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In this work, we present theoretical and numerical optimization method for designing magnetic circuits for Hall effect thrusters. These design problems are very difficult inverse ones that we formulate under the form of topology optimization problems. Then, the obtained problems are non convex subject to Maxwell equations like constraints. Some original approaches have been proposed to solve efficiently these topology optimization problems. These approaches are based on the material density model called SIMP approach (Solid Isotropic Material with Penalization) which is a variante of the homogenization method. The results in my thesis allowed to provide optimization source code named ATOP (Algorithm To Optimize Propulsion) unsung in parallel two scientific computing softwares namely Matlab and FEMM (Finite Element Method Magnetics). In ATOP, we use both local optimization algorithms based on sensitivity analysis of the design problem; and global optimization algorithms mainly of type Branch and Bound based on Interval Arithmetic analysis. ATOP will help to optimize both the topological shape of the magnetic circuits and the time and cost of production (design process) of new generations of electrical thrusters.; Dans ces travaux, nous présentons des méthodes d'optimisation théoriques et numériques pour la conception optimale de circuits magnétiques pour propulseurs à effet Hall. Ces problèmes de conception sont des problèmes inverses très difficiles à résoudre que nous formulons sous forme de problèmes d'optimisation topologique. Les problèmes resultant sont non convexes avec des contraintes aux équations différentielles de Maxwell. Au cours de ces travaux, des approches originales ont été proposées afin de résoudre efficacement ces problèmes d'optimisation topologique. L'approche de densité de matériaux SIMP (Solid Isotropic Material with Penalization) qui est une variante de la méthode d'homogénéisation a été privilégiées. De plus, les travaux de ma thèse ont permis la mise en place de codes d'optimisation dénommé ATOP (Algorithm To Optimize Propulsion) utilisant en parallèle les logiciels de calculs scientifiques Matlab et d'élément finis FEMM (Finite Element Method Magnetics). Dans ATOP, nous utilisant à la fois des algorithmes d'optimisation locale de type descente basés sur une analyse de la sensibilité du problème et des algorithmes d'optimisation globale principalement de type Branch and Bound basés sur l'Arithmétique des Intervals. ATOP permettra d'optimiser à la fois la forme topologique des circuits magnétiques mais aussi le temps et le coût de production de nouvelles génération de propulseurs électriques.

International audience

In this work, we deal with topology optimization for designing electromagnetic devices circuits. The considered problems are inverse ones. One of the difficulties of such problem is the derivative informations because in general the cost function is an implicit function (in our case, it provides from the computation of a PDE which is a Maxwell equation). The design sensitivity is calculated from the Lagrangian formulation of the objective function with the adjoint variable method and it allows us to use first order optimization algorithms and also to solve numerically large scale problem in a relatively short CPU-time. Our method is based on the SIMP method (Solid Isotropic Material with Penalization) which is a variant of the homogenization method. For the numerical simulations, we have built our own solver which includes the finite element software FEMM (Finite Element Method Magnetics) and the Matlab optimization fmincon routine. The talk will be ended by the presentation of our topology optimization solver and the numerical results of some problems for designing Plasma Hall effect Thrusters.

In this work, we deal with topology optimization for designing electromagnetic devices circuits. The considered problems are inverse ones. One of the difficulties of such problem is the derivative informations because in general the cost function is an implicit function (in our case, it provides from the computation of a PDE which is a Maxwell equation). The design sensitivity is calculated from the Lagrangian formulation of the objective function with the adjoint variable method and it allows us to use first order optimization algorithms and also to solve numerically large scale problem in a relatively short CPU-time. Our method is based on the SIMP method (Solid Isotropic Material with Penalization) which is a variant of the homogenization method. For the numerical simulations, we have built our own solver which includes the finite element software FEMM (Finite Element Method Magnetics) and the Matlab optimization fmincon routine. The talk will be ended by the presentation of our topology optimization solver and the numerical results of some problems for designing Plasma Hall effect Thrusters

In this work, we deal with Topology Optimization to solve Inverse Problems of Electric and Electromagnetic Circuits. This poster will address plasma hall effect thruster. On this poster, we shall show the main used materials and imposed caracteristics for designing an electrical thruster. We will give some mathematical formulations to solve optimization problem about optimal electric circuit of Hall effect thrusters