Publication

Outlier-free spline spaces for isogeometric discretizations of biharmonic and polyharmonic eigenvalue problems

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The aim of the project is double: to understand the flexibility of the Isogeometric Analysis tools through the solution of some PDEs problems; to test the improvement in the computational time given by a partial loops vectorization at compile-time of the L ...

2012

Linearization techniques for band structure calculations in absorbing photonic crystals

Daniel Kressner, Peter Cedric Effenberger

Band structure calculations for photonic crystals require the numerical solution of eigenvalue problems. In this paper, we consider crystals composed of lossy materials with frequency-dependent permittivities. Often, these frequency dependencies are modele ...

2011

Modeling Magma Dynamics with a Mixed Fourier Collocation - Discontinuous Galerkin Method

Jan Sickmann Hesthaven

A high-order discretization consisting of a tensor product of the Fourier collocation and discontinuous Galerkin methods is presented for numerical modeling of magma dynamics. The physical model is an advection-reaction type system consisting of two hyperb ...

GLOBAL SCIENCE PRESS2011

Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems

Daniel Kressner, Peter Cedric Effenberger

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 ...

Springer-Verlag2011

A block Newton method for nonlinear eigenvalue problems

Daniel Kressner

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 ...

2009

Balancing sparse Hamiltonian eigenproblems

Daniel Kressner

Balancing a matrix by a simple and accurate similarity transformation can improve the speed and accuracy of numerical methods for computing eigenvalues. We describe balancing strategies for a large and sparse Hamiltonian matrix H. It is first shown how to ...

Elsevier2006

Algorithm 854: Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices II

Daniel Kressner

This article describes Fortran 77 subroutines for computing eigenvalues and invariant subspaces of Hamiltonian and skew-Hamiltonian matrices. The implemented algorithms are based on orthogonal symplectic decompositions, implying numerical backward stabilit ...

Association for Computing Machinery2006

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Two different approaches are proposed to enhance the efficiency of the numerical resolution of optimal control problems governed by a linear advection-diffusion equation. In the framework of the Galerkin-Finite Element (FE) method, we adopt a novel a poste ...

Springer2006

Optimal control and numerical adaptivity for advection-diffusion equations

Alfio Quarteroni, Luca Dede'

We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the Lagrangian functional, rather than stabilizing the state and adjoint ...

EDP Sciences2005

In order to numerically solve the interior and the exterior Dirichlet problems for the Laplacian operator, we have presented in a previous paper a method which consists in inverting, on a finite element space, a non-singular integral operator for circular ...

2002