1,720,963 research outputs found
New magic formulas demonstration shows unexpected features of geometrically defined matrices for polyhedral grids
No full textMagic formulas are the geometric identities at the root of modern compatible schemes for polyhedral grids. We present rigorous yet elementary proofs of the magic formulas originating from Stokes theorem. The proofs enlighten new fundamental aspects of the mass matrices produced with the magic formulas. First, the construction of the mass matrices works for an unexpectedly broad type of mesh cells. Second, they show that dual nodes can be arbitrarily positioned thus extending the construction of the dual barycentric grid
The topology of Helmholtz domains
No full textAbstractThe use of cuts along surfaces for the study of domains in Euclidean 3-space widely occurs in the theoretical and applied literature about electromagnetism, fluid dynamics and elasticity. This paper is aimed at discussing techniques and results of 3-dimensional topology that provide an appropriate theoretical background to the method of cuts along surfaces. We consider two classes of bounded domains that become “simple” after a finite number of cuts along disjoint properly embedded surfaces. The difference between the two classes arises from the different meanings that the word “simple” may assume, when referred to spatial domains. In the definition of Helmholtz domain, we require that the domain may be cut along disjoint surfaces into pieces such that any curl-free smooth vector field defined on a piece admits a potential. On the contrary, in the definition of weakly Helmholtz domain we only require that a potential exists for the restriction to every piece of any curl-free smooth vector field defined on the whole initial domain. We use classical and rather elementary facts of 3-dimensional geometric and algebraic topology to give an exhaustive description of Helmholtz domains, proving that their topology is forced to be quite elementary: in particular, Helmholtz domains with connected boundary are just possibly knotted handlebodies, and the complement of any nontrivial link is not Helmholtz. The discussion about weakly Helmholtz domains is more advanced, and their classification is a more demanding task. Nevertheless, we provide interesting characterizations and examples of weakly Helmholtz domains. For example, we prove that the class of links with weakly Helmholtz complement coincides with the well-known class of homology boundary links
Inverting the discrete curl operator: A novel graph algorithm to find a vector potential of a given vector field
No full textWe provide a novel framework to compute a discrete vector potential of a given discrete vector field on arbitrary polyhedral meshes. The framework exploits the concept of acyclic matching, a combinatorial tool at the core of discrete Morse theory. We introduce the new concept of complete acyclic matchings and we show that they give the same end result of Gaussian elimination. Basically, instead of doing costly row and column operations on a sparse matrix, we compute equivalent cheap combinatorial operations that preserve the underlying sparsity structure. Currently, the most efficient algorithms proposed in literature to find discrete vector potentials make use of tree-cotree techniques. We show that they compute a special type of complete acyclic matchings. Moreover, we show that the problem of computing them is equivalent to the problem of deciding whether a given mesh has a topological property called collapsibility. This fact gives a topological characterization of well-known termination problems of tree-cotree techniques. We propose a new recursive algorithm to compute discrete vector potentials. It works directly on basis elements of 1- and 2-chains by performing elementary Gaussian operations on them associated with acyclic matchings. However, the main novelty is that it can be applied recursively. Indeed, the recursion process allows us to sidetrack termination problems of the standard tree-cotree techniques. We tested the algorithm on pathological triangulations with known topological obstructions. In all tested problems we observe linear computational complexity as a function of mesh size. Moreover, the algorithm is purely graph-based so it is straightforward to implement and does not require specialized external procedures. We believe that our framework could offer new perspectives to sparse matrix computations
The role of the dual grid in low-order compatible numerical schemes on general meshes
No full textIn this work, we uncover hidden geometric aspect of low-order compatible numerical schemes. First, we rewrite standard mimetic reconstruction operators defined by Stokes theorem using geometric elements of the barycentric dual grid, providing the equivalence between mimetic numerical schemes and discrete geometric approaches. Second, we introduce a novel global property of the reconstruction operators, called P0-consistency, which extends the standard consistency requirement of the mimetic framework. This concept characterizes the whole class of reconstruction operators that can be used to construct a global mass matrix in such a way that a global patch test is passed. Given the geometric description of the scheme, we can set up a correspondence between entries of reconstruction operators and geometric elements of a secondary grid, which is built by duality from the primary grid used in the scheme formulation. Finally, we show the that the geometric interpretation is necessary for the correct evaluation of certain physical variables in the post-processing stage. A discussion on how the geometric viewpoint allows to optimize reconstruction operators completes the exposition
The curved mimetic finite difference method: Allowing grids with curved faces
No full textWe present a new mimetic finite difference method for diffusion problems that converges on grids with curved (i.e., non-planar) faces. Crucially, it gives a symmetric discrete problem that uses only one discrete unknown per curved face. The principle at the core of our construction is to abandon the standard definition of local consistency of mimetic finite difference methods. Instead, we exploit the novel and global concept of P0-consistency. Numerical examples confirm the consistency and the optimal convergence rate of the proposed mimetic method for cubic grids with randomly perturbed nodes as well as grids with curved boundaries
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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