scholarly journals A Numerical Method for Estimating the Nonlinear Eigenvalue Numbers of Boundary Element

2019 ◽  
Vol 37 (1) ◽  
pp. 28-34
Author(s):  
Junpeng Wang ◽  
Jinyou Xiao ◽  
Lihua Wen
Keyword(s):  
Modal Analysis ◽  
Numerical Method ◽  
Boundary Element ◽  
Large Scale ◽  
Interpolation Method ◽  
Unbiased Estimation ◽  
Optimal Input ◽  
Nonlinear Eigenvalues ◽  
Input Parameters ◽  
Nonlinear Eigenvalue

Recently, some new proposed methods for solving nonlinear eigenvalue problems (NEPs) have promoted the development of large-scale modal analysis using BEM. However, the efficiency and robustness of such methods are generally still dependent on input parameters, especially on the parameters related to the number of eigenvalues to be solved. This limitation obviously restricts the popularization of the practical engineering application of modal analysis using BEM. Therefore, this paper develops a numerical method for estimating the number of nonlinear eigenvalues of the boundary element method. Firstly, the interpolation method based on the discretized Cauchy integral formula of analytic function is used for obtaining the BEM matrix's derivative with regard to frequency, and this method is easily combined with the mainstream fast algorithm libraries of BEM. Secondly, the method for evaluating the eigenvalue number of BEM under various boundary conditions is obtained by combining the interpolation method with the analytic formula to obtain the eigenvalue number, while the unbiased estimation is used to determine the trace of matrix. Finally, a series of typical examples are used to explore the principle for selecting optimal input parameters in this method, and then a set of optimal input parameters are determined. The overall excellent performance of this method is verified by a complex large-scale example.

Boundary element numerical method for the electric field generated by oblique multi-needle electrodes

2009 ◽  
Vol 52 (2) ◽  
pp. 189-197 ◽  
Author(s):  
FuPing Liu ◽  
AnLing Wang ◽  
AnXuan Wang ◽  
YueZu Cao ◽  
Qiang Chen ◽  
...  
Keyword(s):  
Electric Field ◽  
Numerical Method ◽  
Boundary Element

scholarly journals A Compound Wind Power Forecasting Strategy Based on Clustering, Two-Stage Decomposition, Parameter Optimization, and Optimal Combination of Multiple Machine Learning Approaches

Energies ◽  
2019 ◽  
Vol 12 (18) ◽  
pp. 3586 ◽  
Author(s):  
Sizhou Sun ◽  
Jingqi Fu ◽  
Ang Li
Keyword(s):  
Wind Power ◽  
Large Scale ◽  
Wind Farm ◽  
Search Algorithm ◽  
Interpolation Method ◽  
Least Square ◽  
Support Vector ◽  
Two Stage ◽  
Wind Power Forecasting ◽  
Power Forecasting

Given the large-scale exploitation and utilization of wind power, the problems caused by the high stochastic and random characteristics of wind speed make researchers develop more reliable and precise wind power forecasting (WPF) models. To obtain better predicting accuracy, this study proposes a novel compound WPF strategy by optimal integration of four base forecasting engines. In the forecasting process, density-based spatial clustering of applications with noise (DBSCAN) is firstly employed to identify meaningful information and discard the abnormal wind power data. To eliminate the adverse influence of the missing data on the forecasting accuracy, Lagrange interpolation method is developed to get the corrected values of the missing points. Then, the two-stage decomposition (TSD) method including ensemble empirical mode decomposition (EEMD) and wavelet transform (WT) is utilized to preprocess the wind power data. In the decomposition process, the empirical wind power data are disassembled into different intrinsic mode functions (IMFs) and one residual (Res) by EEMD, and the highest frequent time series IMF1 is further broken into different components by WT. After determination of the input matrix by a partial autocorrelation function (PACF) and normalization into [0, 1], these decomposed components are used as the input variables of all the base forecasting engines, including least square support vector machine (LSSVM), wavelet neural networks (WNN), extreme learning machine (ELM) and autoregressive integrated moving average (ARIMA), to make the multistep WPF. To avoid local optima and improve the forecasting performance, the parameters in LSSVM, ELM, and WNN are tuned by backtracking search algorithm (BSA). On this basis, BSA algorithm is also employed to optimize the weighted coefficients of the individual forecasting results that produced by the four base forecasting engines to generate an ensemble of the forecasts. In the end, case studies for a certain wind farm in China are carried out to assess the proposed forecasting strategy.

Recent Development of the Fast Multipole Boundary Element Method for Modeling Acoustic Problems

2009 ◽  
Author(s):  
Yijun Liu ◽  
Milind Bapat
Keyword(s):  
Boundary Element Method ◽  
Acoustic Wave ◽  
Boundary Element ◽  
Large Scale ◽  
Boundary Integral ◽  
Practical Significance ◽  
Fast Multipole ◽  
Tree Structures ◽  
Wave Problems ◽  
Element Method

Some recent development of the fast multipole boundary element method (BEM) for modeling acoustic wave problems in both 2-D and 3-D domains are presented in this paper. First, the fast multipole BEM formulation for 2-D acoustic wave problems based on a dual boundary integral equation (BIE) formulation is presented. Second, some improvements on the adaptive fast multipole BEM for 3-D acoustic wave problems based on the earlier work are introduced. The improvements include adaptive tree structures, error estimates for determining the numbers of expansion terms, refined interaction lists, and others in the fast multipole BEM. Examples involving 2-D and 3-D radiation and scattering problems solved by the developed 2-D and 3-D fast multipole BEM codes, respectively, will be presented. The accuracy and efficiency of the fast multipole BEM results clearly demonstrate the potentials of the fast multipole BEM for solving large-scale acoustic wave problems that are of practical significance.

