An adaptive homotopy approach for non-selfadjoint eigenvalue problems
Please always quote using this URN:urn:nbn:de:0296-matheon-7058
- This paper presents three different adaptive algorithms for eigenvalue problems associated with non-selfadjoint partial differential operators. The basis for the developed algorithms is a homotopy method. The homotopy method starts from a well-understood selfadjoint problem, for which well-established adaptive methods are available. Apart from the adaptive grid refinement, the progress of the homotopy as well as the solution of the iterative method are adapted to balance the contributions of the different error sources. The first algorithm balances the homotopy, discretization and approximation errors with respect to a fixed step-size $\tau$ in the homotopy. The second algorithm combines the adaptive step-size control for the homotopy with an adaptation in space that ensures an error below a fixed tolerance $\varepsilon$. The third algorithm allows the complete adaptivity in space, homotopy step-size as well as the iterative algebraic eigenvalue solver. All three algorithms are compared in numerical examples.