This work is concerned with the flow of a viscousplastic fluid. We choose a model of Bingham typetaking into account inhomogeneous yield limit of thefluid, which is well-adapted in the description oflandslides. After setting the generalthreedimensional problem, the blocking property isintroduced. We then focus on necessary andsufficient conditions such that blocking of the fluidoccurs.The anti-plane flow intwodimensional andonedimensional cases is considered.A variational formulation in terms of stresses isdeduced. More fine properties dealing with localstagnant regions as well as local regions where thefluid behaves like a rigid body are obtained indimension one.

We present here a discretization of a nonlinear obliquederivative boundary value problem for the heat equation in dimensiontwo. This finite difference scheme takes advantages of thestructure of the boundary condition, which can be reinterpreted as aBurgers equation in the space variables. This enables to obtain anenergy estimate and to prove the convergence of the scheme. We also provide some numerical simulations of thisproblem and a numerical study of the stability of the scheme, whichappears to be in good agreement with the theory.

Dorsey, Di Bartolo and Dolgert (Di Bartolo et al., 1996; 1997) have constructed asymptotic matched solutions at order two for the half-space Ginzburg-Landau model, in the weak-κ limit. These authors deduceda formal expansion for the superheating field in powers of $\kappa^{\frac{1}{2}}$ up to order four, extending the formula by De Gennes (De Gennes, 1966) and the two terms in Parr's formula (Parr, 1976). In this paper, we construct asymptotic matched solutions at all orders leading to a complete expansion in powers of $\kappa^{\frac{1}{2}}$ for the superheating field.

The Boltzmann–Poisson system modeling the electron flow in semiconductorsis used to discuss the validity of the Child–Langmuir asymptotics.The scattering kernel is approximated by a simple relaxation time operator.The Child–Langmuir limit gives an approximation of the current-voltagecharacteristic curves by means of a scalingprocedure in which the ballistic velocity is much larger that the thermal one. We discuss the validity of the Child–Langmuir regime by performing detailed numerical comparisons between the simulation of theBoltzmann–Poisson system and the Child–Langmuir equations in testproblems.

Along with the classical requirements on B-splines bases(minimal support, positivity, normalization)we show that it is natural to introduce an additional“end point property". When dealing with multiple knots,this additional property is exactly the appropriate requirementto obtain the poles of nondegenerate splinesas intersections of osculating flats at consecutive knots.

This paper is concerned with the computation of 3D vertex singularities of anisotropic elastic fields with Dirichlet boundary conditions, focusing on the derivation of error estimates for a finite element method on graded meshes. The singularities are described by eigenpairs of a corresponding operator pencil on spherical polygonal domains. The main idea is to introduce a modified quadratic variational boundary eigenvalue problem which consists of two self-adjoint, positive definite sesquilinear forms and a skew-Hermitean form. This eigenvalue problem is discretized by a finite element method on graded meshes. Based on regularity results for the eigensolutions estimates for the finite element error are derived both for the eigenvalues and the eigensolutions. Finally, some numerical results are presented.

Programming is an area at the interface between scientific computing and applied mathematics which hasbeen very active lately and so it was thought that M2AN should open its pages to it in a special issue.This is because many new tools have appeared ranging from templates in C++ to Java interface library andparallel computing tools. There has been a diffusion of computer sciences into numerical analysis and thesenew tools have made possible the implementation of very complex methods such as finite element methods ofarbitrary degree.This issue is not an overview of the field. The papers have been selected on the basis of their programmingcreativity, the quality of the final product and their relevance to numerical methods. But we have discovered onthe way that the programming community does not publish much outside conference proceedings. Furthermoreit is often difficult to pinpoint the difficulties and solutions. One must avoid tedious lists of function or subroutinedefinitions, but one must also explain in details the new programming ideas such as data driven programsor generic programming, notions which are familiar to few people only.What is new here is that the papers have been screened by reviewers who are themselves programmers andalso applied mathematicians. This successful experience leads to encourage submission of more papers of thiskind in the future as well.

This article presents the guiding principles of the architecture of Trio_U, a new generation of software for thermohydraulic calculations. Trio_U is designed to serve as a thermohydraulic development platform. Its basic conception is object-oriented and it is written in C++. The article demonstrates how this type of design enables an open, modular software architecture.

The C++// language (pronounced C++parallel) was designed and implemented with the aim of importingreusability into parallel and concurrentprogramming, in the framework of a mimd model.From a reduced set of rather simple primitives,comprehensive and versatile libraries are defined.In the absence of any syntactical extension,the C++// user writes standard C++ code.The libraries are themselvesextensible by the final users, making C++// an open system. Two specific techniques to improve performances ofa distributed object language such as C++// arethen presented: Shared-on-Read and Overlapping of Communicationand Computation.The appliance of those techniques is guided by the programmer ata very high-level of abstraction, so the additional work to yieldthose good performance improvements is kept to the minimum.

In this paper we test the feasibility of coupling two heterogeneous mathematical modeling integrated within two different codes residing on distant sites. A prototype is developed using Schwarz type domain decomposition as the mathematical tool for coupling. The computing technology for coupling uses a CORBA environment to implement a distributed client-server programming model. Domain decomposition methods are well suited to reducing complex physical phenomena into a sequence of parallel subproblems in time and space. The whole process is easily tuned to underlying hardware requirements.

