Computation of MHD equilibria by a quasi-inverse finite hybrid element approach

Abstract

Abstract A quasi-inverse finite hybrid element code has been written to supply a precise and consistent solution of the Grad-Shafranov equation to the ideal linear MHD stability code ERATO. To fit the behavior at the plasma surface and in the region around the magnetic axis, adequate coordinate transformations are made. A Picard iteration is used to treat the nonlinearity of the source term. One Picard step is carried out by solving the weak form of the partial differential equation by an isoparametric finite hybrid element approach (FHE). After each Picard step, the nodal points are readjusted such that they fall on the initially prescribed flux surfaces. This enables us to accumulate the nodal points in those regions where good precision is needed for the stability code. While a 4-point integration is necessary for a conforming finite element scheme, a 1-point integration is sufficient in a FHE approach. Coding the FHE is very simple and easily vectorizable. For a given resolution, the precision of global quantities, such as the total flux, is the same for both methods but the FHE approach is faster.