EPSI 2013-2014. Annual Progress Report

[摘要] Initially a separate orthogonal expansion for the low-k components and FEM for high-k components was considered, or a multi-scale FEM method, but a more attractive hybrid FDM/FEM model for parallel computations has been devised with minimal impact to formerly developed code. This system involves using Lagrange polynomials along magnetic field lines to establish a FDM discretization of the toroidal contributions to the perpendicular Laplacian, which is the operator of importance in gyrokinetic solution of the vector potential. The method was found analytically to be stable, due to some dissipation from varying field-line lengths. The accuracy of this method has been evaluated using the method of manufactured solutions (with Bei Wang of Princeton University), whereby we find that for a Poisson problem the maximum error roughly diminishes linearly as a function of the grid resolution (uniformly refined), whereas the L2 norm as square root of the resolution improvement. Most of the error appears to be contributed near boundaries and where the FEM grid has anisotropy, so we are trying to improve this analysis using improved tessellations obtained from Mark Shepard, and publish the results as soon as the problems with the grid have been eliminated.

[发布日期] 2015-03-17

[学科分类] 物理（综合）