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A fast direct solver for nonlocal operators in wavelet coordinates

Harbrecht, Helmut ; Multerer, Michael

In: Journal of computational physics, 2021, vol. 428, p. 15 p

In this article, we consider fast direct solvers for nonlocal operators. The pivotal idea is to combine a wavelet representation of the system matrix, yielding a quasi- sparse matrix, with the nested dissection ordering scheme. The latter drastically reduces the fill-in during the factorization of the system matrix by means of a Cholesky decomposition or an LU decomposition, respectively. This...

A multidomain discretization of the Richards equation in layered soil

Berninger, Heiko ; Kornhuber, Ralf ; Sander, Oliver

In: Computational Geosciences, 2015, vol. 19, no. 1, p. 213-232

The eigenvalues of the Laplacian with Dirichlet boundary condition in $$\mathbb {R}^2$$ R 2 are almost never minimized by disks

Berger, Amandine

In: Annals of Global Analysis and Geometry, 2015, vol. 47, no. 3, p. 285-304

Erratum to: Sharp upper bound for the first eigenvalue

Binoy, Raveendran ; Santhanam, G.

In: Geometriae Dedicata, 2015, vol. 174, no. 1, p. 409-411

Point compression for the trace zero subgroup over a small degree extension field

Gorla, Elisa ; Massierer, Maike

In: Designs, Codes and Cryptography, 2015, vol. 75, no. 2, p. 335-357

Shortest closed billiard orbits on convex tables

Alkoumi, Naeem ; Schlenk, Felix

In: Manuscripta Mathematica, 2015, vol. 147, no. 3-4, p. 365-380

Banded, stable, skew-symmetric differentiation matrices of high order

Hairer, Ernst ; Iserles, Arieh

In: IMA Journal of Numerical Analysis, 2017, vol. 37, no. 3, p. 1087-1103

Canonical parameterizations of metric disks

Lytchak, Alexander ; Wenger, Stefan

In: Duke Mathematical Journal, 2020, vol. 169, no. 4, p. 761–797

We use the recently established existence and regularity of area and energy minimizing disks in metric spaces to obtain canonical parameterizations of metric surfaces. Our approach yields a new and conceptually simple proof of a well-known theorem of Bonk and Kleiner on the existence of quasisymmetric parameterizations of linearly locally connected, Ahlfors 2-regular metric 2-spheres....

On the Gibbs states of the noncritical Potts model on $$\mathbb Z ^2$$

Coquille, Loren ; Duminil-Copin, Hugo ; Ioffe, Dmitry ; Velenik, Yvan

In: Probability Theory and Related Fields, 2014, vol. 158, no. 1-2, p. 477-512

Compression for trace zero points on twisted Edwards curves

Bianco, Giulia ; Gorla, Elisa

In: Journal of Mathematical Cryptology, 2016, vol. 10, no. 1, p. 15-34