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Optimal stability polynomials for numerical integration of initial value problems

Tuesday, July 17, 11AM – 12PM
ACE 6.304

Aron Ahmadia

We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest stable step size and corresponding method for a given problem when the spectrum of the initial value problem is known.

The problem is expressed in terms of a general least deviation feasibility problem. Its solution is obtained by a new fast, accurate, and robust algorithm based on convex optimization techniques. Global convergence of the algorithm is proven in the case that the order of approximation is one and in the case that the spectrum encloses a star-like region. Examples demonstrate the effectiveness of the proposed algorithm even when these conditions are not satisfied.

Bio: Aron is a computational scientist currently working in the KAUST supercomputing laboratory where he has been since 2009 after completing his Ph.D. work at Columbia University. He works at the intersection of applied mathematics, software engineering, and application domains as diverse as adaptive optics, semiconductor lithography, and ice-sheet modeling. His focus is in the collaborative development of robust, reproducible, and scalable software tools for computational science. (http://aron.ahmadia.net)

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