On efficient direct methods for conforming spectral domain decomposition techniques

Abstract

A conforming spectral domain decomposition technique is described for the solution of Stokes flow in rectangularly decomposable domains. The matrices arising from such a spectral discretization procedure possess a block tridiagonal structure where these blocks are full submatrices. Efficient direct solution procedures are proposed to take advantage of the matrix structure. A comparison of the methods in terms of computational efficiency is made. Numerical results are presented for the flow through an abruptly contracting channel.