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The uniformity of electrodeposition is the key to successful application of pattern plating because the quality of electrodeposited copper layer has a huge impact on the performance of printed circuit boards (PCBs). The multi-physics coupling technology was used to accurately analyze and forecast the characteristics of electrochemical system. Further, an optimized plating bath was used to achieve a uniform electrodeposition.

A multi-physics coupling numerical simulation based on the finite element method was used to optimize electrodeposition conditions in pattern plating process. The influences of geometric and electrochemical factors on uniformity of current distribution and electrodeposited layer thickness were discussed by multi-physics coupling.

The model results showed that the distance between cathode and anode and the insulating shield had a great impact on uniformity of electrodeposition. By numerical simulation, it had been proved that using an auxiliary cathode was an effective and simple way to improve uniformity of electrodeposition due to redistributing of the current. This helped to achieve more uniform surface of the copper patterns by preventing the edge effect and the roughness of the copper layer was reduced to 1 per cent in the secondary current distribution model.

The research is still in progress with the development of high-performance computers.

A multi-physics coupling platform is an excellent tool for quickly and cheaply studying the process behaviors under a variety of operating conditions.

The numerical simulation method has laid the foundation for the design and improvement of the plating bath.

By multi-physics coupling technology, we built a bridge between theoretical and experimental study for control of uniformity of pattern plating in PCB manufacturing. This method can help optimize the design of plating bath and uniformity of pattern plating in PCB manufacturing.

Reflow soldering is one of the most significant factors in determining solder joint defect rate. This study aims to introduce an innovative approach for optimizing the multiple performances of the reflow soldering process.

This study aims to minimize the solder joint defect rate of a ball grid array (BGA) package by using the grey‐based Taguchi method. The entropy measurement method was employed together with the grey‐based Taguchi method to compute for the weights of each quality characteristic. The Taguchi L18 orthogonal array was performed, and the optimal parameter settings were determined. Various factors, such as slope, temperature, and reflow profile time, as well as two extreme noise factors, were considered. The thermal stress, peak temperature, reflow time, board‐ and package‐level temperature uniformity were selected as the quality characteristics. These quality characteristics were determined using the numerical method. The numerical method comprises the internal computational flow that models the reflow oven coupled with the structural heating and cooling models of the BGA assembly. The Multi‐physics Code Coupling Interface was used as the coupling software.

The analysis of variance results reveals that the cooling slope was the most influential factor among the multiple quality characteristics, followed by the soaking temperature and the peak temperature. Experimental confirmation test results show that the performance characteristics improved significantly during the reflow soldering process.

The proposed approach greatly reduces solder joint defects and enhances solutions to lead‐free reliability issues in the electronics manufacturing industry.

The findings provide new guidelines to the optimization method which are very useful for the accurate control of the solder joint defect rate within components and printed circuit board (PCB) which is one of the major requirements to achieve high reliability of electronic assemblies.

To present numerical approaches to the solution of physically coupled non‐linear problems, which frequently happen to be characterized by their multi‐domain character.

By adopting coupled solution strategies a considerable attention is devoted, in order to obtain a computationally efficient numerical algorithm, to the selection of appropriate space and time discretization, as well as to a proper discrete approximation method used.

Coupling of two methods, the finite element method and the boundary element method, respectively, has proved to be computationally exceedingly advantageous, particularly in case of moving domains.

As specific case studies computer simulation of an induction heating problem and a mushy‐state forming problem are considered. A thorough discussion on the coupling effects, characterizing the evolutions of respective physical quantities' fields, is given, and their impact on those evolutions is identified.

This paper presents efficient numerical strategies for the solution of a certain class of multi‐physics and multi‐domain problems.

High pressure and high speed of the axial piston pump can improve its power density, but they also deteriorate the thermal-fluid-structure coupling effect of the friction pairs. This paper aims to reveal the coupling mechanism of the pump, for example, valve plate pair, by carrying out research on multi-physics field coupling.

