The Sparse Grid Combination Technique for Computing Eigenvalues in Linear Gyrokinetics

Using the five-dimensional gyrokinetic equations for simulations of hot fusion plasmas requires discretizations with a lot degrees of freedom due to the curse of dimensionality. The sparse grid combination technique could be one remedy to this problem, since it is dividing the original problem into smaller subproblems, which can be solved independently. For this study, the gyrokinetic code GENE has been used for solving the gyrokinetic eigenvalue problem using the combination technique. The performance of different combination schemes is used on a test problem and evaluated with respect to accuracy in retrieving an eigenvalue and the computational effort required. This evaluation suggests, that the sparse grid combination technique is a feasible method to compute eigenvalues of the gyrokinetic eigenvalue problem.