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  1. 1. The Dirac Equation: Numerical and Asymptotic Analysis

    Författare :Hasan Almanasreh; Göteborgs universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Dirac operator; eigenvalue problem; finite element method; spurious eigenvalues; Petrov-Galerkin; cubic Hermite basis functions; stability parameter; meshfree method; $hp$-cloud; intrinsic enrichment; G-convergence; $ Gamma$-convergence; scattering theory; identification; wave operator; stationary approach; Dirac operator;

    Sammanfattning : The thesis consists of three parts, although each part belongs to a specific subject area in mathematics, they are considered as subfields of the perturbation theory. The main objective of the presented work is the study of the Dirac operator; the first part concerns the treatment of the spurious eigenvalues in the computation of the discrete spectrum. LÄS MER

  2. 2. Homogenization in Perforated Domains

    Författare :Martin Strömqvist; Henrik Shahgholian; Scott Armstrong; KTH; []
    Nyckelord :Mathematics; Matematik;

    Sammanfattning : Homogenization theory is the study of the asymptotic behaviour of solutionsto partial differential equations where high frequency oscillations occur.In the case of a perforated domain the oscillations are due to variations in thedomain of the equation. LÄS MER