This special issue collects a total of seven papers selected from the best presentations at the Japan–France Conference on Analytical and Numerical Methods for Scientific Computing in Science and Engineering held at the Université Henri-Poincaré, from 21 to 24 February 2006, and at the International Conference on Distributed Computing and Applications for Business, Engineering and Sciences held at the University of Greenwich, from 25 to 27 August 2005. These papers were selected after careful consideration of the research and the contents of the presentations at these conferences. The review process has followed closely the usual practice of International Journal of Computer Mathematics. The guest editors would like to thank the authors and the reviewers for their input to this special issue.
The present issue opens with a paper by X. Antoine and Y. Boubendir. This paper discusses an original contribution to the convergence improvement of iterative solvers like the GMRES applied to the integral equations modelling two-dimensional scattering problems by penetrable bodies. The aim of the paper is to produce an explicit analytical integral operator which preconditions the system of coupled integral equations for the transmission problem. Based on the Caldèron projectors, the contribution can be considered as a non-trivial extension to penetrable scatterers of recent works by Christiansen and Nédélec on Caldèron preconditioners. Both theoretical developments and numerical experiments show that the new preconditioner is robust in most of the realistic situations.
In their article, P. Fulmanski, A. Laurain, J.-F. Scheid and J. Sokołowski present the numerical solution of shape optimization problems. The topological derivatives are combined with shape derivatives in a numerical method of shape and topology optimization. Evolution of geometrical domains is modelled by a non-linear hyperbolic Hamilton–Jacobi equation. The proposed method turns out to be very efficient and better provides the numerical results compared with the pure level set method. The complete theoretical and numerical results are presented for a simple model problem in the case of the energy functional for the scalar elliptic equation.
The paper of H. Ishiyama and M. Kawahara presents a numerical determination of the optimal shape of body located in the incompressible viscous flow. The optimal shape is defined by the shape which has the minimum fluid force acting on the body. The shape optimization problem is based on an optimal control theory and the performance function is minimized without constraint condition by the Lagrange multiplier method. The approximate solution to the flow problem is obtained by the finite element method based on the mixed interpolation with bubble function.
The paper authored by N. Alaa, A. Cheggour, M. Iguernane, J.R. Roche and A. Tounssi describes a numerical method to solve a system of one-dimensional non-linear differential equations. This system models a nickel-iron electrodeposition process. A domain decomposition numerical algorithm is introduced to take account of anisotropic behaviour of the solution. The existence and uniqueness of the solution on each subdomain and the convergence of the domain decomposition method are shown. Simulations with experimental data shows that the proposed model can predict characteristic features of the nickel–iron system.
The paper by G. Lube, T. Knopp, R. Gritzki, M. Rösler and J. Seifert presents domain decomposition methods to the simulation of indoor air flow. Its accurate prediction for building configurations requires both a well-resolved flow simulation inside the building and taking into account the effect of the ambient. A modified wall-function method (as an overlapping domain decomposition method) avoids a near-wall grid refinement. A non-overlapping iteration-by-subdomains method allows the parallel solution of linearized auxiliary problems. For getting more realistic boundary conditions at openings, the computational domain is extended by a suitable ambient surrounding. Inflow and outflow are then handled by the iteration-of-subdomains method. Finally, realistic predictions require an active coupling between the interior of the building and its surroundings. A hybrid domain decomposition method couples the flow solver with thermal building simulation.
In the paper by F. Lai, F. Magoulès and F. Lherminier, several methods to detect abnormal energy consumption in residential buildings are reviewed. The traditional approach considers the degree-days calculation method for conductive heat losses, along with actual building use cases, effective sun and wind exposure, internal comfort and control constraints. This design stage methodology proves mostly insufficient for operational energy consumption analysis, due to the complexity of obtaining a set of valid physical model parameters in order to perform acceptable simulations. This paper investigates an original approach based on Vapnik's learning theory applied to empirical energy consumption data. The authors first obtain robust energy consumption predictive models, then use the same tool to survey model coefficient evolutions under operational conditions, and detect changes in the physical system with no preliminary knowledge.
The paper by V. Savchenko, M. Savchenko, O. Egorova and I. Hagiwara describes a new approach based on a space mapping technique for improving the quality of triangular, tetrahedral, and hexahedral meshes. This technique provides also: improving the smoothness of a mesh and reducing the difference between adjacent elements after a few iterations without distorting the initial surface. The technique makes it possible to reduce maximum flatness deviations for hexahedral meshes. The proposed technique can be used as a software component in mesh optimization tools, for instance, to modify some parts of the meshes with a highly non-uniform structure without having to re-mesh a complete model and any precalculations. The approach is very simple, scalable with respect to the number of elements and can be easily parallelized.