Local Discontinuous Galerkin Methods with Novel Basis for Fractional Diffusion Equations with Non-smooth Solutions

In this paper,we develop novel local discontinuous Galerkin(LDG)methods for fractional diffusion equations with non-smooth solutions.We consider such problems,for which the solutions are not smooth at boundary,and therefore the traditional LDG methods with piecewise polynomial solutions suffer accuracy degeneracy.The novel LDG methods utilize a solution information enriched basis,simulate the problem on a paired special mesh,and achieve optimal order of accuracy.We analyze the L2 stability and optimal error estimate in L2-norm.Finally,numerical examples are presented for validating the theoretical conclusions.

Accuracy optimization of virtual iterative reduction algorithm under time constraint

The factors like production accuracy and completion time are the determinants of the optimal scheduling of the complex products work-flow,so the main research direction of modern work-flow technology is how to assure the dynamic balance between the factors.Based on the work-flow technology,restraining the completion time,and analyzing the deficiency of traditional minimum critical path algorithm,a virtual iterative reduction algorithm(VIRA)was proposed,which can improve production accuracy effectively with time constrain.The VIRA with simplification as the core abstracts a virtual task that can predigest the process by combining the complex structures which are cyclic or parallel,finally,by using the virtual task and the other task in the process which is the iterative reduction strategy,determines a path which can make the production accuracy and completion time more balanced than the minimum critical path algorithm.The deadline,the number of tasks,and the number of cyclic structures were used as the factors affecting the performance of the algorithm,changing the influence factors can improve the performance of the algorithm effectively through the analysis of detailed data.Consequently,comparison experiments proved the feasibility of the VIRA.

Surface accuracy optimization of mechanical parts with multiple circular holes for additive manufacturing based on triangular fuzzy number

Surface accuracy directly affects the surface quality and performance of mechanical parts.Circular hole,especially spatial non-planar hole set is the typical feature and working surface of mechanical parts.Compared with traditional machining methods,additive manufacturing(AM)technology can decrease the surface accuracy errors of circular holes during fabrication.However,an accuracy error may still exist on the surface of circular holes fabricated by AM due to the influence of staircase effect.This study proposes a surface accuracy optimization approach for mechanical parts with multiple circular holes for AM based on triangular fuzzy number(TFN).First,the feature lines on the manifold mesh are extracted using the dihedral angle method and normal tensor voting to detect the circular holes.Second,the optimal AM part build orientation is determined using the genetic algorithm to optimize the surface accuracy of the circular holes by minimizing the weighted volumetric error of the part.Third,the corresponding weights of the circular holes are calculated with the TFN analytic hierarchy process in accordance with the surface accuracy requirements.Lastly,an improved adaptive slicing algorithm is utilized to reduce the entire build time while maintaining the forming surface accuracy of the circular holes using digital twins via virtual printing.The effectiveness of the proposed approach is experimentally validated using two mechanical models.