Computer Science NASC Seminar

A Composite Spectral Method for Variable Coefficient Elliptic PDEs with its Own Fast Direct Solver

Adrianna Gillman, Dartmouth College

November 30, 2012 10:00AM
Warren Weaver Hall, Room 1302
251 Mercer Street
New York, NY, 10012-1110
(Directions)

Fall 2012 NASC Seminars Calendar

Synopsis

Variable coefficient elliptic PDEs
arise in a variety of applications including non-destructive testing,
geophysics, and designing materials. Typically finite
element or spectral element methods are used to discretize
the PDE resulting in a large linear system which is often solved via an iterative method (e.g. GMRES). Often the system is
ill-conditioned, meaning many iterations are needed to
obtain a solution. For applications with multiple right hand
sides, this approach is computationally prohibitive.
In this talk, we present a high-order accurate discretization
technique designed for variable coefficient problems with smooth solutions. The resulting linear system is solved via a fast direct solver with $O(N)$ complexity where $N$ is the number of discretization points. Each
additional solve is also $O(N)$ but with a much smaller constant.
Numerical results will illustrate the performance of the method.


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