Spectral multidomain technique with Local Fourier Basis

A novel domain decomposition method for spectrally accurate solutions of PDEs is presented. A Local Fourier Basis technique is adapted for the construction of the elemental solutions in subdomains. C¹ continuity is achieved on the interfaces by a matching procedure using the analytical homogeneous solutions of a one dimensional equation. The method can be applied to the solution of elliptic problems of the Poisson or Helmholtz type as well as to time discretized parabolic problems in one or more dimensions. The accuracy is tested for several stiff problems with steep solutions. The present domain decomposition approach is particularly suitable for parallel implementations, in particular, on MIMD type parallel machines.