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Méthodes d'assemblage rapide et de résolution itérative pour un solveur adaptatif en équations intégrales de frontières destiné à l'électromagnétisme

Abstract : In this work we have opened up new and innovative possibilities for BIEM as applied to the resolution of three-dimensional problems in low frequency electromagnetism. These possibilities enable an adaptive meshing to be established, associated with local, approaching resolutions of the integral system. In the first chapter, we will briefly discuss digital methods applied to electromagnetism. The second chapter is devoted to BIEM, where our special choices are justified (the type and order of elements rendering the boundaries discreet), with a description of the algorithms used, e.g. for taking account of symmetries or periodicities of the system studied. In the third chapter, our calculation methods for elementary integrals, combining the analytical and the digital, are described and validated. In chapter four, we present an error estimator, based on the deviation between the interpolated potential value and its value as calculated by the integral method itself: To conclude we use this error estimator in chapter five to automatically produce a meshing suited to each problem to be solved, authorizing also a “non-conform” meshing. A local resolution method offers a significant gain in time during this phase of adaptive meshing. The final meshing is separated into fields, thereby improving the final result by iteration between these fields, and without requiring global resolution, which is extremely costly for large size problems.
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  • HAL Id : tel-00139486, version 1

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Bidjan Haghi-Ashtiani. Méthodes d'assemblage rapide et de résolution itérative pour un solveur adaptatif en équations intégrales de frontières destiné à l'électromagnétisme. Autre. Ecole Centrale de Lyon, 1998. Français. ⟨tel-00139486⟩

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