Auzinger, W., & Koch, O. (2022, July 7). Adaptive exponential splitting [Conference Presentation]. FAATNA20>22: Functional Analysis, Approximation Theory and Numerical Analysis, Matera, Italy. http://hdl.handle.net/20.500.12708/80240
E101 - Institut für Analysis und Scientific Computing
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Date (published):
7-Jul-2022
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Event name:
FAATNA20>22: Functional Analysis, Approximation Theory and Numerical Analysis
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Event date:
5-Jul-2022 - 8-Jul-2022
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Event place:
Matera, Italy
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Keywords:
exponential splitting, adaptivity, wave equations
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Abstract:
For the efficient numerical integration of
evolutionary differential equations with additive right-hand side,
u_t = F1(t,u) + F2(t,u) + ...
approximation by exponential splitting methods based on the solution and systematic recombination
of sub-problems is often a convenient choice.
For the purpose of reliable adaptive stepsize control,
several techniques for practical local error estimation are introduced and discussed,
and further works are devoted to particular applications, e.g., Schrödinger type problems
or hyperbolic problems. The employed techniques comprise optimized pairs of schemes,
Milne-type estimators, and defect-based approaches, and are used with schemes
of various approximation orders. Also, more than two suboperators are
treated. Coefficients of various optimized methods are collected at a web page.
In the simulation of magnetohydrodynamics, it is natural to split
the vector field into4-8operators, even. Additionally, certain positivity
conditions on the coefficients need to be satisfied. We discuss the
construction of methods and present numerical results for hyperbolic test problems.
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Additional information:
Vortrag auf Englisch (25 Minuten), in Präsenz
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Research Areas:
Computational Fluid Dynamics: 50% Mathematical and Algorithmic Foundations: 50%