Programming is an area at the interface between scientific computing and applied mathematics which has been 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 and parallel computing tools. There has been a diffusion of computer sciences into numerical analysis and these new tools have made possible the implementation of very complex methods such as finite element methods of arbitrary degree. This issue is not an overview of the field. The papers have been selected on the basis of their programming creativity, the quality of the final product and their relevance to numerical methods. But we have discovered on the way that the programming community does not publish much outside conference proceedings. Furthermore it is often difficult to pinpoint the difficulties and solutions. One must avoid tedious lists of function or subroutine definitions, but one must also explain in details the new programming ideas such as data driven programs or 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 and also applied mathematicians. This successful experience leads to encourage submission of more papers of this kind in the future as well.

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

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 of applied mathematics, but it is still not widely used. Furthermore, existing numerical methods have been developed under the hypotheses that computing program derivatives is not affordable for real size problems. Exact derivatives have therefore been avoided, or replaced by approximations computed by divided differences. The hypotheses is no longer true due to the maturity of AD added to the quick evolution of machine capacity. This encourages the development of new numerical methods that freely make use of program derivatives, and will require the definition and development of new AD strategies. AD tools must be extended to produce these new derivative programs, in such a modular way that the different sub-problems can be solved independently from one another. Flexibility assures the user to be able to generate whatever specific derivative program he needs, with at the same time the possibility to generate standard ones. This paper sketches a new model of modular, extensible and flexible AD tool that will increase tenfold the DA potential for applied mathematics. In this model, the AD tool consists of an AD kernel named KAD supported by a general program transformation platform.

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.

The C++// language (pronounced C++parallel) was designed and implemented with the aim of importing reusability into parallel and concurrent programming, 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 themselves extensible by the final users, making C++// an open system. Two specific techniques to improve performances of a distributed object language such as C++// are then presented: Shared-on-Read and Overlapping of Communication and Computation. The appliance of those techniques is guided by the programmer at a very high-level of abstraction, so the additional work to yield those good performance improvements is kept to the minimum.

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.

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 software and how new solvers/models can be added to it. A selection of numerical examples are presented.

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.

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.

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 arena that follow this design methodology providing extensible, reusable, and flexible software while staying competitive to traditionally designed 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 special attention to the handling of inconsistent meshes.

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.