FOCM
2011
13 years 2 months ago
2011
We consider a wide class of semi linear Hamiltonian partial differential equations and their approximation by time splitting methods. We assume that the nonlinearity is polynomia...
FOCM
2011
13 years 2 months ago
2011
This paper considers large-scale simulations of wave propagation phenomena. We argue that it is possible to accurately compute a wavefield by decomposing it onto a largely incomp...
FOCM
2011
13 years 2 months ago
2011
The theory of intersection homology was developed to study the singularities of a topologically stratified space. This paper incorporates this theory into the already developed f...
FOCM
2011
13 years 2 months ago
2011
FOCM
2011
13 years 2 months ago
2011
By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbatio...
FOCM
2011
13 years 6 months ago
2011
The matrix rank minimization problem has applications in many fields such as system identification, optimal control, low-dimensional embedding etc. As this problem is NP-hard in ...
FOCM
2011
13 years 6 months ago
2011
We develop a new mathematical model for describing a dynamical system at limited resolution (or finite scale), and we give precise meaning to the notion of a dynamical system havi...
FOCM
2011
13 years 6 months ago
2011
In this paper, we present a numerical technique for performing Lie advection of arbitrary differential forms. Leveraging advances in high-resolution finite volume methods for sca...
FOCM
2011
2011
Accuracy and Stability of Computing High-order Derivatives of Analytic Functions by Cauchy Integrals
13 years 6 months ago
Abstract High-order derivatives of analytic functions are expressible as Cauchy integrals over circular contours, which can very effectively be approximated, e.g., by trapezoidal s...