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This article presents a bridge between topology optimization (TO) and additive manufacturing. On the one hand, it presents an algorithm that considers the design variables as binary and then solves the problem by binary linear programming to optimize a ferromagnetic core. On the other hand, a 3-D printing process is developed to manufacture the shapes obtained by TO. Finally, these magnetic parts are characterized through electrical measurements.

Optimization using finite element analysis and the adjoint variable method to solve engineering problems appears in various application areas. However, to the best of the authors’ knowledge, there is a lack of detailed explanation on the implementation of the adjoint variable method in the context of electromagnetic modeling. This paper aimed to provide a detailed explanation of the method in the simplest possible general framework. Then, an extended explanation is offered in the context of electromagnetism. A discrete design methodology based on adjoint variables for magnetostatics was formulated, implemented, and verified. This comprehensive methodology supports both linear and nonlinear problems. The framework provides a general approach for performing a very efficient and discretely consistent sensitivity analysis for problems involving geometric and physical variables or any combination of the two. The accuracy of the implementation is demonstrated by independent verification based on an analytical test case and using the finite-difference method. The methodology was used to optimize the parameters of a superconducting energy storage device and a magnet press and the optimization of the topology of an electromagnet. The objective function of each problem was successfully decreased, and all constraints stipulated were met.

Metamodels proved to be a very efficient strategy for optimizing expensive black-box models, e.g., Finite Element simulation for electromagnetic devices. It enables the reduction of the computational burden for optimization purposes. However, the conventional approach of using metamodels presents limitations such as the cost of metamodel fitting and infill criteria problem-solving. This paper proposes a new algorithm that combines metamodels with a branch and bound (B&B) strategy. However, the efficiency of the B&B algorithm relies on the estimation of the bounds; therefore, we investigated the prediction error given by metamodels to predict the bounds. This combination leads to high fidelity global solutions. We propose a comparison protocol to assess the approach’s performances with respect to those of other algorithms of different categories. Then, two electromagnetic optimization benchmarks are treated. This paper gives practical insights into algorithms that can be used when optimizing electromagnetic devices.

An improved starting point Newton method applied to 3-D scalar formulation in magnetostatics is proposed in this paper. Compared with the classical Newton method, the inexact-Newton and quasi-Newton methods are reported by testing on a benchmark problem as well as an industrial example. Remarkable convergence acceleration using the proposed strategy is observed, and thus, it significantly reduces the computational time.

This paper aims to propose an Improved Starting Point (ISP-) Newton method applied to vector potential A formulation for circuit coupled magnetostatic problems. These problems are usually known to vary greatly during the time. This impacts the quality of the initial guess of the Newton method and thus increases significantly the computational cost. The Newton method with vector potential formulation A has been analyzed. Numerical examples show the performance of our proposed ISP-Newton method.

The motivation of this communication is to test a method for computing the gradient of a quantity of interest for an electromagnetic device modeled by finite elements method (FEM). The gradient is a key ingredient in many important tasks: sensitivity analysis, robust design, design optimization and reliability analysis. It can be computed efficiently using the adjoint method, its advantage is not only reducing the computational cost of computing the gradient compared to different methods (e.g. finite difference) but also handling the numerical noise that could appear when re-meshing in the case of finite elements analysis.

The parallelization of numerical simulation algorithms, i.e., their adaptation to parallel processing architectures, is an aim to reach in order to hinder exorbitant execution times. The parallelism has been imposed at the level of processor architectures and graphics cards are now used for general-purpose calculation, also known as “General-Purpose computation on Graphics Processing Unit (GPGPU)”. The clear benefit is the excellent performance over price ratio. Besides hiding the low level programming, software engineering leads to a faster and more secure application development. This paper presents the real interest of using GPU processors to increase performance of larger problems which concern electrical machines simulation. Indeed, we show that our auto-generated code applied to several models allows achieving speedups of the order of 10x.

The modeling and simulation of electrical systems use a very large computational algorithms to solve their problems. The Conjugate Gradient (CG) solver is an effective technique for symmetric positive definite systems. It is suitable for systems of the form Ax=b, where A is a known, square, symmetric, positive-definite sparse matrix, x is a unknown solution vector and b is a known vector. A and b are obtained from the discretization of the Finite-Element Method (FEM).