7,958 research outputs found
The adaptive computation of far-field patterns by a posteriori error estimations of linear functionals
This paper is concerned with the derivation of a priori and a posteriori error bounds for a class of linear functionals arising in electromagnetics which represent the far-field pattern of the scattered electromagnetic field. The a posteriori error bound is implemented into an adaptive finite element algorithm, and a series of numerical experiments is presented
On the graph limit question of Vera T. S\'os
In the dense graph limit theory, the topology of the set of graphs is defined
by the distribution of the subgraphs spanned by finite number of random
vertices. Vera T. S\'os proposed a question that if we consider only the number
of edges in the spanned subgraphs, then whether it provides an equivalent
definition. We show that the answer is positive on quasirandom graphs, and we
prove a generalization of the statement.Comment: 4 page
Loading Surface in the Course of Mechanical- Thermal Treatment and Steady-State Creep of Metals
Abstract: Kinetics of the loading surface of a material gives precious information on the
level of the hardening of the material. This paper is concerned with the evolution of the
loading surface during successive actions, such as: (i) plastic deformation, (ii) annealing of
the pre-strained specimen, and (iii) secondary creep of the treated material. The analysis of
the loading surface is carried out in terms of the synthetic theory of irrecoverable
deformation.
Keywords: loading surface; mechanical-thermal treatment; creep and plastic strain;
synthetic theory of irrecoverable deformatio
Finite element approximation of high-dimensional transport-dominated diffusion problems
High-dimensional partial differential equations with nonnegative characteristic form arise in numerous mathematical models in science. In problems of this kind, the computational challenge of beating the exponential growth of complexity as a function of dimension is exacerbated by the fact that the problem may be transport-dominated. We develop the analysis of stabilised sparse finite element methods for such high-dimensional, non-self-adjoint and possibly degenerate partial differential equations.\ud
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(Presented as an invited lecture under the title "Computational multiscale modelling: Fokker-Planck equations and their numerical analysis" at the Foundations of Computational Mathematics conference in Santander, Spain, 30 June - 9 July, 2005.
Maximum flow is approximable by deterministic constant-time algorithm in sparse networks
We show a deterministic constant-time parallel algorithm for finding an
almost maximum flow in multisource-multitarget networks with bounded degrees
and bounded edge capacities. As a consequence, we show that the value of the
maximum flow over the number of nodes is a testable parameter on these
networks.Comment: 8 page
Random local algorithms
Consider the problem when we want to construct some structure on a bounded
degree graph, e.g. an almost maximum matching, and we want to decide about each
edge depending only on its constant radius neighbourhood. We show that the
information about the local statistics of the graph does not help here. Namely,
if there exists a random local algorithm which can use any local statistics
about the graph, and produces an almost optimal structure, then the same can be
achieved by a random local algorithm using no statistics.Comment: 9 page
Independent sets and cuts in large-girth regular graphs
We present a local algorithm producing an independent set of expected size
on large-girth 3-regular graphs and on large-girth
4-regular graphs. We also construct a cut (or bisection or bipartite subgraph)
with edges on large-girth 3-regular graphs. These decrease the gaps
between the best known upper and lower bounds from to , from
to and from to , respectively. We are using
local algorithms, therefore, the method also provides upper bounds for the
fractional coloring numbers of and and fractional edge coloring number . Our algorithms are applications of the technique introduced by Hoppen
and Wormald
A Gagliardo-Nirenberg inequality, with application to duality-based a posteriori error estimation in the L1 norm
We establish the Gagliardo-Nirenberg-type multiplicative interpolation inequality \[ \|v\|_{{\rm L}1(\mathbb{R}^n)} \leq C \|v\|^{1/2}_{{\rm Lip}'(\mathbb{R}^n)} \|v\|^{1/2}_{{\rm BV}(\mathbb{R}^n)}\qquad \forall v \in {\rm BV}(\mathbb{R}^n), \] where is a positive constant, independent of . We then use a local version of this inequality to derive an a posteriori error bound in the norm, with , for a finite-element approximation to a boundary value problem for a first-order linear hyperbolic equation, under the limited regularity requirement that the solution to the problem belongs to .\ud
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Dedicated to Professor Boško S Jovanovic on the occasion of his sixtieth birthda
An undecidability result on limits of sparse graphs
Given a set B of finite rooted graphs and a radius r as an input, we prove
that it is undecidable to determine whether there exists a sequence (G_i) of
finite bounded degree graphs such that the rooted r-radius neighbourhood of a
random node of G_i is isomorphic to a rooted graph in B with probability
tending to 1. Our proof implies a similar result for the case where the
sequence (G_i) is replaced by a unimodular random graph.Comment: 6 page
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