One critical aspect of an information system is indexing, that is, the representation of concepts to get a well formed data structure for search. Until recently, this task was accomplished by creating a bibliographic citation that references the original text. This approach allows a reduction in time and space bounds, although it does not facilitate the user from finding relevant information. I...

We generalize the notion of a jet scheme (truncated arc space) to arbitrary fat points via adjunction, and show that this yields for each fat point, an endomorphism on each schemic Grothendieck ring as defined in [17]. We prove that some of the analogues for linear jets still hold true, like locally trivial fibration over the smooth locus. In this formalism, we can define several generating zet...

The e ciency and accuracy of several time integration schemes are investigated for the unsteady Navier-Stokes equations. This study focuses on the e ciency of higher-order Runge-Kutta schemes in comparison with the popular Backward Di erencing Formulations. For this comparison an unsteady two-dimensional laminar ow problem is chosen, i.e. ow around a circular cylinder at Re=1200. It is conclude...

The discretization of the dynamic Signorini problem with finite elements in space and a time-stepping scheme is not straightforward. Consequently a large variety of methods for this problem have been designed over the last two decades. Up to date, no systematic comparison of such methods has been performed. The aim of the present work is to classify and compare them. For each method, we discuss...

Yee’s scheme for the solution of the Maxwell equations [1] and the MAC algorithm for the solution of the Navier–Stokes equations [2] are examples of co-volume solution techniques. Co-volume methods, which are staggered in both time and space, exhibit a high degree of computationally efficiency, in terms of both CPU and memory requirements compared to, for example, a finite element time domain m...

Symplectic integration methods based on operator splitting are well established in many branches of science. For Hamiltonian systems which split in more than two parts, symplectic methods of higher order have been studied in detail only for a few special cases. In this work, we present and compare different ways to construct high order symplectic schemes for general Hamiltonian systems that can...

By integrating design schemes, we conciliate several designs of the same real world done concurrently. These designs provide structural and semantic knowledge. To take into account the semantic of knowledge throughout the integration process, we have elaborate a fuzzy thesaurus, which allows to collect the semantic of the design-scheme knowledge, in order to nd the words wich are semantically c...

In this paper we introduce two novel numerical integration schemes, within the framework of the heterogeneous multiscale method (HMM) when finite element method is used as the macroscopic solver, to resolve the elliptic problem with multiscale coefficient. For non-self-adjoint elliptic problems, optimal convergence rate is proved for the proposed methods, which naturally yields a new strategy f...

In the context of multiscale computations, techniques have recently been developed that enable microscopic simulators to perform macroscopic level tasks (equation-free multiscale computation). The main tool is the so-called coarse-grained time-stepper, which implements an approximation of the unavailable macroscopic time-stepper using only the microscopic simulator. Several schemes were develop...

In this paper we introduce two novel numerical integration schemes, within the framework of the heterogeneous multiscale method (HMM) when finite element method is used as the macroscopic solver, to resolve the elliptic problem with multiscale coefficient. For non-self-adjoint elliptic problems, optimal convergence rate is proved for the proposed methods, which naturally yields a new strategy f...