Surrogate approximation of the Grad–Shafranov free boundary problem via stochastic collocation on sparse grids
AffiliationDepartment of Mathematics, The University of Arizona
KeywordsFree boundary Grad-Shafranov equation
MetadataShow full item record
CitationElman, H. C., Liang, J., & Sánchez-Vizuet, T. (2022). Surrogate approximation of the Grad–Shafranov free boundary problem via stochastic collocation on sparse grids. Journal of Computational Physics.
JournalJournal of Computational Physics
Rights© 2021 Elsevier Inc. 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 email@example.com.
AbstractIn magnetic confinement fusion devices, the equilibrium configuration of a plasma is determined by the balance between the hydrostatic pressure in the fluid and the magnetic forces generated by an array of external coils and the plasma itself. The location of the plasma is not known a priori and must be obtained as the solution to a free boundary problem. The partial differential equation that determines the behavior of the combined magnetic field depends on a set of physical parameters (location of the coils, intensity of the electric currents going through them, magnetic permeability, etc.) that are subject to uncertainty and variability. The confinement region is in turn a function of these stochastic parameters as well. In this work, we consider variations on the current intensities running through the external coils as the dominant source of uncertainty. This leads to a parameter space of dimension equal to the number of coils in the reactor. With the aid of a surrogate function built on a sparse grid in parameter space, a Monte Carlo strategy is used to explore the effect that stochasticity in the parameters has on important features of the plasma boundary such as the location of the x-point, the strike points, and shaping attributes such as triangularity and elongation. The use of the surrogate function reduces the time required for the Monte Carlo simulations by factors that range between 7 and over 30.
Note24 month embargo; available online 22 September 2021
VersionFinal accepted manuscript
SponsorsNational Science Foundation