This is the first part of a threefold article, aimed at solving numericallythe Poisson problem in three-dimensional prismatic or axisymmetric domains. Inthis first part, the Fourier Singular Complement Method is introduced andanalysed, in prismatic domains. In the second part, the FSCM is studied inaxisymmetric domains with conical vertices, whereas, in the third part,implementation issues, numerical tests and comparisons with other methods arecarried out. The method is based on a Fourier expansion in the directionparallel to the reentrant edges of the domain, and on an improved variant ofthe Singular Complement Method in the 2D section perpendicular to those edges.Neither refinements near the reentrant edges of the domain nor cut-offfunctions are required in the computations to achieve an optimal convergenceorder in terms of the mesh size and the number of Fourier modes used.
展开▼
