Hervé Moulinec | Searcharxiv

arXiv2024

The Laboratory of Mechanics and Acoustics in Marseilles (France): from the first world war to the present day

The Laboratory of Mechanics and Acoustics in Marseilles (France) was created in 1941, under the name of Centre de Recherches Scientifiques, Industrielles et Maritimes (CRSIM). But it was actually issued from the French Naval Research Center created in Toulon by the French Navy to work on submarine detection during World War I. LMA is therefore the result of a long and quite amazing story with several moves and even more name changes. It benefited from all these events and is today established in a new campus with large facilities specially designed for its latest research activities. This article presents the story in some details, summarize the evolution of the research domains through all these years and finally gives a description of the LMA today.

physics.hist-ph↗

arXiv2018

Convergence of iterative methods based on Neumann series for composite materials: theory and practice

Iterative Fast Fourier Transform methods are useful for calculating the fields in composite materials and their macroscopic response. By iterating back and forth until convergence, the differential constraints are satisfied in Fourier space, and the constitutive law in real space. The methods correspond to series expansions of appropriate operators and to series expansions for the effective tensor as a function of the component moduli. It is shown that the singularity structure of this function can shed much light on the convergence properties of the iterative Fast Fourier Transform methods. We look at a model example of a square array of conducting square inclusions for which there is an exact formula for the effective conductivity (Obnosov). Theoretically some of the methods converge when the inclusions have zero or even negative conductivity. However, the numerics do not always confirm this extended range of convergence and show that accuracy is lost after relatively few iterations. There is little point in iterating beyond this. Accuracy improves when the grid size is reduced, showing that the discrepancy is linked to the discretization. Finally, it is shown that none of the three iterative schemes investigated over-performs the others for all possible microstructures and all contrasts.

math.NA↗