scholarly journals Enhanced integration scheme for unfitted polygonal elements

PAMM ◽  
2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Márton Petö ◽  
Fabian Duvigneau ◽  
Daniel Juhre ◽  
Sascha Eisenträger
Keyword(s):  
Integration Scheme ◽  
Polygonal Elements

scholarly journals Enhanced numerical integration scheme based on image compression techniques: Application to rational polygonal interpolants

2020 ◽  
Author(s):  
Márton Petö ◽  
Fabian Duvigneau ◽  
Daniel Juhre ◽  
Sascha Eisenträger
Keyword(s):  
Image Compression ◽  
Numerical Integration ◽  
Integration Scheme ◽  
Single Element ◽  
Shape Functions ◽  
Polygonal Domains ◽  
Strong Discontinuities ◽  
Numerical Integration Scheme ◽  
Polygonal Elements ◽  
Rational Interpolants

Abstract Polygonal finite elements offer an increased freedom in terms of mesh generation at the price of more complex, often rational, shape functions. Thus, the numerical integration of rational interpolants over polygonal domains is one of the challenges that needs to be solved. If, additionally, strong discontinuities are present in the integrand, e.g., when employing fictitious domain methods, special integration procedures must be developed. Therefore, we propose to extend the conventional quadtree-decomposition-based integration approach by image compression techniques. In this context, our focus is on unfitted polygonal elements using Wachspress shape functions. In order to assess the performance of the novel integration scheme, we investigate the integration error and the compression rate being related to the reduction in integration points. To this end, the area and the stiffness matrix of a single element are computed using different formulations of the shape functions, i.e., global and local, and partitioning schemes. Finally, the performance of the proposed integration scheme is evaluated by investigating two problems of linear elasticity.

Numerical Study of the Combined Free-Forced Convection and Mass Transfer Flow Past a Vertical Porous Plate in a Porous Medium with Heat Generation and Thermal Diffusion

2006 ◽  
Vol 11 (4) ◽  
pp. 331-343 ◽  
Author(s):  
M. S. Alam ◽  
M. M. Rahman ◽  
M. A. Samad
Keyword(s):  
Mass Transfer ◽  
Flow Field ◽  
Differential Equations ◽  
Forced Convection ◽  
Heat Generation ◽  
Numerical Study ◽  
Porous Plate ◽  
Integration Scheme ◽  
Suction Parameter ◽  
Transfer Flow

The problem of combined free-forced convection and mass transfer flow over a vertical porous flat plate, in presence of heat generation and thermaldiffusion, is studied numerically. The non-linear partial differential equations and their boundary conditions, describing the problem under consideration, are transformed into a system of ordinary differential equations by using usual similarity transformations. This system is solved numerically by applying Nachtsheim-Swigert shooting iteration technique together with Runge-Kutta sixth order integration scheme. The effects of suction parameter, heat generation parameter and Soret number are examined on the flow field of a hydrogen-air mixture as a non-chemical reacting fluid pair. The analysis of the obtained results showed that the flow field is significantly influenced by these parameters.

scholarly journals Three-Dimensional Elastodynamic Analysis Employing Partially Discontinuous Boundary Elements

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 129
Author(s):  
Yuan Li ◽  
Ni Zhang ◽  
Yuejiao Gong ◽  
Wentao Mao ◽  
Shiguang Zhang
Keyword(s):  
Side Effect ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integration Scheme ◽  
Computational Accuracy ◽  
Time Step ◽  
Corner Points ◽  
Discontinuous Elements ◽  
The Time Domain

Compared with continuous elements, discontinuous elements advance in processing the discontinuity of physical variables at corner points and discretized models with complex boundaries. However, the computational accuracy of discontinuous elements is sensitive to the positions of element nodes. To reduce the side effect of the node position on the results, this paper proposes employing partially discontinuous elements to compute the time-domain boundary integral equation of 3D elastodynamics. Using the partially discontinuous element, the nodes located at the corner points will be shrunk into the element, whereas the nodes at the non-corner points remain unchanged. As such, a discrete model that is continuous on surfaces and discontinuous between adjacent surfaces can be generated. First, we present a numerical integration scheme of the partially discontinuous element. For the singular integral, an improved element subdivision method is proposed to reduce the side effect of the time step on the integral accuracy. Then, the effectiveness of the proposed method is verified by two numerical examples. Meanwhile, we study the influence of the positions of the nodes on the stability and accuracy of the computation results by cases. Finally, the recommended value range of the inward shrink ratio of the element nodes is provided.

