Fast Fourier transform based direct solvers for the Helmholtz and other problems
Dipl.-Ing.in Monika WolfmayrJune 21, 2018, 8:15 a.m. S2 416-1
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 as well as time-periodic parabolic problems. 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. We present numerical results for two- and three-dimensional problems solved by the FFT based direct solver. Moreover, we discuss the application of the FFT based fast solver to time-periodic parabolic problems approximated by truncated Fourier series in time. The resulting equations are discretized by the finite element method, altogether called the multiharmonic finite element method (MhFEM).
This is a joint work with Jari Toivanen (University of Jyväskylä, Finland).