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This paper discusses the robustness of the algebraic multigrid (AMG) method as well as geometric multigrid (GMG) method against mesh distortion in edge‐based finite element analysis.

Analyzes a simple magnetostatic problem, in which the model consists of a cubic iron and the surrounding air region. Prepares three meshes which have same number of elements to evaluate the robustness of multigrid against the distortion of mesh.

The AMG method is shown to be more robust against mesh distortion than the GMG method.

Shows that the AMG is more robust than the GMG. This result is of practical interest to the researchers in this field.

Numerical simulation of the single point incremental forming (SPIF) processes can be very demanding and time consuming due to the constantly changing contact conditions between the tool and the sheet surface, as well as the nonlinear material behaviour combined with non-monotonic strain paths. The purpose of this paper is to propose an adaptive remeshing technique implemented in the in-house implicit finite element code LAGAMINE, to reduce the simulation time. This remeshing technique automatically refines only a portion of the sheet mesh in vicinity of the tool, therefore following the tool motion. As a result, refined meshes are avoided and consequently the total CPU time can be drastically reduced.

SPIF is a dieless manufacturing process in which a sheet is deformed by using a tool with a spherical tip. This dieless feature makes the process appropriate for rapid-prototyping and allows for an innovative possibility to reduce overall costs for small batches, since the process can be performed in a rapid and economic way without expensive tooling. As a consequence, research interest related to SPIF process has been growing over the last years.

In this work, the proposed automatic refinement technique is applied within a reduced enhanced solid-shell framework to further improve numerical efficiency. In this sense, the use of a hexahedral finite element allows the possibility to use general 3D constitutive laws. Additionally, a direct consideration of thickness variations, double-sided contact conditions and evaluation of all components of the stress field are available with solid-shell and not with shell elements. Additionally, validations by means of benchmarks are carried out, with comparisons against experimental results.

It is worth noting that no previous work has been carried out using remeshing strategies combined with hexahedral elements in order to improve the computational efficiency resorting to an implicit scheme, which makes this work innovative. Finally, it has been shown that it is possible to perform accurate and efficient finite element simulations of SPIF process, resorting to implicit analysis and continuum elements. This is definitively a step-forward on the state-of-art in this field.

The purpose of this paper is to provide the methodology for structural design of complex massive structures under impact by a large airplane.

Using case studies, the issues related to multi‐scale modelling of inelastic damage mechanisms for massive structures are discussed, as well as the issues pertaining to the time integration schemes in presence of different scales in time variation of different sub‐problems, brought by a particular nature of loading with a very short duration) and finally the issues related to model reduction seeking to provide an efficient and yet sufficiently reliable basis for parametric studies which are an indispensable part of a design procedure.

Several numerical simulations are presented in order to further illustrate the approaches proposed herein. Concluding remarks are stated regarding the current and future research in this domain.

Proposed design procedure for complex massive engineering structures under impact by a large airplane provides on one side a very reliable representation of inelastic damage mechanisms and external loading represented by the solution of the corresponding contact/impact problem, and on the other side a very efficient basis obtained by model reduction for performing the parametric design studies.

A two‐grid iterative method for 3D linear elasticity problems, discretized using quadratic tetrahedral elements is proposed. The conjugate‐gradient method is used as smoother. As compared to the conjugate‐gradient alone, it is shown, via numerical examples, that the method is much more efficient on the basis of computing time and memory allocation. The convergence property of the method is sensitive to the regularity of the problem.

This paper aims to explore the limitations of the conformal finite difference time-domain method (C-FDTD or Dey–Mittra) when modeling perfect electric conducting (PEC) and lossless dielectric curved surfaces in coarse meshes. The C-FDTD is a widely known approach to reduce error of curved surfaces in the FDTD method. However, its performance limitations are not broadly described in the literature, which are explored as a novelty in this paper.

This paper explores the C-FDTD method applied on field scattering simulations of two curved surfaces, a dielectric and a PEC sphere, through the frequency range from 0.8 to 10 GHz. For each sphere, the mesh was progressively impoverished to evaluate the accuracy drop and performance limitations of the C-FDTD with the mesh impoverishment, along with the wideband frequency range described.

This paper shows and quantifies the C-FDTD method’s accuracy drops as the mesh is impoverished, reducing C-FDTD’s performance. It is also shown how the performance drops differently according to the frequency of interest.

