Component mode synthesis and eigenvalues of second order operators : discretization and algorithm
Computable Bounds for Eigenvalues and Eigenfunctions of Elliptic Differential Operators.
Computation of 3D vertex singularities for linear elasticity : error estimates for a finite element method on graded meshes
This paper is concerned with the computation of 3D vertex singularities of anisotropic elastic fields with Dirichlet boundary conditions, focusing on the derivation of error estimates for a finite element method on graded meshes. The singularities are described by eigenpairs of a corresponding operator pencil on spherical polygonal domains. The main idea is to introduce a modified quadratic variational boundary eigenvalue problem which consists of two self-adjoint, positive definite sesquilinear...
Computation of 3D vertex singularities for linear elasticity: Error estimates for a finite element method on graded meshes
This paper is concerned with the computation of 3D vertex singularities of anisotropic elastic fields with Dirichlet boundary conditions, focusing on the derivation of error estimates for a finite element method on graded meshes. The singularities are described by eigenpairs of a corresponding operator pencil on spherical polygonal domains. The main idea is to introduce a modified quadratic variational boundary eigenvalue problem which consists of two self-adjoint, positive definite sesquilinear...
Computing guided modes for an unbounded stratified medium in integrated optics
We present a finite element method to compute guided modes in a stratified medium. The major difficulty to overcome is related to the unboundedness of the stratified medium. Our method is an alternative to the use of artificial boundary conditions and to the use of integral representation formulae. The domain is bounded in such a way we can write the solution on its lateral boundaries in terms of Fourier series. The series is then truncated for the computations over the bounded domain. The problem...
Computing guided modes for an unbounded stratified medium in integrated optics
We present a finite element method to compute guided modes in a stratified medium. The major difficulty to overcome is related to the unboundedness of the stratified medium. Our method is an alternative to the use of artificial boundary conditions and to the use of integral representation formulae. The domain is bounded in such a way we can write the solution on its lateral boundaries in terms of Fourier series. The series is then truncated for the computations over the bounded domain. The problem...
Coulomb Interaction Effects on the Spin Polarization and Currents in Quantum Wires with Spin Orbit Interaction
We analyze the charge and spin distributions induced in an interacting electron system confined inside a semiconductor quantum wire with spin orbit interaction in the presence of an external magnetic field. The wire, assumed to be infinitely long, is obtained through lateral confinement in three different materials: GaAs, InAs, and InSb. The spin-orbit coupling, linear in the electron momentum is of both Rashba and Dresselhaus type. Within the Hartree-Fock approximation the many-body Hamiltonian...