This contribution gives an overview of current research in applying object oriented programming to scientific computing at the computational mechanics laboratory (LABMEC) at the school of civil engineering – UNICAMP. The main goal of applying object oriented programming to scientific computing is to implement increasingly complex algorithms in a structured manner and to hide the complexity behind a simple user interface. The following areas are current topics of research and documented within the paper: hp-adaptive finite elements in one-, two- and three dimensions with the development of automatic refinement strategies, multigrid methods applied to adaptively refined finite element solution spaces and parallel computing.

The aim of this paper is to present how to make a dedicaded computed language polymorphic and multi type, in C++ to solve partial differential equations with the finite element method.The driving idea is to make the language as close as possible to the mathematical notation.

We describe both the classical Lagrangian and the Eulerian methods for first order Hamilton–Jacobi equations of geometric optic type. We then explain the basic structure of the softwareand how new solvers/models can be added to it. A selection of numerical examples are presented.

During the development of a parallel solver for Maxwell equations by integral formulations and Fast Multipole Method (FMM), we needed to optimize a critical part including a lot of communications and computations. Generally, many parallel programs need to communicate, but choosing explicitly the way and the instant may decrease the efficiency of the overall program. So, the overlapping of computations and communications may be a way to reduce this drawback. We will see a implementation of this techniques using dynamic and adaptive overlapping based on the EasyMSG high level C++ library over MPI, a case of SPMD programming.

Object oriented design has proven itself as a powerful tool in the field of scientific computing. Several software packages, libraries and toolkits exist, in particular in the FEM arenathat follow this design methodology providing extensible, reusable,and flexible software while staying competitive to traditionallydesigned point tools in terms of efficiency. However, the common approach to identify classes is to turn data structures and algorithms of traditional implementations into classes such that the level of abstraction is essentially not raised. In this paper we discuss an alternative way to approach the design challenge which we call “concept oriented design”. We apply this design methodology to Petrov-Galerkin methods leading to a class library for both, boundary element methods (BEM) and finite element methods (FEM). We show as a particular example the implementation of hp-FEM using the library with specialattention to the handling of inconsistent meshes.

Development of user-friendly and flexible scientific programs is a key to their usage, extension and maintenance. This paper presents an OOP (Object-Oriented Programming) approach for design of finite element analysis programs. General organization of the developed software system, called FER/SubDomain, is given which includes the solver and the pre/post processors with a friendly GUI (Graphical User Interfaces). A case study with graphical representations illustrates some functionalities of the program.

Automatic differentiation (AD) has proven its interest in many fields ofapplied mathematics, but it is still not widely used. Furthermore, existingnumerical methods have been developed under the hypotheses that computingprogram derivatives is not affordable for real size problems. Exact derivativeshave therefore been avoided, or replaced by approximations computed by divideddifferences. The hypotheses is no longer true due to the maturity of AD addedto the quick evolution of machine capacity. This encourages the development ofnew numerical methods that freely make use of program derivatives, and willrequire the definition and development of new AD strategies. AD tools mustbe extended to produce these new derivative programs, in such a modular waythat the different sub-problems can be solved independently from one another.Flexibility assures the user to be able to generate whatever specificderivative program he needs, with at the same time the possibility to generatestandard ones. This paper sketches a new model of modular, extensible andflexible AD tool that will increase tenfold the DA potential for appliedmathematics. In this model, the AD tool consists of an AD kernel namedKAD supported by a general program transformation platform.

We present in this article two components: these components can in fact serve various goalsindependently, though we consider them here as an ensemble. The first component is a technique forthe rapid and reliable evaluation prediction of linear functional outputs of elliptic (andparabolic) partial differential equations with affine parameter dependence. The essential features are (i) (provably) rapidly convergent globalreduced–basis approximations — Galerkin projection onto a spaceW N spanned by solutions of the governing partial differentialequation at N selected points in parameter space; (ii) a posteriori error estimation — relaxations of the error–residualequation that provide inexpensive yet sharp and rigorous bounds forthe error in the outputs of interest; and (iii) off–line/on–linecomputational procedures — methods which decouple the generationand projection stages of the approximation process. This component is ideally suited — consideringthe operation count of the online stage — for the repeated and rapid evaluation required in thecontext of parameter estimation, design, optimization, andreal–time control. The second component is a framework for distributed simulations. This frameworkcomprises a library providing the necessary abstractions/concepts for distributed simulations and asmall set of tools — namely SimTeXand SimLaB— allowing an easy manipulation of thosesimulations. While the library is the backbone of the framework and is therefore general, thevarious interfaces answer specific needs. We shall describe both components and present how theyinteract.

A finite element code, called ZéBuLoN was parallelised some years ago. This code is entirely written using an object oriented framework (C++ is the support language). The aim of this paper is to present some problems which arose during the parallelization, and some innovative solutions. Especially, a new concept of message passing is presented which allows to take into account SMP machines while still using the parallel virtual machine abstraction.