Fast Fourier transform based direct solvers for the Helmholtz and other problems

Dipl.-Ing.in Monika Wolfmayr

June 21, 2018, 10:15 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).