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Multiscale high-order/low-order (HOLO) algorithms and applications. (English) Zbl 1380.65316
Summary: We review the state of the art in the formulation, implementation, and performance of so-called high-order/low-order (HOLO) algorithms for challenging multiscale problems. HOLO algorithms attempt to couple one or several high-complexity physical models (the high-order model, HO) with low-complexity ones (the low-order model, LO). The primary goal of HOLO algorithms is to achieve nonlinear convergence between HO and LO components while minimizing memory footprint and managing the computational complexity in a practical manner. Key to the HOLO approach is the use of the LO representations to address temporal stiffness, effectively accelerating the convergence of the HO/LO coupled system. The HOLO approach is broadly underpinned by the concept of nonlinear elimination, which enables segregation of the HO and LO components in ways that can effectively use heterogeneous architectures. The accuracy and efficiency benefits of HOLO algorithms are demonstrated with specific applications to radiation transport, gas dynamics, plasmas (both Eulerian and Lagrangian formulations), and ocean modeling. Across this broad application spectrum, HOLO algorithms achieve significant accuracy improvements at a fraction of the cost compared to conventional approaches. It follows that HOLO algorithms hold significant potential for high-fidelity system scale multiscale simulations leveraging exascale computing.

MSC:
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
76N15 Gas dynamics, general
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
86A05 Hydrology, hydrography, oceanography
65C05 Monte Carlo methods
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
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