholtz equation

This is an elliptic PDE. You should consider 2D. It is important in phenomena of wave propagation.

\[\nabla^2 A+ k^2 A =0, \]

where \(A=A(x,y,z)\) is the wave amplitude and \(k\) is the wave number.

Google: Helmholtz equation, wave scattering.

Challenges: geometry, boundary conditions etc.