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
Warren Weaver Hall, Room 1302
251 Mercer Street
New York, NY, 10012-1110
Fall 2012 NASC Seminars Calendar
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.