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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 finite element meshing and remeshing from the theoretical as well as practical points of view. Topics such as adaptive techniques for meshing and remeshing, parallel processing in the finite element modelling, etc. are also included. The bibliography at the end of this paper contains 1,727 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1990 and 2001.

The purpose of this paper is to propose a new elemental enrichment technique to improve the accuracy of the simulations of thermal problems containing weak discontinuities.

The enrichment is introduced in the elements cut by the materials interface by means of adding additional shape functions. The weak form of the problem is obtained using Galerkin approach and subsequently integrating the diffusion term by parts. To enforce the continuity of the fluxes in the “cut” elements, a contour integral must be added. These contour integrals named here the “inter-elemental heat fluxes” are usually neglected in the existing enrichment approaches. The proposed approach takes these fluxes into account.

It has been shown that the inter-elemental heat fluxes cannot be generally neglected and must be included. The corresponding method can be easily implemented in any existing finite element method (FEM) code, as the new degrees of freedom corresponding to the enrichment are local to the elements. This allows for their static condensation, thus not affecting the size and structure of the global system of governing equations. The resulting elements have exactly the same number of unknowns as the non-enriched finite element (FE).

It is the first work where the necessity of including inter-elemental heat fluxes has been demonstrated. Moreover, numerical tests solved have proven the importance of these findings. It has been shown that the proposed enrichment leads to an improved accuracy in comparison with the former approaches where inter-elemental heat fluxes were neglected.

The penalty boundary method (PBM) is a new method for performing finite element analysis using a regular overlapping mesh that does not have to coincide with the geometric boundaries. The PBM uses CAD solid geometry directly to generate element matrix equations and apply boundary conditions, removing the need for a separate representation of the geometry. The preliminary results show that the PBM can significantly reduce the time and manual intervention required to prepare finite element models and perform analyses. This paper presents the PBM approach for representing the problem domain on an overlapping mesh that results in a more traditional method for applying natural boundary conditions.

The purpose of this paper is to assess the effect of the statical admissibility of the recovered solution and the ability of the recovered solution to represent the singular solution; also the accuracy, local and global effectivity of recovery‐based error estimators for enriched finite element methods (e.g. the extended finite element method, XFEM).

The authors study the performance of two recovery techniques. The first is a recently developed superconvergent patch recovery procedure with equilibration and enrichment (SPR‐CX). The second is known as the extended moving least squares recovery (XMLS), which enriches the recovered solutions but does not enforce equilibrium constraints. Both are extended recovery techniques as the polynomial basis used in the recovery process is enriched with singular terms for a better description of the singular nature of the solution.

Numerical results comparing the convergence and the effectivity index of both techniques with those obtained without the enrichment enhancement clearly show the need for the use of extended recovery techniques in Zienkiewicz‐Zhu type error estimators for this class of problems. The results also reveal significant improvements in the effectivities yielded by statically admissible recovered solutions.

The paper shows that both extended recovery procedures and statical admissibility are key to an accurate assessment of the quality of enriched finite element approximations.

In this work an adaptive scheme to solve diffusion problems, using linear and quadratic triangles, is presented. The densification algorithm, based on the subdivision of the selected elements, and the error estimator used are described first. We pay special attention to the behaviour of the estimator. It has two contributions: the residual term and the flux‐jump term. Babuska and co‐workers have shown that for bilinear quadrilterals, the first term is negligible, but for biquadratic, it is the dominant term. We show evidence suggesting that these results cannot be extended to triangular elements when the problem has a singular solution. We found, in this case, that if the flux‐jump term is neglected, the expected rate of convergence cannot be obtained. Finally, some remarks about the whole adaptive process are discussed.

The purpose of this paper is as follows: to significantly reduce the computation time (by a factor of 1,000 and more) compared to known numerical techniques for real-world problems with complex interfaces; and to simplify the solution by using trivial unfitted Cartesian meshes (no need in complicated mesh generators for complex geometry).

