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This paper seeks to develop an adaptive finite volume algorithm, and to present an extensive numerical analysis of it.

The effectiveness of the developed algorithm is demonstrated through practical and computationally challenging problems. The algorithm is tested for a wide range of singularities.

The convergence of the presented algorithm is independent of the regularity of the problems. It is shown that the our algorithm produces more accurate and well conditioned matrix systems.

Though the presented algorithm works for extreme singularities on rectangular meshes, it may not be as efficient if the underlying meshes are distorted, and it may not converge. Further research is under way for including the multi‐point approximation technique into the algorithm.

Almost all reservoir simulators use the two‐point method, and this algorithm is based on this method. The algorithm can be easily incorporated into the reservoir simulators. The results show that such an implementation will greatly improve the computational efficiency of the simulators. The work is useful for computational scientists, and especially for the researchers in oil industries. The paper reports the numerical work with practical applications.

The paper develops an adaptive finite volume algorithm. It is shown that adaptive meshes represent the underlying problem more accurately, and matrix systems associated with adaptive meshes are easier to solve compared with matrix systems associated with uniform meshes.

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

Bayesian cubature (BC) has emerged to be one of most competitive approach for estimating the multi-dimensional integral especially when the integrand is expensive to evaluate, and alternative acquisition functions, such as the Posterior Variance Contribution (PVC) function, have been developed for adaptive experiment design of the integration points. However, those sequential design strategies also prevent BC from being implemented in a parallel scheme. Therefore, this paper aims at developing a parallelized adaptive BC method to further improve the computational efficiency.

By theoretically examining the multimodal behavior of the PVC function, it is concluded that the multiple local maxima all have important contribution to the integration accuracy as can be selected as design points, providing a practical way for parallelization of the adaptive BC. Inspired by the above finding, four multimodal optimization algorithms, including one newly developed in this work, are then introduced for finding multiple local maxima of the PVC function in one run, and further for parallel implementation of the adaptive BC.

The superiority of the parallel schemes and the performance of the four multimodal optimization algorithms are then demonstrated and compared with the k-means clustering method by using two numerical benchmarks and two engineering examples.

Multimodal behavior of acquisition function for BC is comprehensively investigated. All the local maxima of the acquisition function contribute to adaptive BC accuracy. Parallelization of adaptive BC is realized with four multimodal optimization methods.

In this paper, a set of safe adaptive genetic algorithms (sGAs) is proposed based on the Splicing/Decomposable encoding scheme and the efficient speed‐up strategies developed by Xu et al.. The proposed algorithms implement the self‐adaptation of the problem representation, selection and recombination operators at the levels of population, individual and component which commendably balance the conflicts between “reliability” and “efficiency”, as well as “exploitation” and “exploration” existed in the evolutionary algorithms. It is shown that the algorithms converge to the optimum solution in probability one. The proposed sGAs are experimentally compared with the classical genetic algorithm (CGA), non‐uniform genetic algorithm (nGA) proposed by Michalewicz, forking genetic algorithm (FGA) proposed by Tsutsui et al. and the classical evolution programming (CEP). The experiments indicate that the new algorithms perform much more efficiently than CGA and FGA do, comparable with the real‐coded GAs — nGA and CEP. All the algorithms are further evaluated through an application to a difficult real‐life application problem: the inverse problem of fractal encoding related to fractal image compression technique. The results for the sGA is better than those of CGA and FGA, and has the same, sometimes better performance compared to those of nGA and CEP.

Pressure-based methods have been demonstrated to be powerful for solving many practical problems in engineering. In many pressure-based methods, inner iterative processes are proposed to get efficient solutions. However, the number of inner iterations is set empirically and kept fixed during the whole computation for different problems, which is overestimated in some computations but underestimated in other computations. This paper aims to develop an algorithm with adaptive inner iteration processes for steady and unsteady incompressible flows.

In this work, with the use of two different criteria in two inner iterative processes, a mechanism is proposed to control inner iteration processes to make the number of inner iterations vary during computing according to different problems. By doing so, adaptive inner iteration processes can be achieved.

The adaptive inner iterative algorithm is verified to be valid by solving classic steady and unsteady incompressible problems. Results show that the adaptive inner iteration algorithm works more efficient than the fixed inner iteration one.

The algorithm with adaptive inner iteration processes is first proposed in this paper. As the mechanism for controlling inner iteration processes is based on physical meaning and the feature of iterative calculations, it can be used in any methods where there exist inner iteration processes. It is not limited for incompressible flows. The performance of the adaptive inner iteration processes in compressible flows is conducted in a further study.

The main aim of this study is to generate curved-form cut on the edge of an adaptive layer. The resulting surface would have much less geometry deviation error and closely fit its computer aided design (CAD) model boundary.

This method is inspired by the manual peeling of an apple in which a knife's orientation and movement are continuously changed and adjusted to cut each slice with minimum waste. In this method, topology and geometry information are extracted from the previously generated adaptive layers. Then, the thickness of an adaptive layer and the bottom and top contours of the adjacent layers are fed into the proposed algorithm in the form of the contour and normal vector to create curved-form sloping surfaces. Following curved-form adaptive slicing, a customized machine path compatible with a five-axis abrasive waterjet (AWJ) machine will be generated for any user-defined sheet thicknesses.

The implemented system yields curved-form adaptive slices for a variety of models with diverse types of surfaces (e.g. flat, convex, and concave), different slicing direction, and different number of sheets with different thicknesses. The decrease in layer thickness and increase of the number of the sloped cuts can make the prototype as close as needed to the CAD model.

