SUMMARYIn this article, a finding on finite element superconvergence is reported. The Laplacian operator with Dirichlet boundary condition is considered. The linear finite element solutions have an O(h 2+ )( ≈ 0.5)-superconvergence in l 2 norm at nodes on an almost equilateral triangular mesh generated based on centroidal Voronoi tessellation, for an arbitrary 2D bounded domain. Extensive numerical examples are presented to demonstrate the superconvergence property.
We present a novel adaptive finite element method (AFEM) for elliptic equations which is based upon the Centroidal Voronoi Tessellation (CVT) and superconvergent gradient recovery. The constructions of CVT and its dual Centroidal Voronoi Delaunay Triangulation (CVDT) are facilitated by a localized Lloyd iteration to produce almost equilateral two dimensional meshes. Working with finite element solutions on such high quality triangulations, superconvergent recovery methods become particularly effective so that asymptotically exact a posteriori error estimations can be obtained. Through a seamless integration of these techniques, a convergent adaptive procedure is developed. As demonstrated by the numerical examples, the new AFEM is capable of solving a variety of model problems and has great potential in practical applications.
In order to detect the size information of complex flat parts, this paper proposed a method for flat part measurement based on local line-angle contour segmentation. After processing the images taken by photos and edge detection, we obtained sub-pixel part contours. Then, the local line-angles of the part contours were calculated, processed and analyzed, and so on the features of the connection between the geometric primitives of different line segments on its contour were obtained. The segmentation of the part contour came true. Next, a line segmentation error model was built, and then we got the parameters of the contour segment and the key points of the components by iterative fitting the segmented line and pinpointing the location of the segmentation. Afterwards a binocular vision model provided the spatial point cloud of the key points. As a result, the size information of the parts were acquired after analyzation and calculation. The present method can successfully measure the multiple size of the complex flat parts, which is more efficient and precise.
With the proposal of "Made in China 2025", the manufacturing industry is rapidly integrating with information technology, accelerating the pace of construction of smart factories, and reducing labor costs by establishing factories with few people and no one.Scheduling algorithm of flexible shop is the key technology to realize automatic processing of production line. The limited resources of shop can be allocated rationally through scheduling algorithm to complete automatic production.According to the requirements of automatic production line, this chapter realizes the assignment of processing task and handling task in turn.The classical genetic algorithm is easy to fall into local optimization and slow convergence.An improved genetic algorithm is adopted to introduce dynamic crossover and mutation probability. In addition, when the algorithm performs crossover operation, the individuals are first sorted according to their fitness values, and then cross operation is carried out successively.Through the simulation experiment, it is found that the task completion time obtained by the improved algorithm is 146 units of time, compared with the 198 units of time obtained before the improvement, the task completion time is reduced by 26%, and the improved algorithm has better convergence speed, so the improved algorithm has better optimization performance.
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