1,175 research outputs found
A parallel edge orientation algorithm for quadrilateral meshes
One approach to achieving correct finite element assembly is to ensure that
the local orientation of facets relative to each cell in the mesh is consistent
with the global orientation of that facet. Rognes et al. have shown how to
achieve this for any mesh composed of simplex elements, and deal.II contains a
serial algorithm to construct a consistent orientation of any quadrilateral
mesh of an orientable manifold.
The core contribution of this paper is the extension of this algorithm for
distributed memory parallel computers, which facilitates its seamless
application as part of a parallel simulation system.
Furthermore, our analysis establishes a link between the well-known
Union-Find algorithm and the construction of a consistent orientation of a
quadrilateral mesh. As a result, existing work on the parallelisation of the
Union-Find algorithm can be easily adapted to construct further parallel
algorithms for mesh orientations.Comment: Second revision: minor change
Principal and syntactic congruences in congruence-distributive and congruence-permutable varieties
We give a new proof that a finitely generated congruence-distributive variety has finitely determined syntactic congruences (or, equivalently, term finite principal congruences), and show that the same does not hold for finitely generated congruence-permutable varieties, even under the additional assumption that the variety is residually very finite
Finitely forcible graphons with an almost arbitrary structure
Graphons are analytic objects representing convergent sequences of large
graphs. A graphon is said to be finitely forcible if it is determined by
finitely many subgraph densities, i.e., if the asymptotic structure of graphs
represented by such a graphon depends only on finitely many density
constraints. Such graphons appear in various scenarios, particularly in
extremal combinatorics.
Lovasz and Szegedy conjectured that all finitely forcible graphons possess a
simple structure. This was disproved in a strong sense by Cooper, Kral and
Martins, who showed that any graphon is a subgraphon of a finitely forcible
graphon. We strenghten this result by showing for every that
any graphon spans a proportion of a finitely forcible graphon
RPA Green's Functions of the Anisotropic Heisenberg Model
We solve in random-phase approximation the anisotropic Heisenberg model,
including nearest and next-nearest neighbour interactions by calculating all
Green's functions and pair correlation functions in a cumulant decoupling
scheme. The general exposition is pedagogic in tone and is intended to be
accessible to any graduate student or physicist who is not an expert in the
field.Comment: 26 pages, 4 figure
Occurrence of amphibian deformities along the Hungarian section of the River Danube, Tisza and Ipoly
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