Isogeometric analysis in reduced magnetohydrodynamics

Abstract

Isogeometric analysis (IGA) consists of using computer-aided design (CAD) models defining the geometry of the computational domain using both B-splines and non- uniform rational B-splines (NURBS) to represent the unknowns that are the solution of a partial differential equation using a finite element principle. In this paper, we review the main ideas of IGA and apply it to a reduced magnetohydrodynamic (MHD) model that is used in tokamak simulations. This is a first step towards arbitrary high-order and smooth approximations of reduced MHD generalizing the Bezier splines approach of Czarny and Huysmans( 2008 J.Comput.Phys. 227 7423-45).