Modern iterative algorithms for waveguides

Waveguides are used in a number of fields, e.g., electromagnetics and fluid mechanics. These require the study of physical domains are typically very large leading to a high computational cost for many direct discretization methods. Recent research approaches in the community have been done by viewing the domain as an infinite domain, leading to a nonlinear eigenvalue problems [1], allowing the use of advanced recent research on nonlinear eigenvalue problems and provide the possibility to preconditioning. The nonlinear eigenvalue problem is highly structured and we design iterative methods for this structure. New approaches are developed from a numerical linear algebra perspective, e.g. using Arnoldi’s method and modern iterative methods for linear systems, as well as a perspective of numerical methods for partial differential equations. Our approach allows the use of modern algorithms for current high-performance computing architecture.

• E. Ringh, G. Mele, J. Karlsson and E. Jarlebring, Sylvester-based preconditioning for the waveguide eigenvalue problem, Linear Algebra Appl., 542:441–463, 2018
• G. Mele and E. Jarlebring, On restarting the tensor infinite Arnoldi method, BIT numerical mathematics, 58:133-162, 2018