Higher-order finite difference schemes via minimum<br/><br/>Sobolev norm techniques and fast solvers

Tuesday, August 3, 2010 - 2:00pm - 2:30pm
Keller 3-180
Shivkumar Chandrasekaran (University of California)
We show how to construct higher-order (10 and above) finite-difference schemes using
Minimum Sobolev Norm techniques that lead to O(N2) condition number discretizations of second-order elliptic PDEs. Numerical experiments comparing with standard FEM solvers show the benefit of the new approach. We then discuss fast numerical methods to convert the discrete equations into discretized integral equations that can have bounded condition number, and hence achieve even higher numerical accuracy.
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