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SIAMSC
2016
3 years 11 days ago
Fast Structured Direct Spectral Methods for Differential Equations with Variable Coefficients, I. The One-Dimensional Case
We study the rank structures of the matrices in Fourier- and Chebyshev-spectral methods for differential equations with variable coefficients in one dimension. We show analyticall...
Jie Shen, Yingwei Wang, Jianlin Xia
SIAMREV
2016
3 years 11 days ago
Approximating Spectral Densities of Large Matrices
In physics, it is sometimes desirable to compute the so-called Density Of States (DOS), also known as the spectral density, of a Hermitian (or symmetric) matrix A. The spectral den...
Lin Lin, Yousef Saad, Chao Yang
SIAMREV
2016
3 years 11 days ago
Geodesic Transport Barriers in Jupiter's Atmosphere: A Video-Based Analysis
Jupiter’s zonal jets and Great Red Spot are well known from still images. However, the planet’s atmosphere is highly unsteady, which suggests that the actual material transport...
Alireza Hadjighasem, George Haller
SIAMREV
2016
3 years 11 days ago
A Newton-Galerkin Method for Fluid Flow Exhibiting Uncertain Periodic Dynamics
The determination of stable limit-cycles plays an important role in quantifying the characteristics of dynamical systems. In practice, exact knowledge of model parameters is rarely...
Michael Schick, Vincent Heuveline, O. P. Le Ma&ici...
SIAMNUM
2016
3 years 11 days ago
Error Estimates of a First-order Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations
This paper establishes a O(h 1 4 ) error estimate in the L∞ t (L1 x)-norm for the approximation of scalar conservation equations using an explicit continuous finite element tech...
Jean-Luc Guermond, Bojan Popov
SIAMNUM
2016
3 years 11 days ago
A Higher Order Finite Element Method for Partial Differential Equations on Surfaces
A new higher order finite element method for elliptic partial differential equations on a stationary smooth surface Γ is introduced and analyzed. We assume that Γ is characteri...
Jörg Grande, Arnold Reusken
SIAMNUM
2016
3 years 11 days ago
Backward Step Control for Global Newton-Type Methods
We present and analyze a new damping approach called backward step control for the globalization of the convergence of Newton-type methods for the numerical solution of nonlinear r...
Andreas Potschka
SIAMMA
2016
3 years 11 days ago
Analysis of the Incompatibility Operator and Application in Intrinsic Elasticity with Dislocations
The incompatibility operator arises in the modeling of elastic materials with dislocations and in the intrinsic approach to elasticity, where it is related to the Riemannian curvat...
Samuel Amstutz, Nicolas Van Goethem
SIAMMA
2016
3 years 11 days ago
Convergence of Regularized Nonlocal Interaction Energies
Inspired by numerical studies of the aggregation equation, we study the effect of regularization on nonlocal interaction energies. We consider energies defined via a repulsiveatt...
Katy Craig, Ihsan Topaloglu
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