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FOCM
2011
90views more  FOCM 2011»
10 years 10 months ago
Hamiltonian Interpolation of Splitting Approximations for Nonlinear PDEs
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...
Erwan Faou, Benoît Grebert
FOCM
2011
188views more  FOCM 2011»
10 years 10 months ago
Compressive Wave Computation
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...
Laurent Demanet, Gabriel Peyré
FOCM
2011
96views more  FOCM 2011»
10 years 10 months ago
Persistent Intersection Homology
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...
Paul Bendich, John Harer
FOCM
2011
80views more  FOCM 2011»
10 years 10 months ago
The Serendipity Family of Finite Elements
Douglas N. Arnold, Gerard Awanou
FOCM
2011
107views more  FOCM 2011»
10 years 10 months ago
Quantifying Transversality by Measuring the Robustness of Intersections
By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbatio...
Herbert Edelsbrunner, Dmitriy Morozov, Amit K. Pat...
FOCM
2011
175views more  FOCM 2011»
11 years 1 months ago
Convergence of Fixed-Point Continuation Algorithms for Matrix Rank Minimization
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 ...
Donald Goldfarb, Shiqian Ma
FOCM
2011
113views more  FOCM 2011»
11 years 1 months ago
Finite Resolution Dynamics
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...
Stefano Luzzatto, Pawel Pilarczyk
FOCM
2011
84views more  FOCM 2011»
11 years 1 months ago
Discrete Lie Advection of Differential Forms
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...
Patrick Mullen, Alexander McKenzie, Dmitry Pavlov,...
FOCM
2011
117views more  FOCM 2011»
11 years 1 months ago
Accuracy and Stability of Computing High-order Derivatives of Analytic Functions by Cauchy Integrals
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...
Folkmar Bornemann
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