Keynote Speaker

Mayya Tokman, University of California, Merced

Why, What and How of Exponential Integration

Simulating dynamics of a complex system evolving over a wide range of temporal and spatial scales is one of the most common tasks in scientific computing, and a problem that is encountered across science and engineering.  To accomplish this task a system of coupled nonlinear differential equations has to be solved over long periods of time. For centuries this problem was addressed through development of different quadrature rules for integrals of functions, which led to construction of explicit and implicit time integration methods of different types.  But in 1960’s a different approach of computing the solution of the system directly was proposed. Coupled with advances in numerical linear algebra in 1980’s, this approach led to development of practical exponential integration methods that offer significant computational advantages for a number of important problems.  In this talk, we will discuss why exponential integration is an attractive way to solve the so-called stiff systems of equations.  We will explain what considerations must be taken into account to construct an efficient exponential time integrator and what classes of exponential methods exist.  We will also demonstrate how such methods perform in real-world applications drawing from such fields as computer graphics, plasma physics, climate and weather predictions.

Conference Poster

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