Publications related to Scientific Computing and Uncertainty Quantification - CADMOS Chair

Adaptive isogeometric methods with hierarchical splines: Optimality and convergence rates

We consider an adaptive isogeometric method (AIGM) based on (truncated) hierarchical B-splines and continue the study of its numerical properties. We prove that our AIGM is optimal in the sense that delivers optimal convergence rates as soon as the solutio ...

2018

Indiscreet logarithms in finite fields of small characteristic

Robert Granger, Thorsten Kleinjung, Jens Markus Zumbrägel

Recently, several striking advances have taken place regarding the discrete logarithm problem (DLP) in finite fields of small characteristic, despite progress having remained essentially static for nearly thirty years, with the best known algorithms being ...

2018

Arithmetic and metric aspects of open de Rham spaces

Dimitri Stelio Wyss, Tamás Hausel, Michael Lennox Wong

In this paper we determine the motivic class---in particular, the weight polynomial and conjecturally the Poincar'e polynomial---of the open de Rham space, defined and studied by Boalch, of certain moduli of irregular meromorphic connections on the trivia ...

2018

Four-Variable Expanders Over The Prime Fields

Adrian Claudiu Valculescu, Van Thang Pham

Let F-p be a prime field of order p > 2, and let A be a set in F-p with very small size in terms of p. In this note, we show that the number of distinct cubic distances determined by points in A x A satisfies vertical bar(A - A)(3) + (A - A)(3 vertical bar ...

AMER MATHEMATICAL SOC2018

Entropy stable essentially non-oscillatory methods based on RBF reconstructions

Jan Sickmann Hesthaven, Fabian Mönkeberg

To solve hyperbolic conservation laws on general grids we propose to use high-order essentially nonoscillatory methods based on radial basis functions. We introduce an entropy stable arbitrary high-order finite dierence method (RBF-TeCNOp) and an entropy s ...

2018

From Wallis to Ramanujan, in companionship with RW Gosper

Manuel Ojanguren

Accelerating the convergence of some hypergeometric series with Gosper's method leads, in a most elementary way, to some series discovered by Ramanujan, Bauer and Dougall. In particular, it is shown that one of them can be traced back to the well-known for ...

2018

MATHICSE Technical Report : A Bayesian numerical homogenization method for elliptic multiscale inverse problems

Assyr Abdulle, Andrea Di Blasio

A new strategy based on numerical homogenization and Bayesian techniques for solvingmultiscale inverse problems is introduced. We consider a class of elliptic problems which vary ata microscopic scale, and we aim at recovering the highly oscillatory tensor ...

MATHICSE2018

Weyl sums and the Lyapunov exponent for the skew-shift Schrödinger cocycle

Marius Christopher Lemm, Rui Han

We study the one-dimensional discrete Schrödinger operator with the skew-shift potential

2\lambda\cos\left(2\pi \left(\binom{j}{2} \omega+jy+x\right)\right)

. This potential is long conjectured to behave like a random one, i.e., it is expected to produce ...

2018

Central limit theorems for multilevel Monte Carlo methods

Sebastian Krumscheid, Hakon Andreas Hoel

In this work, we show that uniform integrability is not a necessary condition for central limit theorems (CLT) to hold for normalized multilevel Monte Carlo MLMC estimators, and we provide near optimal weaker conditions under which the CLT is achieved. In ...

2018

Tensor product of correspondence functors

Jacques Thévenaz, Serge Bouc

As part of the study of correspondence functors, the present paper investigates their tensor product and proves some of its main properties. In particular, the correspondence functor associated to a finite lattice has the structure of a commutative algebra ...

2018

Scientific Computing and Uncertainty Quantification - CADMOS Chair

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Adaptive isogeometric methods with hierarchical splines: Optimality and convergence rates

Indiscreet logarithms in finite fields of small characteristic

Arithmetic and metric aspects of open de Rham spaces

Four-Variable Expanders Over The Prime Fields

Entropy stable essentially non-oscillatory methods based on RBF reconstructions

From Wallis to Ramanujan, in companionship with RW Gosper

MATHICSE Technical Report : A Bayesian numerical homogenization method for elliptic multiscale inverse problems

Weyl sums and the Lyapunov exponent for the skew-shift Schrödinger cocycle

Central limit theorems for multilevel Monte Carlo methods

Tensor product of correspondence functors

Adaptive isogeometric methods with hierarchical splines: Optimality and convergence rates

Arithmetic and metric aspects of open de Rham spaces

Indiscreet logarithms in finite fields of small characteristic

Four-Variable Expanders Over The Prime Fields

Entropy stable essentially non-oscillatory methods based on RBF reconstructions

From Wallis to Ramanujan, in companionship with RW Gosper

MATHICSE Technical Report : A Bayesian numerical homogenization method for elliptic multiscale inverse problems

Weyl sums and the Lyapunov exponent for the skew-shift Schrödinger cocycle

Central limit theorems for multilevel Monte Carlo methods

Tensor product of correspondence functors