The algorithm is designed for use with five-axis AWJ cutting of any kind of geometrical complex surfaces. Future research would deal with the nesting problem of the layers being spread on the predefined sheet as the input to the five-axis AWJ cutter machine to minimize the cutting waste.

The algorithm generates adaptive layers with concave or convex curved-form surfaces that conform closely to the surface of original CAD model. This will pave the way for the accurate fabrication of metallic functional parts and tooling that are made by the attachment of one layer to another. Validation of the output has been tested only as the simulation model. The next step is the customization of the output for the physical tests on a variety of five-axis machines.

This paper proposes a new close to CAD design sloped-edge adaptive slicing algorithm applicable to a variety of five-axis processes that allow variable thickness layering and slicing in different orientations (e.g. AWJ, laser, or plasma cutting). Slices can later be bonded to build fully solid prototypes.

A new h‐refinement adaptive tetrahedral mesh generation algorithm is presented. Three‐dimensional domains, to be analysed by the finite element method, are initially modelled by a coarse background mesh of tetrahedral elements. This mesh forms the input for finite element analysis and error estimation by the Zienkiewicz‐Zhu simple error estimator. Adaptive mesh refinement proceeds by selecting an element for remeshing whose longest edge is shared by elements that also require refinement. This group of elements is refined by inserting a new node at the mid‐point of the shared edge thereby bisecting all elements within the group. Adaptive parameters are calculated for the new node and elements. Refinement then proceeds until no further group of elements can be found for refinement or no elements within the current mesh require further refinement. The shape quality of the current mesh is then enhanced by the iterative application of nodal relaxation plus three topological transformations. The entire refinement process is repeated iteratively until the required degree of mesh refinement is reached. Ten‐noded linear strain tetrahedral finite element meshes have been used for the finite element and error estimation analyses. Four examples of adaptive tetrahedral mesh generation for linear elastic stress/displacement analysis are presented which show that this algorithm is robust and efficient in terms of reduction of the domain error with a minimum number of degrees of freedom being generated, number of iterations, and therefore finite element analyses, required and computational time for refinement when compared to the advancing front method and Delaunay triangulation.

The purpose of this paper is to accurately obtain the deformation of a hybrid robot and rapidly enable real-time compensation in friction stir welding (FSW). In this paper, a prediction algorithm based on the back-propagation neural network (BPNN) optimized by the adaptive genetic algorithm (GA) is presented.

Via the algorithm, the deformations of a five-degree-of-freedom (5-DOF) hybrid robot TriMule800 at a limited number of positions are taken as the training set. The current position of the robot and the axial force it is subjected to are used as the input; the deformation of the robot is taken as the output to construct a BPNN; and an adaptive GA is adopted to optimize the weights and thresholds of the BPNN.

This algorithm can quickly predict the deformation of a robot at any point in the workspace. In this study, a force-deformation experiment bench is built, and the experiment proves that the correspondence between the simulated and actual deformations is as high as 98%; therefore, the simulation data can be used as the actual deformation. Finally, 40 sets of data are taken as examples for the prediction, the errors of predicted and simulated deformations are calculated and the accuracy of the prediction algorithm is verified.

The entire algorithm is verified by the laboratory-developed 5-DOF hybrid robot, and it can be applied to other hybrid robots as well.

Robots have been widely used in FSW. Traditional series robots cannot bear the large axial force during welding, and the deformation of the robot will affect the machining quality. In some research studies, hybrid robots have been used in FSW. However, the deformation of a hybrid robot in thick-plate welding applications cannot be ignored. Presently, there is no research on the deformation of hybrid robots in FSW, let alone the analysis and prediction of their deformation. This research provides a feasible methodology for analysing the deformation and compensation of hybrid robots in FSW. This makes it possible to calculate the deformation of the hybrid robot in FSW without external sensors.

T-spline is the latest powerful modeling tool in the field of computer-aided design. It has all the merits of non-uniform rational B-spline (NURBS) whilst resolving some flaws in it. This work applies T-spline surfaces to additive manufacturing (AM). Most current AM products are based on Stereolithograph models. It is a kind of discrete polyhedron model with huge amounts of data and some inherent defects. T-spline offers a better choice for the design and manufacture of complex models.

In this paper, a direct slicing algorithm of T-spline surfaces for AM is proposed. Initially, a T-spline surface is designed in commercial software and saved as a T-spline mesh file. Then, a numerical method is used to directly calculate all the slicing points on the surface. To achieve higher manufacturing efficiency, an adaptive slicing algorithm is applied according to the geometrical properties of the T-spline surface.

Experimental results indicate that this algorithm is effective and reliable. The quality of AM can be enhanced at both the designing and slicing stages.

The T-spline and direct slicing algorithm discussed here will be a powerful supplement to current technologies in AM.

The purpose of this paper is to propose a novel decoding algorithm, to decrease the complexity in decoding conventional block turbo codes.

In this algorithm, the signal‐to‐noise ratio (SNR) values of channels are adaptively estimated. After analyzing the relationship between the statistics of the received vectors R and the channel SNR, an adaptive method of tuning the decoding complexity is presented.

Simulation results show that the proposed algorithm has greatly decreased the decoding complexity and sped up the decoding process while achieving better bit error rate performance.

Simulation experiments described in this paper show that the proposed algorithm can decrease the decoding complexity, shorten the decoding time and achieve good decoding performance.