Finite difference for solving Helmholtz differential equation in 2D

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Finite difference for solving Helmholtz differential equation in 2D

Feb 2, 2012 compiled on — Wednesday July 06, 2016 at 08:27 AM

This Demonstration implements a recently published algorithm of an improved finite difference scheme for solving the Helmholtz partial differential equation $2 2 − ∇ u − k u = f(x,y)$ on a rectangle with uniform grid spacing. Dirichlet and Sommerfeld boundary conditions are supported. You can specify different source functions $f(x,y)$ . You ca nprescribe Sommerfeld boundary conditions on up to three edges of the rectangle at the same time. You can vary the $k$ value and the angle of incident $θ$ .

The numerical scheme is converted to standard $Au = b$ system and solved. You can view the generated matrix $A$ and its eigenvalues as well as the solution data using the pull down menu in the top row.