2017/11/15 by Hervé Moulinec, Moulinec, Hervé, Pierre Suquet +3 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1711.05880
openalex publication_date 2017/11/15 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Iterative Fast Fourier Transform methods are useful for calculating the\nfields in composite materials and their macroscopic response. By iterating back\nand forth until convergence, the differential constraints are satisfied in\nFourier space, and the constitutive law in real space. The methods correspond\nto series expansions of appropriate operators and to series expansions for the\neffective tensor as a function of the component moduli. It is shown that the\nsingularity structure of this function can shed much light on the convergence\nproperties of the iterative Fast Fourier Transform methods. We look at a model\nexample of a square array of conducting square inclusions for which there is an\nexact formula for the effective conductivity (Obnosov). Theoretically some of\nthe methods converge when the inclusions have zero or even negative\nconductivity. However, the numerics do not always confirm this extended range\nof convergence and show that accuracy is lost after relatively few iterations.\nThere is little point in iterating beyond this. Accuracy improves when the grid\nsize is reduced, showing that the discrepancy is linked to the discretization.\nFinally, it is shown that none of the three iterative schemes investigated\nover-performs the others for all possible microstructures and all contrasts.\n