I shall talk about how to design fast spectral-Galerkin algorithms forsome prototypical partial differential equations. We shall start withalgorithms in one dimension, then using a tensor product approach fortwo and three dimensions, and hyperbolic cross/spectral sparse gridfor higher dimensional problems.
Creator:
Shen, Jie (Purdue University)
Created:
2010-10-31
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We present a multi-resolution scheme, based on piecewise polynomialapproximations at the stochastic level, for the resolution ofnonlinear hyperbolic problems subjected to parametricuncertainties. The numerical method rely on a Galerkin projectiontechnique at the stochastic level, with a finite-volume discretizationand a Roe solver (with entropy ...
Creator:
Le Maître, Olivier Pierre (Centre National de la Recherche Scientifique (CNRS))
Created:
2010-10-18
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Joint with R. Hiptmair, Konstantin Grella, Eividn Fonn of SAM, ETH.We report on an ongoing project on Sparse Tensor Finite Element Discretizations for High Dimensional Linear Transport Problems.After reviewing several well-posed variational formulations and the regularity of weak solutions of these problems, we discuss their stable discretizatio...
Creator:
Schwab, Christoph (ETH Zürich)
Created:
2010-11-03
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We are concerned with the stability and approximation properties of enriched meshfree methods for the discretization of PDE on arbitrary domains. In particular we focus on the particle-partition of unity method (PPUM) yet the presented results hold for any partition of unity based enrichment scheme. The goal of our enrichment scheme is to recove...
Creator:
Schweitzer, Marc Alexander (Rheinische Friedrich-Wilhelms-Universität Bonn)
Created:
2010-11-03
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.