Speaker
Description
Exponential integrators are a class of time integration methods used to solve large systems of evolution equations. They integrate the linear part of the problem (almost) exactly and use an explicit scheme for the nonlinearity. This makes them highly accurate and stable, especially when the nonlinearity is weak. These integrators are widely used in stiff problems of semilinear parabolic equations and in highly oscillatory problems such as wave and Schrödinger-type equations.
Their implementation involves the computation of matrix functions (such as exponentials and trigonometric functions) on vectors, which can be done explicitly for small problems, or by iterative methods (such as Krylov subspace methods) for larger problems. When these computations are efficient, exponential integrators offer significant advantages.
In this talk, we consider two new approaches to improve the performance of exponential Runge-Kutta methods: μ-mode integrators for evolution equations in Kronecker form and accelerated methods using simplified linearization. Numerical experiments in 2D and 3D show the effectiveness of these approaches.
This research is a collaboration with Marco Caliari (Verona), Fabio Cassini (Verona), and Lukas Einkemmer (Innsbruck).