Considering the influences of temperature on material properties and thermal fluid on structure, the thermal-fluid elastic mechanics model is established. A complete set of fast and effective thermal-fluid-structure coupling method is presented, by which the numerical analysis is conducted for the valve plate pair.

According to calculations, it is revealed that the temperature and pressure evolution laws of oil film with time, the pressure distribution law of the fluid, stress and displacement distribution laws of the solid in the valve plate pair. In addition, the forming history of the wedge-shaped oil film and mating clearance change law with rotational speed and outlet pressure in the valve plate pair are presented.

For an axial piston pump operating under high speed, high pressure and wide temperature range, the multi-physics field coupling analysis is an indispensable means and method. This paper provides theoretical evidence for the development of the pump and lays a solid foundation for the research of the same kind of problem.

Multiphysics problems are solved either with monolithic or segregated approaches. For accomplishing contrary discretisation requirements of the physics, disparate meshes are essential. This paper is comparing experimental results of different interpolation methods for a segregated coupling with monolithic approaches, implemented using a global and a local nearest neighbour method. The results show the significant influence of discretisation for multiphysics simulation.

Applying disparate meshes to the monolithic as well as the segregated calculation of finite element problems and evaluating the related numerical error is content of the contribution. This is done by an experimental evaluation of a source and a material coupling applied to a multiphysics problem. After an introduction to the topic, the evaluated multiphysics model is described based on two bidirectional coupled problems and its finite element representation. Afterwards, the considered methods for approximating the coupling are introduced. Then, the evaluated methods are described and the experimental results are discussed. A summary concludes this work.

An experimental evaluation of the numerical errors for different multiphysics coupling methods using disparate meshes is presented based on a bidirectional electro-thermal simulation. Different methods approximating the coupling values are introduced and challenges of applying these methods are given. It is also shown, that the approximation of the coupling integrals is expensive. Arguments for applying the different methods to the monolithic and the segregated solution strategies are given and applied on the example. The significant influence of the mesh density within the coupled meshes is shown. Since the projection and the interpolation methods do influence the result, a careful decision is advised.

In this contribution, existing coupling methods are described, applied and compared on their application for coupling disparate meshes within a multiphysics simulation. Knowing their performance is relevant when deciding for a monolithic or a segregated calculation approach with respect to physics dependent contrary discretisation requirements. To the authors’ knowledge, it is the first time these methods are compared with a focus on an application in multiphysics simulations and experimental results are discussed.

The purpose of this paper is to address the formulation, implementation, and adaptation of closely coupled multi‐physics problems with h‐ and p‐adaptive finite element methods. A general formulation is chosen allowing for coupled problems of various types. Adaptation algorithms for h‐ and p‐refinement are given.

A generic system of second‐order differential equations is used, where the field of each individual problem is represented as an entry in the list of field variables. Specific problems are implemented by mapping material coefficients to the coefficients of the generic form. An example with four natures is investigated with close coupling between electric, mechanical and thermal fields. h‐ and p‐refinement using a single mesh is considered, where the element order may differ for individual fields.

In coupled problems, the error in each single field is affected by approximation properties of all other field quantities. In order to allow for optimal convergence order in the number of degrees of freedom, the error contributions of all fields have to be considered. Separate error estimation in each field is needed especially in h‐adaptation on a single mesh. Energy coupling coefficients were introduced to derive an adaptation criterion. Convergence analysis of h‐ and p‐adaptation proves the feasibility of the approach.

Piezopyroelectricity considers thermal effects in high‐frequency piezoelectric materials, which is a coupled problem of four natures. The paper introduces an adaptation criterion for such complicated coupled problems and proves feasibility.

The purpose of this paper is to develop thermal modelling to investigate the thermal response of sample boards (at board level) during the preheating stage of the reflow process and to validate with experimental measurements.

A thermal‐coupling method that adopted the Multi‐physics Code Coupling Interface (MpCCI) was utilized. A forced‐convection reflow oven was modelled using computational fluid dynamic software (FLUENT 6.3.26), whereas structural heating at the board level was conducted using finite‐element method software (ABAQUS 6.9).

