Computational Mathematics and Scientific Computing Seminar

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Continuous analogues of Krylov methods for differential operators

Speaker: Alex Townsend, Cornell

Location: Warren Weaver Hall 1302

Date: April 6, 2018, 10 a.m.

Synopsis:

Krylov subspace methods are a popular class of iterative algorithms for solving Ax=b via matrix-vector products, with their convergence rates often depending on the condition number of A. In this talk we develop analogues of the conjugate gradient method, MINRES, and GMRES for solving Lu = f via operator-function products, where L is an unbounded elliptic differential operator. Our Krylov methods employ operator preconditioning, have good convergence properties, and preserve the bilinear form associated to L. They are practical algorithms too that are very competitive compared to classical spectral discretizations. This is joint work with Marc Aurèlle Gilles.