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In FEM computations, the mesh quality improves the accuracy of the approximation solution and reduces the computation time. The dynamic bubble system meshing technique can provide high-quality meshes, but the packing process is time-consuming. This paper aims to improve the running time of the bubble meshing by using the advantages of parallel computing on graphics processing unit (GPU).

This paper is based on the analysis of the processing time on CPU. A massively parallel computing-based CUDA architecture is proposed to improve the bubble displacement and database updating. Constraints linked to hardware considerations are taken into account. Finally, speedup factors are provided on test cases and real scale examples.

The numerical experiences show the efficiency of parallel performance reaches a speedup of 35 compared to the serial implementation.

This contribution is so far limited to two-dimensional (2D) geometries although the extension to three-dimension (3D) is straightforward regarding the meshing technique itself and the GPU implementation. The authors’ works are based on a CUDA environment which is widely used by developers. C\C++ and Java were the programming languages used. Other languages may of course lead to slightly different implementations.

This approach makes it possible to use bubble meshing technique for both initial design and optimization, as excellent meshes can be built in few seconds.

Compared to previous works, this contribution shows that the scalability of the bubble meshing technique needs to solve two key issues: reach a T(N) global cost of the implementation and reach a very fast size map interpolation strategy.

This paper deals with the three‐dimensional modeling of massive conductors carrying a total imposed current and involving multiply connected regions. Both stationary motion and time harmonic eddy current problems are considered. The aim of the modeling is to determine the current distribution and the eddy current’s effects inside the conductor, as well as to calculate the Lorentz force acting on a conducting region. The choice of a suitable formulation based on solving the current vector potential T and the magnetic scalar potential φ is argued, then various methods for the restoration of the Ampere law in the multiply connected regions are presented. Two methods for calculating an auxiliary vector potential T₀ are applied in order to calculate the force acting on the armature of a railgun and the repulsion between the electrodes of a vacuum circuit breaker, then the results are compared.

The trajectory of François Perroux across the Vichy regime poses about all possible range of methodological issues to the historian of ideas: individual versus collective biography, ideational versus ideological reading, internal versus external analysis, etc. The chapter outlines key elements about Perroux’s trajectory showing the entanglements and boundaries of science and politics in the transition from democratic to authoritarian rule and vice versa. A particular emphasis on uncertainties and adjustments shows, against the tendency to a teleological explanation induced by a linear interpretation of his career, that different paths were considered by Perroux, but that his choices were nevertheless constrained by the forces of both the scientific and political fields.

This chapter aims to address the question of the evolution of economists’s reception of Marxism in France, and thus to complete the more general history of the development of Marxism among French academics. To do so, we follow the relationship to Marx’s work of the economist François Perroux, a priori typical of the reversal reception of Marxist ideas in the 1950s, moving from open hostility to enthusiasm. Indeed, an incisive critic of Marx’s writings before the war, then head of the scientific institution of the Vichy regime, Perroux became in the postwar period a leading figure in the diffusion of Marx’s ideas in France. He founded the ISMEA (Institute of Mathematical and Applied Economic Sciences) which published the journal Études de marxologie, and eventually penned the preface to Marx’s economic works in 1963 for the Pléiade. By following this sinuous path, we show that the way Perroux related to Marx’s work helps us shed light on the various shifts in Perroux’s relationship to the science and politics of his time.

This paper compares three different radial basis function neural networks, as well as the diffuse element method, according to their ability of approximation. This is very useful for the optimization of electromagnetic devices. Tests are done on several analytical functions and on the TEAM workshop problem 25.