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- Title
Design of IMEXRK time integration schemes via Delaunay-based derivative-free optimization with nonconvex constraints and grid-based acceleration.
- Authors
Alimo, Ryan; Cavaglieri, Daniele; Beyhaghi, Pooriya; Bewley, Thomas R.
- Abstract
This paper develops a powerful new variant, dubbed Δ -DOGS( Ω Z ), of our Delaunay-based Derivative-free Optimization via Global Surrogates family of algorithms, and uses it to identify a new, low-storage, high-accuracy, Implicit/Explicit Runge–Kutta (IMEXRK) time integration scheme for the stiff ODEs arising in high performance computing applications, like the simulation of turbulence. The Δ -DOGS( Ω Z ) algorithm, which we prove to be globally convergent under the appropriate assumptions, combines (a) the essential ideas of our Δ -DOGS(Ω ) algorithm, which is designed to efficiently optimize a nonconvex objective function f(x) within a nonconvex feasible domain Ω defined by a number of constraint functions c κ (x) , with (b) our Δ -DOGS(Z) algorithm, which reduces the number of function evaluations on the boundary of the search domain via the restriction that all function evaluations lie on a Cartesian grid, which is successively refined as the iterations proceed. The optimization of the parameters of low-storage IMEXRK schemes involves a complicated set of nonconvex constraints, which leads to a challenging disconnected feasible domain, and a highly nonconvex objective function; our simulations indicate significantly faster convergence using Δ -DOGS( Ω Z ) as compared with the original Δ -DOGS(Ω ) optimization algorithm on the problem of tuning the parameters of such schemes. A low-storage third-order IMEXRK scheme with remarkably good stability and accuracy properties is ultimately identified using this approach, and is briefly tested on Burgers' equation.
- Subjects
TIME integration scheme; HIGH performance computing; MATHEMATICAL optimization; COMPUTATIONAL fluid dynamics; GLOBAL optimization
- Publication
Journal of Global Optimization, 2021, Vol 79, Issue 3, p567
- ISSN
0925-5001
- Publication type
Article
- DOI
10.1007/s10898-019-00855-1