A frequency-domain parallel method for the numerical approximation of parabolic problems Original Research Article

A naturally parallelizable numerical method is introduced and analyzed for parabolic partial differential equations. Instead of solving the problem in the space-time formulation, we propose to solve it in the space-frequency formulation. Existence and uniqueness are given. Error estimates are given for each single frequency. Also given is a full estimate for errors coming from truncation, numerical quadrature rule in Fourier inversion and finite element discretization in the space-frequency domain. A numerical experiment on a parallel MIMD machine is also given.