Integral equation methods for extreme-parameter materials and novel boundary conditions

Johannes Markkanen

    Research output: ThesisDoctoral ThesisCollection of Articles


    This thesis aims to develop accurate and efficient numerical methods for modeling electromagnetic properties of materials with extreme parameters and nonconventional boundary conditions. Materials with the permittivity and permeability dyadics being strongly inhomogeneous or anisotropic or having parameters near zero or infinity are considered as extreme materials. Nonconventional boundary conditions investigated in this thesis are called DB and D'B' boundary conditions, which require the vanishing of the normal components of the fluxes (DB) or their normal derivatives (D'B'). This thesis consists of three main topics. In the first part, a surface integral equation-based solution for electromagnetic wave scattering by objects with the DB boundary condition is developed. The integral equations are solved by the method of moments. The DB boundary condition is enforced by restricting the freedom of the unknown surface current densities. The developed method is then used for analyzing electromagnetic scattering by the ideal DB objects. The second part examines properties of different volume integral equation formulations and their discretizations. The accuracy and stability of these formulations are analyzed when the material parameters are complicated or pushed to the extreme limits. It is shown that the formulation with the equivalent volume currents as unknowns is more stable than the conventional ones when the material parameters are extremely anisotropic. The third part focuses on material approximations of the DB and D'B' boundary conditions in terms of an interface against some extreme-parameter material. Scattering properties of these approximations are investigated by using the volume integral equation method developed in the second part.
    Translated title of the contributionIntegraaliyhtälömenetelmät äärimmäisille materiaaleille ja uusille reunaehdoille
    Original languageEnglish
    QualificationDoctor's degree
    Awarding Institution
    • Aalto University
    • Sihvola, Ari, Supervising Professor
    • Ylä-Oijala, Pasi, Thesis Advisor
    Print ISBNs978-952-60-5242-7
    Electronic ISBNs978-952-60-5243-4
    Publication statusPublished - 2013
    MoE publication typeG5 Doctoral dissertation (article)


    • integral equation methods
    • method of moments
    • DB boundary condition
    • D'B' boundary condition
    • anisotropy
    • extreme materials


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