The J-method for the Gross–Pitaevskii eigenvalue problem

Abstract This paper studies the J -method of [ E. Jarlebring, S. Kvaal, W. Michiels. SIAM J. Sci. Comput. 36-4:A1978-A2001, 2014 ] for nonlinear eigenvector problems in a general Hilbert space framework. is basis variational discretization techniques and mesh-independent numerical analysis. A simple modification method mimics an energy-decreasing discrete gradient flow. In case Gross–Pitaevskii eigenvalue problem, we prove global convergence towards eigenfunction damped version -method. More importantly, when iterations are sufficiently close to eigenfunction, damping can be switched off recover local linear rate previously known from setting. quantitative analysis closely connected -method’s unique feature sensitivity with respect spectral shifts. Contrary classical flows, this allows both selective approximation excited states as well amplification beyond rates spirit Rayleigh quotient iteration problems. These advantageous properties demonstrated series experiments involving exponentially localized under disorder potentials vortex lattices rotating traps.