Related papers: DefElement: an encyclopedia of finite element defi…

In this paper, we show how to use a Relational Database Management System in support of Finite Element Analysis. We believe it is a new way of thinking about data management in well-understood applications to prepare them for two major…

Numerical methods: mimetic finite differences and finite elements, are analyzed from a numerical point of view. It seeks to conclude on the efficiency, order of convergence and computational cost of these methods. The analysis is done in…

Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reasons for this undeniable success is the great versatility of…

Differential-elimination algorithms apply a finite number of differentiations and eliminations to systems of partial differential equations. For systems that are polynomially nonlinear with rational number coefficients, they guarantee the…

A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…

Fundamental differences between materials originate from the unique nature of their constituent chemical elements. Before specific differences emerge according to the precise ratios of elements in a given crystal structure, a material can…

Deformable elastic bodies in viscous and viscoelastic media constitute a large portion of synthetic and biological complex fluids. We present a parallelized 3D-simulation methodology which fully resolves the momentum balance in the solid…

Intuitively, the concept of similarity is the notion to measure an inexact matching between two entities of the same reference set. The notions of similarity and its close relative dissimilarity are widely used in many fields of Artificial…

In the context of supervised parametric models, we introduce the concept of e-values. An e-value is a scalar quantity that represents the proximity of the sampling distribution of parameter estimates in a model trained on a subset of…

Preserving access to file content requires preserving not just bits but also meaningful logical structures. The ongoing development of the Data Format Description Language (DFDL) is a completely general standard that addresses this need.…

This is a report on our long term project to find an algorithm to decide if a finitely presented group has a non-trivial action on a tree.

When are two algorithms the same? How can we be sure a recently proposed algorithm is novel, and not a minor twist on an existing method? In this paper, we present a framework for reasoning about equivalence between a broad class of…

Explanation facilities are a particularly important feature of expert system frameworks. It is an area in which traditional rule-based expert system frameworks have had mixed results. While explanations about control are well handled,…

Event-B is a formal approach oriented to system modeling and analysis. It supports refinement mechanism that enables stepwise modeling and verification of a system. By using refinement, the complexity of verification can be spread and…

Identifying anomalies has become one of the primary strategies towards security and protection procedures in computer networks. In this context, machine learning-based methods emerge as an elegant solution to identify such scenarios and…

This paper proposes a method for deriving formal specifications of systems. To accomplish this task we pass through a non trivial number of steps, concepts and tools where the first one, the most important, is the concept of method itself,…

Text classification is the process of classifying documents into predefined categories based on their content. Existing supervised learning algorithms to automatically classify text need sufficient documents to learn accurately. This paper…

We show that every finite semilattice can be represented as an atomized semilattice, an algebraic structure with additional elements (atoms) that extend the semilattice's partial order. Each atom maps to one subdirectly irreducible…

The complexity of a system description is a function of the entropy of its symbolic description. Prior to computing the entropy of the system description, an observation scale has to be assumed. In natural language texts, typical scales are…

Code generation based software platforms, such as Firedrake, have become popular tools for developing complicated finite element discretisations of partial differential equations. We extended the code generation infrastructure in Firedrake…