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Usage of modular scissors in the implementation of FEM

Frydrych, Dalibor (2010)

Programs and Algorithms of Numerical Mathematics

Finite Element Method (FEM) is often perceived as a unique and compact programming subject. Despite the fact that many FEM implementations mention the Object Oriented Approach (OOA), this approach is used completely, only in minority of cases in most real-life situations. For example, one of building stones of OOA, the interface-based polymorphism, is used only rarely. This article is focusing on the design reuse and at the same time it gives a complex view on FEM. The article defines basic principles...

Uses of new sensitivity and DAE solving methods in SmartMOBILE for verified analysis of mechanical systems

Ekaterina Auer, Wolfram Luther (2009)

International Journal of Applied Mathematics and Computer Science

Software for modeling and simulation (MSS) of mechanical systems helps to reduce production costs for industry. Usually, such software relies on (possibly erroneous) finite precision arithmetic and does not take into account uncertainty in the input data. The program SmartMOBILE enhances the existing MSS MOBILE with verified techniques to provide a guarantee that the obtained results are correct and measure the influence of data uncertainty. In this paper, we outline the main features and functionalities...

Using a graph grammar system in the finite element method

Barbara Strug, Anna Paszyńska, Maciej Paszyński, Ewa Grabska (2013)

International Journal of Applied Mathematics and Computer Science

The paper presents a system of Composite Graph Grammars (CGGs) modelling adaptive two dimensional hp Finite Element Method (hp-FEM) algorithms with rectangular finite elements. A computational mesh is represented by a composite graph. The operations performed over the mesh are defined by the graph grammar rules. The CGG system contains different graph grammars defining different kinds of rules of mesh transformations. These grammars allow one to generate the initial mesh, assign values to element...

Using Discourse Context to Interpret Object-Denoting Mathematical Expressions

Wolska, Magdalena, Grigore, Mihai, Kohlhase, Michael (2011)

Towards a Digital Mathematics Library. Bertinoro, Italy, July 20-21st, 2011

We present a method for determining the context-dependent denotation of simple object-denoting mathematical expressions in mathematical documents. Our approach relies on estimating the similarity between the linguistic context within which the given expression occurs and a set of terms from a flat domain taxonomy of mathematical concepts; one of 7 head concepts dominating a set of terms with highest similarity score to the symbol’s context is assigned as the symbol’s interpretation. The taxonomy...

Using fuzzy relational databases to represent agricultural and environmental information. An example within the scope of olive cultivation in Granada.

Juan Manuel Serrano, M.ª Amparo Vila, Víctor Aranda, Gabriel Delgado (2001)

Mathware and Soft Computing

A query system for several types of users and for information retrieval about olive cultivation and its environmental support in the province of Granada (Spain) is introduced. The system is based on fuzzy data and is flexible. The main problems which this model solves are those relating to uncertain and imprecise data processing (as in the case of environmental and cultivation information), spatial and punctual data representation, and fusion of cultivation-resulting and scientific-experimental...

Using fuzzy similarity relations to revise and update a knowledge base.

Ricardo Rodríguez, Pere García, Lluis Godo (1996)

Mathware and Soft Computing

Similarity-based models were first used by Ruspini to give semantics to fuzzy logic. In these models, incomplete information is represented by an evidential set, i.e. a set of possible worlds that are compatible with the evidence, together with a fuzzy similarity relation} on the set of possible worlds that allows to describe the resemblance of arbitrary subsets of worlds to those belonging to the evidencial set. On the other hand, the question addressed by theory change formalisms is which kind...

Using genetic feature selection for optimizing user profiles.

Henrik Legind Larsen, Nicolás Marín, María José Martín-Bautista, M. Amparo Vila (2000)

Mathware and Soft Computing

Most of the techniques used in text classification are determined by the occurrences of the words (terms) appearing in the documents, combined with the user feedback over the documents retrieved. However, in our model, the most relevant terms will be selected from a previous fuzzy classification given by the genetic algorithm guided by the user feedback, but using techniques from Machine Learning. A feature selection process is carried out through a Genetic Algorithm in order to find the most discriminatory...

Using symbolic computation in the characterization of frictional instabilities involving orthotropic materials

Mohamed A. Agwa, António Pinto da Costa (2015)

International Journal of Applied Mathematics and Computer Science

The present work addresses the problem of determining under what conditions the impending slip state or the steady sliding of a linear elastic orthotropic layer or half space with respect to a rigid flat obstacle is dynamically unstable. In other words, we search the conditions for the occurrence of smooth exponentially growing dynamic solutions with perturbed initial conditions arbitrarily close to the steady sliding state, taking the system away from the equilibrium state or the steady sliding...

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