14:10
Session 8B: Mathematical Techniques
Chair: Jens Haueisen
14:10
20 mins
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ON THE EXTENDED FINITE ELEMENT METHOD USE IN OPTIMISATION OF ELECTRICAL DEVICES
Alexandru Avram, Vasile Topa, Marius Purcar, Calin Munteanu
Abstract: This paper describes an innovative numerical algorithm specially developed for optimization of the electrical devices. The proposed numerical algorithm consists in coupling the eXtended Finite Element Method (XFEM) and a stochastic algorithm type in order to handle moving material interfaces in electrical applications. On the one hand, the algorithm proposed benefits from the mesh free approach using XFEM to prevent from mesh distortion situations. On the other hand, the optimization loop based on a stochastic algorithm type is used for generate optimum solutions. The innovation of proposed algorithm consists in applying a mix integration technique in the XFEM numerical scheme in order to reduce computational time. The main value of the proposed approach is a fast, powerful and robust optimization algorithm used in handling topological changes with a high degree of automation in comparison with other methods.
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14:30
20 mins
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Moving Mesh Method for the Finite Element Discretized Westervelt Equation
Bas Dirkse, Domenico Lahaye, Martin Verweij, Chris Budd
Abstract: Purpose - In nonlinear acoustics the propagation of an ultrasound pressure pulse is modeled with the Westervelt equation. In this paper we investigate the use of Finite Element methods for the numerical solution of the Westervelt equation, because these methods can employ nonuniform meshes and can solve the equation on complicated domains. In particular we investigate the possibility of using nonuniform moving grids.
Design/methodology/approach - We have formulated a numerically advantageous finite element semi-discrete system for the one-dimensional Westervelt equation and developed a method for a nonuniform moving mesh technique that follows the propagating ultrasound pulse. Then we developed a time solving algorithm based on a backward differential scheme that can handle time-dependent meshes.
Findings - Our research shows that our moving mesh technique, which follows the propagating acoustic pulse, will improve the accuracy of the solution significantly compared to a uniform mesh with the same number of elements. We show that we can achieve the same accuracy with our moving mesh method as for a uniform mesh with much more elements, in our numerical examples a factor 3.5. This depends however on the geometry and the pulse parameters.
Originality/value - The Westervelt equation is not commonly solved using Finite Element methods and we have developed a numerically efficient semi-discrete Finite Element formulation of the problem. The main value of this paper is combining this formulation with a nonuniform moving mesh method to improve accuracy and efficiency.
Keywords - Westervelt equation, Finite Element method, Moving Mesh.
Paper type - Research paper.
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14:50
20 mins
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MONO AND BI LEVEL OPTIMIZATION ARCHITECTURE COMPARISON FOR ELECTRIC VEHICLE POWERTRAIN DESIGN
Pierre Caillard, Frédéric Gillon, Michel Hecquet, Sid-Ali Randi, Noelle Janiaud
Abstract: In this paper, an optimization process is used to design an electric vehicle powertrain, including driving cycle and performance constraints. The integration of the machine control is detailed through two optimization architectures: a mono-level formulation where the control variables are added to the design variables and a bi-level method where the control is determined with a nested optimization loop for each operating points. The choice between structures is discussed and the computational time is analyzed in relation with specifications.
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