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An application of Gaussian process modeling for high-order accurate adaptive mesh refinement prolongation

Steven I. Reeves, Dongwook Lee, Adam Reyes, Carlo Graziani and Petros Tzeferacos

Vol. 17 (2022), No. 1, 1–41

We present a new polynomial-free prolongation scheme for adaptive mesh refinement (AMR) simulations of compressible and incompressible computational fluid dynamics. The new method is constructed using a multidimensional kernel-based Gaussian process (GP) prolongation model. The formulation for this scheme was inspired by the two previous studies on the GP methods introduced by A. Reyes et al. (Journal of Scientific Computing, 76 (2017), and Journal of Computational Physics, 381 (2019)). We extend the previous GP interpolations and reconstructions to a new GP-based AMR prolongation method that delivers a third-order accurate prolongation of data from coarse to fine grids on AMR grid hierarchies. In compressible flow simulations, special care is necessary to handle shocks and discontinuities in a stable manner. For this, we utilize the shock handling strategy using the GP-based smoothness indicators developed in the previous GP work by Reyes et al. We compare our GP-AMR results with the test results using the second-order linear AMR method to demonstrate the efficacy of the GP-AMR method in a series of test suite problems using the AMReX library, in which the GP-AMR method has been implemented.

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adaptive mesh refinement, prolongations, high-order methods, Gaussian processes, computational fluid dynamics
Mathematical Subject Classification 2010
Primary: 65N50
Received: 18 March 2020
Revised: 24 April 2021
Accepted: 2 May 2021
Published: 26 February 2022
Steven I. Reeves
Machine Learning Software Engineering
Advanced Micro Devices
Santa Clara, CA
United States
Department of Applied Mathematics
University of California
Santa Cruz, CA
United States
Dongwook Lee
Department of Applied Mathematics
University of California
Santa Cruz, CA
United States
Adam Reyes
Department of Physics and Astronomy
University of Rochester
Rochester, NY
United States
Carlo Graziani
Mathematics and Computer Science
Argonne National Laboratory
Lemont, IL
United States
Petros Tzeferacos
Department of Physics and Astronomy
University of Rochester
Rochester, NY
United States
Laboratory for Laser Energetics
University of Rochester
Rochester, NY
United States