With this study, coarse meshes, with smaller execution time and reduced memory usage, can be further explored reliably accounting the desired accuracy, enabling a better trade-off between accuracy and computational effort.

This paper quantifies the limitations of the C-FDTD in coarse meshes in a wideband manner, which brings a broader and newer insight upon C-FDTD’s limitations in coarse meshes or relatively small objects in electromagnetic simulation.

This paper presents some linear adaptive non‐nested multigrid methods which are applied to linear elastic problems discretized with triangular and tetrahedral finite elements using unstructured and Delaunay mesh generators. The Zienkiewicz‐Zhu error estimator and a h‐refinement procedure are used to obtain the non‐nested meshes used by the multigrid methods. We solve problems with a specified percentage error in the energy norm using the optimal performance of multigrid methods.

The viscous finite volume lambda formulation is presented. The suggested technique is apt to compute viscous flows with heat fluxes. The inviscid terms are evaluated by means of the non‐conservative, very accurate upwind methodology, known as the finite volume lambda formulation. The diffusive terms, on the contrary, are approximated by a central scheme. Both methods are characterized by a nominal second order accuracy in space. Efficiency is enhanced by means of a multigrid technique which directly combines each grid level with each stage of an explicit multistage time integration technique. A laminar viscous flow about a NACA 0012 airfoil and a turbulent one about a RAE 2822 airfoil have been computed as well as the two‐ and three‐dimensional turbulent flows inside the Stanitz elbow. The computed numerical results are in very good agreement with well assessed published numerical or experimental results. The suggested multigrid technique allows significant work reductions for laminar as well as for turbulent flow computations.

The purpose of this paper is to introduce a new method to model a stranded wire efficiently in 3D finite element simulations.

In this method, the stranded wires are numerically approximated with the Cauer ladder network (CLN) model order reduction method in 2D. This approximates the eddy current effect such as the skin and proximity effect for the whole wire. This is then projected to a mesh which does not include each strand. The 3D fields are efficiently calculated with the CLN method and are projected in the 3D geometry to be used in simulations of electrical components with a current vector potential and a homogenized conductivity at each time step.

In applications where the stranded wire geometry is known and does not change, this homogenization approach is an efficient and accurate method, which can be used with any stranded wire configuration, homogenized stranded wire mesh and any input signal dependent on time steps or frequencies.

In comparison to other methods, this method has no direct frequency dependency, which makes the method usable in the time domain for an arbitrary input signal. The CLN can also be used to interconnected stranded cables arbitrarily in electrical components.

When simulating fluid-structure interaction (FSI), it is often essential that the no-slip condition is accurately enforced at the wetted boundary of the structure. This paper aims to evaluate the relative strengths and limitations of the penalty and Lagrange multiplier methods, within the context of modelling FSI, through a comparative analysis.

In the immersed boundary method, the no-slip condition is typically imposed by augmenting the governing equations of the fluid with an artificial body force. The relative accuracy and computational time of the penalty and Lagrange multiplier formulations of this body force are evaluated by using each to solve three test problems, namely, flow through a channel, the harmonic motion of a cylinder through a stationary fluid and the vortex-induced vibration (VIV) of a cylinder.

The Lagrange multiplier formulation provided an accurate solution, especially when enforcing the no-slip condition, and was robust as it did not require “tuning” of problem specific parameters. However, these benefits came at a higher computational cost relative to the penalty formulation. The penalty formulation achieved similar levels of accuracy to the Lagrange multiplier formulation, but only if the appropriate penalty factor was selected, which was difficult to determine a priori.

Both the Lagrange multiplier and penalty formulations of the immersed boundary method are prominent in the literature. A systematic quantitative comparison of these two methods is presented within the same computational environment. A novel application of the Lagrange multiplier method to the modelling of VIV is also provided.

A family of preconditioned dual‐primal FETI iterative algorithms for the solution of algebraic systems arising from edge element approximations in two dimensions is presented.

The primal constraints, which determine the size of the coarse problem to be solved at each iteration step, are here suitable averages over subdomain edges. The condition number of the corresponding methods is independent of the number of subdomains and possibly large jumps of the coefficients.

For h finite elements, it grows only polylogarithmically with the number of unknowns associated with individual substructures, while for hp approximations on geometrically refined meshes, it is independent of arbitrarily large aspect ratios.

Proposes an algorithm with a rate of convergence that is independent of possibly large jumps of the coefficients and mesh aspect ratios.