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The purpose of this paper is to improve the multistep algorithm using evolutionary algorithm (EA) for the topology optimization of magnetostatic shielding, and the paper reveals the effectiveness of methodology by comparison with conventional optimization method. Furthermore, the design target is to obtain the novel shape of magnetostatic shielding.

The EAs based on random search allow engineers to define general-purpose objects with various constraint conditions; however, many iterations are required in the FEA for the evaluation of the objective function, and it is difficult to realize a practical solution without island and void distribution. Then, the authors proposed the multistep algorithm with design space restriction, and improved the multistep algorithm in order to get better solution than the previous one.

The variant model of optimized topology derived from improved multistep algorithm is defined to clarify the effectiveness of the optimized topology. The upper curvature of the inner shielding contributed to the reduction of magnetic flux density in the target domain.

Because the converged topology has many pixel element unevenness, the special smoother to remove the unevenness will play an important role for the realization of practical magnetostatic shielding.

The optimized topology will give us useful detailed structure of magnetostatic shielding.

First, while the conventional algorithm could not find the reasonable shape, the improved multistep optimization can capture the reasonable shape. Second, An additional search is attached to the multistep optimization procedure. It is shown that the performance of improved multistep algorithm is better than that of conventional algorithm.

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.

The use of the prominent finite difference time‐domain (FDTD) method for the time‐domain solution of electromagnetic wave propagation past devices with small geometrical details can require very fine grids and can lead to unmanageable computational time and storage. The purpose of this paper is to extend the analysis of a discontinuous Galerkin time‐domain (DGTD) method (able to handle possibly non‐conforming locally refined grids, based on portions of Cartesian grids) and investigate the use of perfectly matched layer regions and the coupling with a fictitious domain approach. The use of a DGTD method with a locally refined, non‐conforming mesh can help focusing on these small details. In this paper, the adaptation to the DGTD method of the fictitious domain approach initially developed for the FDTD is considered, in order to avoid the use of a volume mesh fitting the geometry near the details.

Based on a DGTD method, a fictitious domain approach is developed to deal with complex and small geometrical details.

The fictitious domain approach is a very interesting complement to the FDTD method, since it makes it possible to handle complex geometries. However, the fictitious domain approach requires small volume elements, thus making the use of the FDTD on wide, regular, fine grids often unmanageable. The DGTD method has the ability to handle easily locally refined grids and the paper shows it can be coupled to a fictitious domain approach.

Although the stability and dispersion analysis of the DGTD method is complete, the theoretical analysis of the fictitious domain approach in the DGTD context is not. It is a subject of further investigation (which could provide important insights for potential improvements).

This is believed to be the first time a DGTD method is coupled with a fictitious domain approach.

The purpose of this paper is to develop a numerical approach inspired by Geometrical Product Specifications (GPS) standards for the assessment of geometrical defects appearing during Additive Manufacturing (AM) by Laser Beam Melting (LBM).

The study is based on finite element (FE) simulations of thermal distortions, then an assessment of flatness defects (warping induced by the high-residual stresses appearing during the manufacturing) from the deformed surfaces provided by simulation, and finally the correction of the calculated flatness defects from preliminary comparison between simulated and experimental data.

For an elementary geometrical feature (a wall), it was possible to identify the variation in the flatness defect as a function of the dimensions. For a complex geometry exhibiting a significant flatness defect, it was possible to improve the geometric quality using the numerical tool.

To the best of the author’s knowledge, this work is the first attempt using a numerical approach inspired by GPS standards to identify variations in thermal distortions caused by LBM, which is an initial step toward optimization. This paper is mainly focused on flatness defect assessment, even though the approach is potentially applicable for all types of geometrical defects (shape, orientation or position defects).

The study opens prospects for the optimization of complex parts elaborated using LBM, based on the minimization of the geometric defects caused by thermal distortions.

The prospects in terms of shape optimization will extend the potential to benefit from the new possibilities offered by LBM additive manufacturing.

Unlike the usual approach, the proposed methodology does not require any artifacts or comparisons with the computer-aided-design (CAD) model for geometrical distortion assessment. The present approach opens up the possibility of performing metrology from FE simulation results, which is particularly promising in the AM field.

The use of the prominent FDTD method for the time domain solution of electromagnetic wave propagation past devices with small geometrical details can require very fine grids and can lead to very important computational time and storage. The purpose is to develop a numerical method able to handle possibly non‐conforming locally refined grids, based on portions of Cartesian grids in order to use existing pre‐ and post‐processing tools.

A Discontinuous Galerkin method is built based on bricks and its stability, accuracy and efficiency are proved.

