Bulletin of the
Korean Mathematical Society BKMS

We introduce and analyze a frequency-domain method for parabolic partial differential equations. The method is naturally parallelizable. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we propose to solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution in the space-time domain. Existence and uniqueness as well as error estimates are given. Fourier invertibility is also examined. Numerical experiments are presented.

Keywords: parabolic problems, finite element methods, parallel algorithm, Fourier transform

MSC numbers: Primary 65N30, 65M60; Secondary 35K20