Monika Wolfmayr
Faculty of Information Technology, University of Jyväskylä, Finland
In this talk, we consider the derivation and application of a fast direct solver employing fast Fourier transform (FFT) in order to solve the Helmholtz equation. We discuss the method for solving the Helmholtz equation in a two- or three-dimensional rectangular domain with an absorbing boundary condition. The Helmholtz problem is discretized by standard bilinear and trilinear finite elements on an orthogonal mesh yielding a separable system of linear equations. The computational complexity of the proposed FFT based direct solver is O(N log N) operations. We present numerical results for two- and three-dimensional problems solved by the FFT based direct solver. This is a joint work with Jari Toivanen (Faculty of Information Technology, University of Jyväskylä, Finland).