It is found to be possible to conserve exactly the electromagnetic energy and weakly preserves the divergence of the fields (on conforming grids). For non‐conforming grids, the local sets of basis functions are enriched at subgrid interfaces in order to get rid of possible spurious wave reflections.

Although the dispersion analysis is incomplete, the numerical results are really encouraging it is shown the proposed numerical method makes it possible to handle devices with extremely small details. Further investigations are possible with different, higher‐order discontinuous finite elements.

This paper can be of great value for people wanting to migrate from FDTD methods to more up to date time‐domain methods, while conserving existing pre‐ and post‐processing tools.

To compare slip surface and moving band techniques for modelling movement in 3D with FEM.

The slip surface and moving band techniques are used to model the rotation of electrical machines in 3D with FEM. The proposed techniques are applied to a permanent magnet synchronous machine. The comparison is carried out at no‐load for the electromotive force (EMF) and the cogging torque. The torque is also compared for the short circuit case.

For both the locked‐step and moving band approaches there is no difficulty in establishing the scalar potential and potential vector formulations. However, if step displacement is not equal to the mesh step, the results can show numerical irregularities. Some improvements have been proposed in order to limit this problem.

The results of the EMF and the cogging torque are improved.

This study aims to develop an efficient algorithm for generation of conforming mesh for seepage analysis through 3D discrete fracture networks (DFN).

The algorithm is developed based on a refined conforming Delaunay triangulation scheme, which is then validated using analytical solutions. The algorithm is well able to meet the challenge of meshing complex geometry of DFNs.

A series of sensitivity analysis have been performed to evaluate the effect of meshing parameters on steady state solution of Darcy flow using a finite element scheme. The results show that an optimized minimum internal angle of meshing elements should be predetermined to guarantee termination of the algorithm.

The developed algorithm is computationally efficient, fast and is of low cost. Furthermore, it never changes the geometrical structure and connectivity pattern of the DFN.

The purpose of this paper is to demonstrate successful use of least-squares finite element method (LSFEM) with h-type mesh refinement and coarsening for the solution of two-dimensional, inviscid, compressible flows.

Unsteady Euler equations are discretized on meshes of linear and quadratic triangular and quadrilateral elements using LSFEM. Backward Euler scheme is used for time discretization. For the refinement of linear triangular elements, a modified version of the simple bisection algorithm is used. Mesh coarsening is performed with the edge collapsing technique. Pressure gradient-based error estimation is used for refinement and coarsening decision. The developed solver is tested with flow over a circular bump, flow over a ramp and flow through a scramjet inlet problems.

Pressure difference based error estimator, modified simple bisection method for mesh refinement and edge collapsing method for mesh coarsening are shown to work properly with the LSFEM formulation. With the proper use of mesh adaptation, time and effort necessary to prepare a good initial mesh reduces and mesh independency control of the final solution is automatically taken care of.

LSFEM is used for the first time for the solution of inviscid compressible flows with h-type mesh refinement and coarsening on triangular elements. It is shown that, when coupled with mesh adaptation, inherent viscous dissipation of LSFEM technique is no longer an issue for accurate shock capturing without unphysical oscillations.

The purpose of this paper is to analyse the influence of penalty parameters for an interior penalty Galerkin method, namely, the symmetric interior penalty Galerkin method.

First of all, the solution of a simple model problem is computed and compared to the exact solution, which is a periodic function. Afterwards, a two-dimensional magnetostatic field problem described by the magnetic vector potential A is considered. In particular, penalty parameters depending on the polynomial degree, the properties of the elements and the material are considered. The analysis is performed by varying the polynomial degree and the mesh sizes on a structured and an unstructured mesh. Additionally, the penalty parameter is varied in a specific range.

Choosing the penalty parameter correctly plays an important role as the stability and the convergence of the numerical scheme can be affected. For a structured mesh, a limiting value for the penalty parameter can be calculated beforehand, whereas for an unstructured mesh, the choice of the penalty parameter can be cumbersome.

This paper shows that there exist different penalty parameters which can be taken into account to solve the considered problems. One can choose a global penalty parameter to obtain a stable solution, which is a sharp estimation. There has always to be the consideration to guarantee the coercivity of the bilinear form while minimising the number of iterations.

This paper aims to describe the application of the virtual element method (VEM) to contact problems between elastic bodies.

Polygonal elements with arbitrary shape allow a stable node-to-node contact enforcement. By adaptively adjusting the polygonal mesh, this methodology is extended to problems undergoing large frictional sliding.

The virtual element is well suited for large deformation contact problems. The issue of element stability for this specific application is discussed, and the capability of the method is demonstrated by means of numerical examples.

This work is completely new as this is the first time, as per the authors’ knowledge, the VEM is applied to large deformation contact.