Multilevel Monte Carlo methods for the Grad-Shafranov free boundary problem
AffiliationDepartment of Mathematics, The University of Arizona
KeywordsGeneral Physics and Astronomy
Hardware and Architecture
Adaptive finite element discretization
Free boundary Grad-Shafranov problem
Multilevel Monte Carlo Finite-Element
MetadataShow full item record
CitationElman, H. C., Liang, J., & Sánchez-Vizuet, T. (2024). Multilevel Monte Carlo methods for the Grad-Shafranov free boundary problem. Computer Physics Communications, 109099.
JournalComputer Physics Communications
Rights© 2024 Elsevier B.V. All rights reserved.
Collection InformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at firstname.lastname@example.org.
AbstractThe equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad-Shafranov equation. The presence of uncertainty in the model parameters introduces the need to quantify the variability in the predictions. This is often done by computing a large number of model solutions on a computational grid for an ensemble of parameter values and then obtaining estimates for the statistical properties of solutions. In this study, we explore the savings that can be obtained using multilevel Monte Carlo methods, which reduce costs by performing the bulk of the computations on a sequence of spatial grids that are coarser than the one that would typically be used for a simple Monte Carlo simulation. We examine this approach using both a set of uniformly refined grids and a set of adaptively refined grids guided by a discrete error estimator. Numerical experiments show that multilevel methods dramatically reduce the cost of simulation, with cost reductions typically on the order of 60 or more and possibly as large as 200. Adaptive griding results in more accurate computation of geometric quantities such as x-points associated with the model.
Note24 month embargo; first published 19 January 2024
VersionFinal accepted manuscript
SponsorsU.S. Department of Energy