A Finite Element Preconditioner for Semi-structured Spectral Element Applications

Samuel Schofield, University of Arizona

In many three-dimensional science and engineering applications fluid flow is calculated in a domain for which the geometry is homogeneous in one flow direction. Spectral element methods have been shown to be effective for handling complex geometries in two and three dimensions. Recently, existing spectral element codes have been adapted to exploit semi-structured geometry to reduce the three-dimensional problem to independent two-dimensional subproblems.

A finite element preconditioner was developed for use in these semi-structured spectral element applications. Several techniques for creating triangular finite element discretizations of the spectral element node points were explored. The discretization has to accommodate complex boundaries in addition to the node distribution arising from deformed quadrilaterals used in the spectral element method. The resulting two-dimensional matrix problem can then be efficiently solved with the use of a sparse direct solver.

Abstract Author(s): Samuel Schofield