This Demonstration implements a recently published algorithm for an improved finite difference scheme for solving the Helmholtz partial differential equation
on a rectangle with uniform grid spacing. Dirichlet and Sommerfeld boundary conditions are supported. You can specify different source functions
. You can prescribe Sommerfeld boundary conditions on up to three edges of the rectangle at the same time. You can vary the
value and the angle of incidence
. The numerical scheme is converted to a standard system of linear equations
system, which can then be solved. You can view the generated matrix
and its eigenvalues as well as the solution data using the dropdown menu in the top row.