Helmholtz equation

In mathematics, the Helmholtz equation, named after Hermann von Helmholtz, is the Partial differential equation:

Where∇2 is the Laplacian operator. K is the wave number, and A is the amplitude. In the GRAPES model, the prognostic equations after spatial discredization is a typical Helmholtz equation with its huge and sparse coefficient matrix; the Helmholtz equation is solved using the Pre_GCR scheme.