Computing The Complex Eigenvalue Spectrum for Resistive Magnetohydrodynamics

The spectrum of resistive MHD is evaluted by applying the Galerkin method in conjunction with finite elements. This leads to the general eigenvalue problem Ax = λBx. where A is a general non-Hermitian and B a symmetric positive-definite matrix. As this is a stiff problem, large matrix dimensions evolve. The QR algorithm can only be applied for a coarse grid. The fine grids necessary are treated by applying inverse vector iteration. Specific eigenvalue curves in the complex plane are obtained. By applying a continuation procedure it is possible by inverse vector iteration to map out in succession complete branches of the spectrum, e.g. all resistive Alfven modes, for matrix dimensions of up to 3.742.