Learned Infinite Elements

Spectral Elements on Infinite Domains

A few new (?) facts about infinite elements

We discuss the (conjugated) Bubnov–Galerkin and Petrov–Galerkin infinite element (IE) discretizations to Helmholtz equation including the use of elements of locally variable order, optimal choice of IE shape functions, calculation of Echo Area (EA), and automatic hp-adaptivity. The discussion is illustrated with 2D numerical experiments. 2005 Elsevier B.V. All rights reserved. MSC classificatio...

Sortable Elements in Infinite Coxeter Groups

In a series of previous papers, we studied sortable elements in finite Coxeter groups, and the related Cambrian fans. We applied sortable elements and Cambrian fans to the study of cluster algebras of finite type and the noncrossing partitions associated to Artin groups of finite type. In this paper, as the first step towards expanding these applications beyond finite type, we study sortable el...

Convergence of Infinite Exponentials with Complex Elements

b-> bi where a„ = log bn. (Wherever the logarithm is used in this article it is understood to be the principal branch of the function.) However, this way of writing an infinite exponential is ambiguous since it is not clear what value of z is to be used, and since different choices of z may lead to different convergence behavior of the sequence. Instead of 2=1, we could have used 2 = 0 without ...

Numerical Modeling of Railway Track Supporting System using Finite-Infinite and Thin Layer Elements

The present contribution deals with the numerical modeling of railway track-supporting systems-using coupled finite-infinite elements-to represent the near and distant field stress distribution, and also employing a thin layer interface element to account for the interfacial behavior between sleepers and ballast. To simulate the relative debonding, slipping and crushing at the contact area betw...