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Title: Multiscale high-order/low-order (HOLO) algorithms and applications

Abstract

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.

Authors:
 [1]; ; ; ; ;  [1];  [2];  [1]
  1. Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)
  2. Institute for Defense Analyses, Alexandria, VA 22311 (United States)
Publication Date:
OSTI Identifier:
22622241
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 330; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ACCURACY; ALGORITHMS; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; CONVERGENCE; EFFICIENCY; FLEXIBILITY; LAGRANGIAN FUNCTION; NONLINEAR PROBLEMS; PERFORMANCE; PLASMA; RADIATION TRANSPORT; REVIEWS; SEGREGATION; SPECTRA

Citation Formats

Chacón, L., E-mail: chacon@lanl.gov, Chen, G., Knoll, D.A., Newman, C., Park, H., Taitano, W., Willert, J.A., and Womeldorff, G.. Multiscale high-order/low-order (HOLO) algorithms and applications. United States: N. p., 2017. Web. doi:10.1016/J.JCP.2016.10.069.
Chacón, L., E-mail: chacon@lanl.gov, Chen, G., Knoll, D.A., Newman, C., Park, H., Taitano, W., Willert, J.A., & Womeldorff, G.. Multiscale high-order/low-order (HOLO) algorithms and applications. United States. doi:10.1016/J.JCP.2016.10.069.
Chacón, L., E-mail: chacon@lanl.gov, Chen, G., Knoll, D.A., Newman, C., Park, H., Taitano, W., Willert, J.A., and Womeldorff, G.. Wed . "Multiscale high-order/low-order (HOLO) algorithms and applications". United States. doi:10.1016/J.JCP.2016.10.069.
@article{osti_22622241,
title = {Multiscale high-order/low-order (HOLO) algorithms and applications},
author = {Chacón, L., E-mail: chacon@lanl.gov and Chen, G. and Knoll, D.A. and Newman, C. and Park, H. and Taitano, W. and Willert, J.A. and Womeldorff, G.},
abstractNote = {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.},
doi = {10.1016/J.JCP.2016.10.069},
journal = {Journal of Computational Physics},
number = ,
volume = 330,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 2017},
month = {Wed Feb 01 00:00:00 EST 2017}
}