Xiaoyi Wang¹, Xinyue Chang², Wenxuan Wang^1,*, Zijie Qiao³, Feng Zhang^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.2, pp. 1775-1796, 2024, DOI:10.32604/cmes.2023.043913

Abstract The objective of reliability-based design optimization (RBDO) is to minimize the optimization objective while satisfying the corresponding reliability requirements. However, the nested loop characteristic reduces the efficiency of RBDO algorithm, which hinders their application to high-dimensional engineering problems. To address these issues, this paper proposes an efficient decoupled RBDO method combining high dimensional model representation (HDMR) and the weight-point estimation method (WPEM). First, we decouple the RBDO model using HDMR and WPEM. Second, Lagrange interpolation is used to approximate a univariate function. Finally, based on the results of the first two steps, the original nested loop reliability optimization model is… More >

Dave Martin^a,b,† , Hicham Chaouki^a,b, Jean-Loup Robert^a, Donald Ziegler^c, Mario Fafard^a,b

Frontiers in Heat and Mass Transfer, Vol.7, pp. 1-9, 2016, DOI:10.5098/hmt.7.31

Abstract The two dimensional phase change problem was solved using the extended finite element method with a Lagrange formulation to apply the interface boundary condition. The Lagrange multiplier space is identical to the solution space and does not require stabilization. The solid-liquid interface velocity is determined by the jump in heat flux across the i nterface. Two methods to calculate the jump are used and c ompared. The first is based on an averaged temperature gradient near the interface. The second uses the Lagrange multiplier values to evaluate the jump. The Lagrange multiplier based approach was shown to be more robust… More >

Dave Martin^a,b,† , Hicham Chaouki^a,b, Jean-Loup Robert^a, Donald Ziegler^c, Mario Fafard^a,b

Frontiers in Heat and Mass Transfer, Vol.7, pp. 1-11, 2016, DOI:10.5098/hmt.7.40

Abstract A two phase model for two-dimensional solidification problems with variable densities was developed by coupling the Stefan problem with the Stokes problem and applying a mass conserving velocity condition on the phase change interface. The extended finite element method (XFEM) was used to capture the strong discontinuity of the velocity and pressure as well as the jump in heat flux at the i nterface. The melting temperature and velocity condition were imposed on the interface using a Lagrange multiplier and the penalization method, respectively. The resulting formulations were then coupled using a fixed point iteration a lgorithm. Three examples were… More >

Xiang Li¹, Guangyan Huang^1,2,*, Zhiwei Guo^1,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.26, No.4, pp. 1-3, 2023, DOI:10.32604/icces.2023.09269

Abstract SPH method is widely used to study the dynamic response of metal casing under explosive loading because of its superiority in simulating metal fracture phenomenon [1-3]. The distribution of the fragment from uncoupled charge structures with segmental shaped explosive were studied. The X-ray photographic images of fragmentation obtained from explosion experiment were compared with the numerical results based on SPH method and Lagrange method. The fragmentation shows that the numerical results based on the Lagrange method are in good agreement with the experimental results while some errors appear in results based on SPH method. The velocity of the fragments at… More >

S. Vidhya^1,*, V. Kalaivani²

Computer Systems Science and Engineering, Vol.45, No.3, pp. 2673-2692, 2023, DOI:10.32604/csse.2023.027724

Abstract In recent decades, the cloud computing contributes a prominent role in health care sector as the patient health records are transferred and collected using cloud computing services. The doctors have switched to cloud computing as it provides multiple advantageous measures including wide storage space and easy availability without any limitations. This necessitates the medical field to be redesigned by cloud technology to preserve information about patient’s critical diseases, electrocardiogram (ECG) reports, and payment details. The proposed work utilizes a hybrid cloud pattern to share Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) resources over the private and public cloud. The stored… More >

Ying Li¹, Longxiang Xu¹, Fangjun Mei¹, Shihui Ying^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.1, pp. 657-672, 2023, DOI:10.32604/cmes.2022.021277

Abstract We propose new hybrid Lagrange neural networks called LaNets to predict the numerical solutions of partial differential equations. That is, we embed Lagrange interpolation and small sample learning into deep neural network frameworks. Concretely, we first perform Lagrange interpolation in front of the deep feedforward neural network. The Lagrange basis function has a neat structure and a strong expression ability, which is suitable to be a preprocessing tool for pre-fitting and feature extraction. Second, we introduce small sample learning into training, which is beneficial to guide the model to be corrected quickly. Taking advantages of the theoretical support of traditional… More >

C. K. Morarji^1,*, N. Sathish Kumar²

Intelligent Automation & Soft Computing, Vol.35, No.3, pp. 2875-2892, 2023, DOI:10.32604/iasc.2023.025776

Abstract One of the recent advancements in the electrical power systems is the smart-grid technology. For the effective functioning of the smart grid, the process like monitoring and controlling have to be given importance. In this paper, the Wireless Sensor Network (WSN) is utilized for tracking the power in smart grid applications. The smart grid is used to produce the electricity and it is connected with the sensor to transmit or receive the data. The data is transmitted quickly by using the Probabilistic Neural Network (PNN), which aids in identifying the shortest path of the nodes. While transmitting the data from… More >

Amr M. S. Mahdy^1,*, Mohamed S. Mohamed¹, Ahoud Y. Al Amiri², Khaled A. Gepreel¹

Intelligent Automation & Soft Computing, Vol.31, No.2, pp. 899-915, 2022, DOI:10.32604/iasc.2022.017801

Abstract In this manuscript, we solve the ordinary model of nonlinear smoking mathematically by using the second kind of shifted Chebyshev polynomials. The stability of the equilibrium point is calculated. The schematic of the model illustrates our proposition. We discuss the optimal control of this model, and formularize the optimal control smoking work through the necessary optimality cases. A numerical technique for the simulation of the control problem is adopted. Moreover, a numerical method is presented, and its stability analysis discussed. Numerical simulation then demonstrates our idea. Optimal control for the model is further discussed by clarifying the optimal control through… More >

Zihao Zong, Tielin Shi, Qi Xia^*

CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.1, pp. 283-295, 2021, DOI:10.32604/cmes.2021.015975

Abstract A parameter-free approach is proposed to determine the Lagrange multiplier for the constraint of material volume in the level set method. It is inspired by the procedure of determining the threshold of sensitivity number in the BESO method. It first computes the difference between the volume of current design and the upper bound of volume. Then, the Lagrange multiplier is regarded as the threshold of sensitivity number to remove the redundant material. Numerical examples proved that this approach is effective to constrain the volume. More importantly, there is no parameter in the proposed approach, which makes it convenient to use.… More >

Miaomiao Yang, Wentao Ma, Yongbin Ge^*

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.1, pp. 25-54, 2021, DOI:10.32604/cmes.2021.012575

Abstract In this paper, Chebyshev interpolation nodes and barycentric Lagrange interpolation basis function are used to deduce the scheme for solving the Helmholtz equation. First of all, the interpolation basis function is applied to treat the spatial variables and their partial derivatives, and the collocation method for solving the second order differential equations is established. Secondly, the differential equations on a given test node. Finally, based on three kinds of test nodes, numerical experiments show that the present scheme can not only calculate the high wave numbers problems, but also calculate the variable wave numbers problems. In addition, the algorithm has… More >