We introduce numerical study on the discrete counterpart of Gauss' theorem. The purpose is to seek and establish a third approach, beside the analytical and the kernel-independent approaches, for efficient dimension reduction and preconditioning of equations initially in differential form. Integration is done locally, or globally, using analytic...
Creator:
Sun, Xiaobai (Duke University)
Created:
2010-08-02
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
A spectrally accurate method for the fast evaluation of N-particle sums of the periodic Stokeslet is presented. Such sums occur in boundary integral- and potential methods for viscous flow problems. Two different decomposition methods, leading to one sum in real space and one in reciprocal space, are considered. An FFT based method is applied to...
Creator:
Tornberg, Anna-Karin (Royal Institute of Technology (KTH))
Created:
2010-08-02
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
System-level electromagnetic design problems are multiscale and very challenging to solve. They remain a significant barrier to system design optimization for a foreseeable future. Such multiscale problems often contain three electrical scales, i.e., the fine scale (geometrical feature size much smaller than a wavelength), the coarse scale (geom...
Creator:
Liu, Qing Huo (Duke University)
Created:
2010-08-02
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Solving electromagnetics problem is a challenging task, especially when the structure is multi-scale. These structures are often encountered in circuits in electronic packaging, small antenna designs, as well as small sensor designs. A challenging problem in computational electromagnetics is in solving multi-scale problems in the low frequency r...
Creator:
Chew, Weng Cho (University of Hong Kong)
Created:
2010-08-02
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Joint work with Cris Cecka and Pierre-David Letourneau (Stanford University).The fast multipole method (FMM) is a technique allowing the fast calculation of sums in O(N) or O(N ln N) steps with some prescribed tolerance. Original FMMs required analytical expansions of the kernel, for example using spherical harmonics or Taylor expansions. In rec...
Creator:
Darve, Eric Felix (Stanford University)
Created:
2010-08-02
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Joint work with H. Reid, L. Zhang, C. Coelho, Z. Zhu, T. Klemas, and S. Johnson.Despite decades of zealous effort, there are remarkably fewapplications where fast integral equation solvers dominate. To helpexplain why, we will describe effective strategies, assess performance,and present remaining challenges associated with applying fast solvers...
Creator:
White, Jacob K. (Massachusetts Institute of Technology)
Created:
2010-08-02
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We present an efficient integral equation approach to solve the heat equation in a two-dimensional, multiply connected domain, and with Dirichlet boundary conditions. Instead of using integral equations based on the heat kernel, we take the approach of discretizing in time, first. This leads to a non-homogeneous modified Helmholtz equation that ...
Creator:
Kropinski, Mary-Catherine Andrea (Simon Fraser University)
Created:
2010-08-02
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The talk will describe recently developed fast solvers for thelinear systems arising upon the discretization of ellipticPDEs. While most existing fast methods tend to be based oniterative solvers such as GMRES, the new techniques directlyconstruct an approximate inverse (or LU factorization) of thecoefficient matrix. This makes the techniques ro...
Creator:
Martinsson, Per-Gunnar J. (University of Colorado)
Created:
2010-08-02
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
