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| 1 | Artificial Neural Network Methods for the Solution of Second Order Boundary Value Problems显示文摘We present a method for solving partial differential equations using artificial neural networks and an adaptive collocation strategy.In this procedure,a coarse grid of training points is used at the initial training stages,while more points are added at later stages based on the value of the residual at a larger set of evaluation points.This method increases the robustness of the neural network approximation and can result in significant computational savings,particularly when the solution is non-smooth.Numerical results are presented for benchmark problems for scalar-valued PDEs,namely Poisson and Helmholtz equations,as well as for an inverse acoustics problem. | Cosmin Anitescu Elena Atroshchenko Naif Alajlan Timon Rabczuk | 2019 | Computers, Materials & Continua2019，，4： | 72 |
| 2 | Optimizing the neural network hyperparameters utilizing genetic algorithm显示文摘Neural networks(NNs),as one of the most robust and efficient machine learning methods,have been commonly used in solving several problems.However,choosing proper hyperparameters(e.g.the numbers of layers and neurons in each layer)has a significant influence on the accuracy of these methods.Therefore,a considerable number of studies have been carried out to optimize the NN hyperpaxameters.In this study,the genetic algorithm is applied to NN to find the optimal hyperpaxameters.Thus,the deep energy method,which contains a deep neural network,is applied first on a Timoshenko beam and a plate with a hole.Subsequently,the numbers of hidden layers,integration points,and neurons in each layer are optimized to reach the highest accuracy to predict the stress distribution through these structures.Thus,applying the proper optimization method on NN leads to significant increase in the NN prediction accuracy after conducting the optimization in various examples. | Saeid NIKBAKHT Cosmin ANITESCU Timon RABCZUK | 2021 | Journal of Zhejiang University-Science A(Applied Physics & Engineering)2021，22，6： | 5 |
| 3 | High velocity impact of metal sphere on thin metallic plate using smooth particle hydrodynamics(SPH)method显示文摘The modeling of high velocity impact is an important topic in impact engineering.Due to various constraints,experimental data are extremely limited.Therefore,detailed numerical simulation can be considered as a desirable alternative.However,the physical processes involved in the impact are very sophisticated;hence a practical and complete reproduction of the phenomena involves complicated numerical models.In this paper,we present a smoothed particle hydrodynamics(SPH)method to model two-dimensional impact of metal sphere on thin metallic plate.The simulations are applied to different materials(Aluminum,Lead and Steel);however the target and projectile are formed of similar metals.A wide range of velocities(300,1000,2000,and 3100 m/s)are considered in this study.The goal is to study the most sensitive input parameters(impact velocity and plate thickness)on the longitudinal extension of the projectile,penetration depth and damage crater. | Hossein ASADI KALAMEH Arash KARAMALI Cosmin ANITESCU Timon RABCZUK | 2012 | Frontiers of Structural and Civil Engineering2012，6，2： | 4 |
| 4 | 基于PHT-样条加强等几何分析配置方法显示文摘结合传统等几何分析配置法和传统等几何分析伽辽金法,提出一种基于PHT-样条函数的加强等几何分析配置方法.对于一个偏微分方程问题,基于具有局部细分特性的PHT-样条基础函数,应用传统等几何分析配置法在问题域内配置点定义线性方程组,并应用传统等几何分析伽辽金法施加边界条件,以保证多片结构连接的稳定;再将2组线性方程组及施加的边界条件合成一个整体系统.实例计算结果表明,该方法既具有配置法固有的计算效率高的优点,又改善了边界计算出现的不稳定问题,可有效地用于局部细分和多片结构的计算. | 贾悦 Cosmin Anitescu Yongjie Jessica Zhang 徐岗 李春 Timon Rabczuk | 2018 | 计算机辅助设计与图形学学报2018，30，4： | 1 |
| 5 | 基于改进的PHT-样条自适应等几何配点法显示文摘将传统等几何配点法扩展至任意高阶单元并且满足自适应局部细分功能,提出一种基于改进的PHT样条单元的自适应等几何配点法。改进的PHT样条单元依然具有传统PHT样条单元局部细分功能,但因为传统PHT样条函数在层级网格划分后需要对部分基函数的定义域进行截断处理,所以在层级细分过于频繁区域,部分函数可能因为严重变形而影响计算稳定性,而改进的PHT样条函数无需截断处理,定义域内基函数始终具有稳定形态,这使得改进的PHT样条单元更适合高阶连续性计算及多层网格细分。该算法结合PHT样条单元的特点,选取高斯点作为配置点。为了简化边界施加条件,采用了耦合线性方程组的方法,在问题域内采用高斯配点法,在问题域边界采用传统伽辽金方法,最终耦合2组线性方程组。本算法的局部细分准则基于复原解和复原解误差。实例计算结果表明,基于改进的PHT样条的自适应等几何配点法可以扩展至任意高阶单元计算,并满足最佳收敛率,且与理论值吻合。 | 贾悦 ANITESCU Cosmin 李春 | 2022 | 图学学报2022，43，1： | 1 |
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