2019/05/16 by Zlatko Drmač, Drmač, Zlatko, Ivana Šain Glibić +1
Engineering · Physics and Astronomy · #Acoustic Wave Phenomena Research #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1905.07013
openalex publication_date 2019/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quartic eigenvalue problem (λ4 A + λ3 B + λ2C + λD + E)x = 0 naturally arises e.g. when solving the Orr-Sommerfeld equation in the analysis of the stability of the Poiseuille flow, in theoretical analysis and experimental design of locally resonant phononic plates, modeling a robot with electric motors in the joints, calibration of catadioptric vision system, or e.g. computation of the guided and leaky modes of a planar waveguide. This paper proposes a new numerical method for the full solution (all eigenvalues and all left and right eigenvectors) that is based on quadratification, i.e. reduction of the quartic problem to a spectraly equivalent quadratic eigenvalue problem, and on a careful preprocessing to identify and deflate zero and infinite eigenvalues before the linearized quadratification is forwarded to the QZ algorithm. Numerical examples and backward error analysis confirm that the proposed algorithm is superior to the available methods.