Event Type:

Department Colloquium

Date/Time:

Thursday, February 2, 2006 - 08:00

Location:

Kidd 364 (NOTE: unusual day and time)

Guest Speaker:

Institution:

University of Minnesota

Abstract:

The spectral volume method (a discontinuous Petrov-Galerkin method) was developed by ZJ Wang and Y Liu in 2002 to resolve the difficulty related to the reconstruction stencil in standard high-order finite volume schemes for hyperbolic conservation laws. A key element of the new method is the spectral volume reconstruction, for which a good partition of the simplex (triangle in 2D) is required. In this talk, I present several systematic techniques, based on the Voronoi diagram, to partition the one-, two-, and three-dimensional simplex. Almost optimal polynomial interpolation points are used as the input. The resultant partitions are very accurate (have small Lebesgue constants), the number of edges (roughly proportional to computational cost) for 2D partitions is shown to at most twice the minimum number of edges for the same order reconstruction. Certain optimizations are also made to those partitions. The optimized partitions have the smallest Lebesgue constant among currently available partitions. Speaker is Candidate for The Mathematics Department Numerical Analysis position. Refreshments will precede talk at 330 p.m. in Kidder 302.