Linearization techniques for band structure calculations in absorbing photonic crystals
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This work is concerned with numerical methods for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In particular, we focus on eigenvalue problems for which the evaluation of the matrix-valued function is computationally expensive. ...
This paper is concerned with the numerical solution of symmetric large-scale Lyapunov equations with low-rank right-hand sides and coefficient matrices depending on a parameter. Specifically, we consider the situation when the parameter dependence is suffi ...
Invariant pairs have been proposed as a numerically robust means to represent and compute several eigenvalues along with the corresponding (generalized) eigenvectors for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In this wor ...
We present a systematic numerical approach to compute the eigenmodes and the related eigenfrequencies of a disordered photonic crystal, characterized by small fluctuations of the otherwise periodic dielectric profile. The field eigenmodes are expanded on t ...
We discuss in this thesis the numerical approximation of fluid-structure interaction (FSI) problems with a particular concern (albeit not exclusive) on hemodynamics applications. Firstly, we model the blood as an incompressible fluid and the artery wall as ...
The numerical solution of linear systems with certain tensor product structures is considered. Such structures arise, for example, from the finite element discretization of a linear PDE on a d-dimensional hypercube. Linear systems with tensor product struc ...
Society for Industrial and Applied Mathematics2009
We consider matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. One of the most fundamental differences from the linear case is that distinct eigenvalues may have linearly dependent eigenvectors or even share the same eigenvector. Th ...
An incompressible variational ideal ballooning mode equation is discretized with the COOL finite element discretization scheme using basis functions composed of variable order Legendre polynomials. This reduces the second order ordinary differential equati ...
We consider a class of nonlinear eigenvalue problems including equations such as −Δu(x) + q(x)u(x) + γ u(x)2 ξ(x)2 + u(x)2 u = λu(x) for x ∈ R , where γ > 0, q ∈ L∞(RN ) and ξ ∈ L2(RN ) are given and we are interested in eigenvalues λ ∈ R for which this eq ...
American Mathematical Society, P.O. Box 6248 Ms. Phoebe Murdock, Providence, Ri 02940 Usa2011
In this thesis we address the numerical approximation of the incompressible Navier-Stokes equations evolving in a moving domain with the spectral element method and high order time integrators. First, we present the spectral element method and the basic to ...