Fast Multipole Virtual Boundary Element - Least Square Method for Solving 2-D Elastic Problems

2011 ◽  
Vol 204-210 ◽  
pp. 2196-2201
Author(s):  
Yan Tao Jiang ◽  
Si Tian Chen ◽  
Cheng Hua Li
Keyword(s):  
Boundary Element ◽  
Large Scale ◽  
Fast Multipole Method ◽  
Main Idea ◽  
Least Square Method ◽  
Least Square ◽  
Fast Multipole ◽  
Large Scale Problems ◽  
Virtual Boundary ◽  
Virtual Boundary Element

In this paper, the fast multipole virtual boundary element - least square method (Fast Multipole VBE - LSM) is proposed and used to simulate 2-D elastic problems, which is based on the fast multipole method (FMM) and virtual boundary element - least square method (VBE - LSM).The main idea of the method is to change computational model by applying the FMM to conventional VBE - LSM. The memory and operations could be reduced to be of linear proportion to the degree of freedom (DOF) and large scale problems could be effectively solved on a common desktop with this method. Numerical results show that this method holds virtues of high feasibility, accuracy and efficiency. Moreover, the idea of this method can be generalized and extended in application.

Boundary Element Method Used in Random Response Calculation of the Plate-Beam Structure

1991 ◽  
Author(s):  
J. M. Zhu ◽  
L. Huang
Keyword(s):  
Boundary Element Method ◽  
Numerical Method ◽  
Boundary Element ◽  
Pressure Fluctuation ◽  
Random Vibration ◽  
Power Plants ◽  
Measured Data ◽  
Random Response ◽  
Beam Structure ◽  
Element Method

Abstract The furnace walls of the large boilers in power plants are combined structures consisting of orthotopic plate and equally spaced beams, which are usually submitted to random vibration under the excitation of the pressure fluctuation induced by combustion in the furnace. In this paper, a numerical method based on BEM to compute the random response of the structure is offered. The agreement between the computing results and the measured data in a practical example verifies the effectiveness of the method.

Pre- and Post-Tsunami Depth Changes of Submarine Topography for the Analysis of Submarine Landslide-Induced Tsunami: Proposal of Digitization Method and Application to the Case of the 1923 Great Kanto Earthquake Tsunamis

2021 ◽  
Author(s):  
Kazuki Murata ◽  
Shinji Sassa ◽  
Tomohiro Takagawa ◽  
Toshikazu Ebisuzaki ◽  
Shigenori Maruyama
Keyword(s):  
Large Scale ◽  
Interpolation Method ◽  
Weighted Average ◽  
Tokyo Bay ◽  
Submarine Landslides ◽  
Sagami Bay ◽  
Seabed Topography ◽  
Kanto Earthquake ◽  
Before And After ◽  
Tsunami Event

Abstract We first propose and examine a method for digitizing analog data of submarine topography by focusing on the seafloor survey records available in the literature to facilitate a detailed analysis of submarine landslides and landslide-induced tsunamis. Second, we apply this digitization method to the seafloor topographic changes recorded before and after the 1923 Great Kanto earthquake tsunami event and evaluate its effectiveness. Third, we discuss the coseismic large-scale seafloor deformation at the Sagami Bay and the mouth of the Tokyo Bay, Japan. The results confirmed that the latitude / longitude and water depth values recorded by the lead sounding measurement method can be approximately extracted from the sea depth coordinates by triangulation survey through the overlaying of the currently available GIS map data without geometric correction such as affine transformation. Further, this proposed method allows us to obtain mesh data of depth changes in the sea area by using the interpolation method based on the IDW (Inverse Distance Weighted) average method through its application to the case of the 1923 Great Kanto Earthquake. Finally, we analyzed and compared the submarine topography before and after the 1923 tsunami event and the current seabed topography. Consequently, we found that these large-scale depth changes correspond to the valley lines that flow down as the topography of the Sagami Bay and the Tokyo Bay mouth.

Study on Temperature Distribution of Pebble-Bed HTR Fuel Element by Using Boundary Element Method

2013 ◽  
Author(s):  
Haitao Wang ◽  
Xin Wang
Keyword(s):  
Fuel Element ◽  
Boundary Element ◽  
Large Scale ◽  
Maximum Temperature ◽  
Element Formulation ◽  
Desktop Computer ◽  
Pebble Bed ◽  
Graphite Matrix ◽  
Fuel Particles ◽  
Fuel Elements

Spherical fuel elements with a diameter of 60mm are basic units of the nuclear fuel for the pebble-bed high temperature gas-cooled reactor (HTR). Each fuel element is treated as a graphite matrix containing around 10,000 randomly distributed fuel particles. The essential safety concept of the pebble-bed HTR is based on the objective that maximum temperature of the fuel particles does not exceed the design value. In this paper, a microstructure-based boundary element model is proposed for the large-scale thermal analysis of a spherical fuel element. This model presents detailed structural information of a large number of coated fuel particles dispersed in a spherical graphite matrix in order that temperature distributions at the level of fuel particles can be evaluated. The model is meshed with boundary elements in conjunction with the fast multipole method (FMM) in order that such large-scale computation is performed only in a personal desktop computer. Taking advantage of the fact that fuel particles are of the same shape, a similar sub-domain approach is used to establish the temperature translation mechanism between various layers of each fuel particle and to simplify the associated boundary element formulation. The numerical results demonstrate large-scale capacity of the proposed method for the multi-level temperature evaluation of the pebble-bed HTR fuel elements.

Sign in / Sign up

Export Citation Format

Share Document