This study extends the recently developed optimal local truncation error method (OLTEM) for the Poisson equation with constant coefficients to a much more general case of discontinuous coefficients that can be applied to domains with different material properties (e.g. different inclusions, multi-material structural components, etc.). This study develops OLTEM using compact 9-point and 25-point stencils that are similar to those for linear and quadratic finite elements. In contrast to finite elements and other known numerical techniques for interface problems with conformed and unfitted meshes, OLTEM with 9-point and 25-point stencils and unfitted Cartesian meshes provides the 3-rd and 11-th order of accuracy for irregular interfaces, respectively; i.e. a huge increase in accuracy by eight orders for the new 'quadratic' elements compared to known techniques at similar computational costs. There are no unknowns on interfaces between different materials; the structure of the global discrete system is the same for homogeneous and heterogeneous materials (the difference in the values of the stencil coefficients). The calculation of the unknown stencil coefficients is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of OLTEM at a given stencil width. The numerical results with irregular interfaces show that at the same number of degrees of freedom, OLTEM with the 9-points stencils is even more accurate than the 4-th order finite elements; OLTEM with the 25-points stencils is much more accurate than the 7-th order finite elements with much wider stencils and conformed meshes.

The significant increase in accuracy for OLTEM by one order for 'linear' elements and by 8 orders for 'quadratic' elements compared to that for known techniques. This will lead to a huge reduction in the computation time for the problems with complex irregular interfaces. The use of trivial unfitted Cartesian meshes significantly simplifies the solution and reduces the time for the data preparation (no need in complicated mesh generators for complex geometry).

It has been never seen in the literature such a huge increase in accuracy for the proposed technique compared to existing methods. Due to a high accuracy, the proposed technique will allow the direct solution of multiscale problems without the scale separation.

This paper aims to determine the optimum set of temperatures through correlation study to attain the most effective capillary flow of underfill in a multi-stack ball grid array (BGA) chip device.

Finite volume method is implemented in the simulation. A three-layer multi-stack BGA is modeled to simulate the underfill flow. The simulated models were well validated with the previous experimental work on underfill process.

The completion filling time shows high regression R-squared value of up to 0.9918, which indicates a substantial acceleration on the underfill process because of incorporation of thermal delta. An introduction of 11 °C thermal delta to the multi-stacks BGA managed to reduce the filling time by up to 16.4%.

Temperature-induced capillary flow is a relatively new type of driven underfill designed specifically for package on package BGA components. Its simple implementation can further improve the productivity of existing underfill process in the industry that is desirable in reducing the process lead time.

The effect of temperature-induced capillary flow in underfill encapsulation on multi-stacks BGA by means of statistical correlation study is a relatively new topic, which has never been reported in any other research according to the authors’ knowledge.

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.

In this paper, the polygonal-FEM technique is presented in modeling large deformation – large sliding contact on non-conformal meshes. The purpose of this paper is to present a new technique in modeling arbitrary interfaces and discontinuities for non-linear contact problems by capturing discontinuous deformations in elements cut by the contact surface in uniform non-conformal meshes.

The geometry of contact surface is used to produce various polygonal elements at the intersection of the interface with the regular FE mesh, in which the extra degrees-of-freedom are defined along the interface. The contact constraints are imposed between polygonal elements produced along the contact surface through the node-to-surface contact algorithm.

Numerical convergence analysis is carried out to study the convergence rate for various polygonal interpolation functions, including the Wachspress interpolation functions, the metric shape functions, the natural neighbor-based shape functions, and the mean value shape functions. Finally, numerical examples are solved to demonstrate the efficiency of proposed technique in modeling contact problems in large deformations.

A new technique is presented based on the polygonal-FEM technique in modeling arbitrary interfaces and discontinuities for non-linear contact problems by capturing discontinuous deformations in elements cut by the contact surface in uniform non-conformal meshes.