重构核粒子法在二维及三维势问题中的应用

目录摘要Abstract第一章绪论。。11.1研究背景..1.2无网格法的发展.。1.3无网格方法的发展趋势1.4小结.…5第二章重构核粒子法62.1引言...62.2重构核粒子法...。。62.3小结..第三章势问题..3.1势问题中的重构核粒子法11第四章数值算例..144.1二维势问题.........S...144.2三维势问题....164.3小结.18第五章结论与展望.195.1结论.195.2展望.19参考文献.20致谢22附录….23摘要重构核粒子法在二维及三维势问题中的应用张慧凯专业：建筑电气与智能化指导老师：彭飘飘摘要：本文介绍了一种新颖的无网格法，并对此方法进行了应用，该方法是重枸核粒子法。它是源自于光滑粒子法衍生而来的一种新方法，学者们辛勤钻研发现这个方法具有变时频特性和多分辨率特性等的好处，相较于有限元方法，具有很多其他方法所不具有的优势。该方法的基本原理是为了精确再现多项式在插值点的准确值，因此，需要构造一个具有平滑性质的重枸核函数并将其用于形函数中。诸多实验和数据表明，重构核粒子法具有应用多样化的好处。然而，该方法也存在一个显著的缺点，即计算结果容易受到不同核函数的影响。因此，在使用重枸核粒子法时需要特别关注所选核函数对计算结果的影响，并进行造当的选择。本文选取了两个算例来证明该方法的精确性和稳定性，并将数值解与解析解进行比较来验证方法的有效性和正确性。实验表明，该方法的数值解与解析解匹配度非常好，并且收敛速度也比较高。总之，重构核粒子法是一种理论还不够完备，但应用广泛的无网格方法，在工程数值计算中有着重要的应用价值。使用该方法时需要注意所选用的核函数，以达到更加准确的计算结果。关键词：重构核粒子法，势问题，二维，三维，无网格法Application of reconstructed nuclear particle method to two-dimensional andthree-dimensional potential problemsAbstract:In this paper,a novel meshless method is introduced and applied,which is the reconstructednuclear particle method.It is a new method derived from the smooth particle method.Scholars havestudied hard and found that this method has the advantages of variable time-frequency characteristics andmulti-resolution characteristics.Compared with the finite element method,it has many advantages thatother methods do not have.The basic principle of this method is to reproduce the exact value of thepolynomial at the interpolation point,so it is necessary to construct a smooth reconstruction kernelfunction and apply it in the form function.Many experiments and data show that the reconstructed nuclearparticle method has the advantage of diversified applications.However,this method also has a significant disadvantage,that is,the calculation results are easilyaffected by different kernel functions.Therefore,special attention should be paid to the influence of theselected kernel function on the calculation results and appropriate selection should be made when usingthe reconstructed kernel particle method.In this paper,two examples are selected to prove the accuracyand stability of the method,and the numerical solution is compared with the analytical solution to verifythe validity and correctness of the method.The experimental results show that the numerical solutionmatches well with the analytical solution,and the convergence rate is relatively high.In short,the reconstructed nuclear particle method is a meshless method which is not complete intheory,but is widely used,and has important application value in engineering numerical calculation.When using this method,it is necessary to pay attention to the kernel function selected to achieve moreaccurate calculation results