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Abstract :
[en] Repetitive finite element (FE) computations are needed when studying variations of geometrical and physical characteristics, which is the case for, e.g., parameterized analyses, optimisation, movement modelling, multi-physical coupling and model refinement. It is worth then benefiting from previous computations instead of starting a new complete solution for any new variation.
A subproblem approach with perturbations of solutions is developed to efficiently tackle such repetitive computations. It consists in iteratively solving successive subproblems, the addition of their solutions giving the solution of a complete problem. At the discrete level, each subproblem is defined in its own domain and mesh, which decreases the problem complexity and allows distinct mesh refinements. A special attention is given to the proper discretization of the source constraints of each subproblem. This approach allows a natural progression from simple to elaborate models: from 1D to 3D geometries, from statics to dynamics, from low to high frequencies, from perfect to real materials, from linear to nonlinear materials, from initially simple models with magnetic or electric equivalent circuits to detailed geometrical models with the FE method, etc. Each model refinement can be quantified to justify its utility.
A general frame is developed for electrostatic, electrokinetic, magnetostatic and magnetodynamic FE formulations, with their possible couplings. The perturbation method offers a way to follow the solution and its complexity through graphical representations and animations, which facilitates the understanding of the developed numerical tools as well as various physical behaviors. Numerous applications benefit from this sub-problem approach and will be presented. They concern magnetic circuits, skin and proximity effects, moving systems, eddy current non-destructive testing, magnetic screening, grounding systems, etc.
