An Isogeometric Analysis approach for the study of the gyrokinetic quasi-neutrality equation

In this work, a new discretization scheme for the gyrokinetic quasi-neutrality equation is proposed. It is based on Isogeometric Analysis; the IGA which relies on NURBS functions, accommodates arbitrary coordinates and the use of complicated computation domains. Moreover, arbitrary high order degree of basis functions can be used and their regularity enables the use of a low number of elements. Here, this approach is successfully tested on elliptic problems like the quasi-neutrality equation arising in gyrokinetic models. In this last application, when polar coordinates are considered, a fast solver can be used and the non locality is dealt with a suitable decomposition which reduces the resolution of the gyrokinetic quasi-neutrality equation to a sequence of local 2D elliptic problems.