The simulation showed a complex flow pattern having characteristics of a free‐jet region, stagnation‐flow region, wall jet‐region, recirculation region and vortices. A sharp maximum heat‐transfer coefficient was detected in the stagnation region of the jet, resulting in a spatial variation of local heat transfer on a thermal profile board (TPB). This coefficient affected the temperature distribution in the TPB with different specific heat capacitances and thermal conductivity of the structure. The simulation results were in good agreement with the experimental data and analytical model. The cold region and temperature uniformity (ΔT) increased with increasing complexity of the TPB. The cold region can occur in two possible locations in the TPB. Both occurrences can be related to the flow field of the reflow oven. ΔT of the TPB decreased when the conveyor speed (v) was reduced. A suitable conveyor speed (1.0 cm/s) was determined to maintain ΔT below 10°C, which prevented the thermally critical package from overheating.

The paper provies a methodology for designing a thermal profile for reflow soldering production.

The findings provide fundamental guidelines to the thermal‐coupling method at the board and package levels, very useful for accurate control of ΔT at the board and package levels, one of the major requirements in achieving a high degree of reliability for electronic assemblies.

Optimized plating conditions, included proper designs of insulating shield (IS), auxiliary cathode (AC) and different patterns, contribute to the uniformity enhancement of copper deposition.

Plating experiments were implemented in vertical continuous plating (VCP) line for manufacturing in different conditions. Multiphysics coupling simulation was brought to investigate and predict the plating uniformity improvement of copper pattern. In addition, the numerical model was based on VCP to approach the practical application.

With disproportionate current distribution, different plating pattern design formed diverse copper thickness distribution (CTD). IS and AC improved plating uniformity of copper pattern because of current redistribution. Moreover, optimized plating condition for effectively depositing more uniformed plating copper layer in varied pattern designs were derived by simulation and verified by plating experiment.

The comparison between experiment and simulation revealed that multiphysics coupling is an efficient, reliable and of course environment-friendly tool to perform research on the uniformity of pattern plating in manufacturing.

The purpose of this paper is to present a reduced order computational strategy for a multi-physics simulation involving a fluid flow, electromagnetism and heat transfer in a hot-wall chemical vapour deposition reactor. The main goal is to produce a multi-parametric solution for fast exploration of the design space to perform numerical prototyping and process optimisation.

Different reduced order techniques are applied. In particular, proper generalized decomposition is used to solve the parameterised heat transfer equation in a five-dimensional space.

The solution of the state problem is provided in a compact separated-variable format allowing a fast evaluation of the process-specific quantities of interest that are involved in the optimisation algorithm. This is completely decoupled from the solution of the underlying state problem. Therefore, once the whole parameterised solution is known, the evaluation of the objective function is done on-the-fly.

Reduced order modelling is applied to solve a multi-parametric multi-physics problem and generate a fast estimator needed for preliminary process optimisation. Different order reduction techniques are combined to treat the flow, heat transfer and electromagnetism problems in the framework of separated-variable representations.

The material point method (MPM)is a particle-based numerical method suitable for solid–liquid simulation and large deformation problems. However, MPM is generally used in solid deformation at present, to develop a multi-physics coupling MPM; the purpose of this study is to extend the MPM to simulate the heat and fluid flow and address the thermal-hydrological (TH) coupling problems.

The porous medium was discretized into two sets of Lagrangian points, and the motion of fluid points follows the Darcy’s law. Two sets of heat transport equations were established for the heat conduction and heat exchange in the pore fluid and solid skeleton. Fractures were considered by adding the porosity gradient term in the governing equations; also a transition function was introduced to smoothen the fracture boundary.

Four cases of heat and fluid flow in porous medium and fractures were presented to verify the feasibility of the proposed method. And the effects of fractures on heat and fluid flow were investigated. Additionally, a case of geothermal extraction was solved and the importance of the interstitial convective heat transfer coefficient was analyzed.

The proposed method extends the conventional MPM, using two sets of material points and two sets of heat transport equations to simulate the heat and fluid flow and address the TH coupling problems, which can be applied in both porous medium and fractures.