Semi-Lagrangian exponential time-integration method for the shallow water equations on the cubed sphere grid

2020 ◽  
Vol 35 (6) ◽  
pp. 355-366
Author(s):  
Vladimir V. Shashkin ◽  
Gordey S. Goyman
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Shallow Water Equations ◽  
Time Integration ◽  
Standard Test ◽  
Integration Scheme ◽  
Test Problems ◽  
Cubed Sphere ◽  
Lagrangian Scheme ◽  
Inertia Gravity Waves

AbstractThis paper proposes the combination of matrix exponential method with the semi-Lagrangian approach for the time integration of shallow water equations on the sphere. The second order accuracy of the developed scheme is shown. Exponential semi-Lagrangian scheme in the combination with spatial approximation on the cubed-sphere grid is verified using the standard test problems for shallow water models. The developed scheme is as good as the conventional semi-implicit semi-Lagrangian scheme in accuracy of slowly varying flow component reproduction and significantly better in the reproduction of the fast inertia-gravity waves. The accuracy of inertia-gravity waves reproduction is close to that of the explicit time-integration scheme. The computational efficiency of the proposed exponential semi-Lagrangian scheme is somewhat lower than the efficiency of semi-implicit semi-Lagrangian scheme, but significantly higher than the efficiency of explicit, semi-implicit, and exponential Eulerian schemes.

scholarly journals Carbon Price Forecasting Based on Improved CEEMDAN and Extreme Learning Machine Optimized by Sparrow Search Algorithm

2021 ◽  
Vol 13 (9) ◽  
pp. 4896
Author(s):  
Jianguo Zhou ◽  
Dongfeng Chen
Keyword(s):  
Prediction Model ◽  
Extreme Learning Machine ◽  
Emission Reduction ◽  
Search Algorithm ◽  
Carbon Price ◽  
Integration Scheme ◽  
Combination Model ◽  
Price Prediction ◽  
Price Series ◽  
Learning Machine

Effective carbon pricing policies have become an effective tool for many countries to encourage emission reduction. An accurate carbon price prediction model is helpful for the implementation of energy conservation and emission reduction policies and the decision-making of governments and investors. However, it is difficult for a single prediction model to achieve high prediction accuracy because of the high complexity of the carbon price series. Many studies have proved the nonlinear characteristics of carbon trading prices, but there are very few studies on the chaotic nature of carbon price series. As a consequence, this paper proposes an innovative hybrid model for carbon price prediction. A decomposition-reconstruction-prediction-integration scheme is designed to predict carbon prices. Firstly, several intrinsic mode functions (IMFs) and one residue were obtained from the raw data decomposed by ICEEMDAN. Next, the decomposed subsection is reconstructed into a new sequence according to the calculation results by the Lempel-Ziv complexity algorithm. Then, considering the chaotic characteristics of sequence, the input variables of the models are determined through the phase space reconstruction (PSR) algorithm combined with the partial autocorrelation function (PACF). Finally, the Sparrow search algorithm (SSA) is introduced to optimize the extreme learning machine (ELM) model, which is applied in the carbon price prediction for the purpose of verifying the validity of the proposed combination model, which is applied to the pilots of Hubei, Beijing, and Guangdong. The empirical results show that the combination model outperformed the 13 other models in predicting accuracy, speed, and stability. The decomposition-reconstruction-prediction-integration strategy is a method for predicting the carbon price efficiently.

scholarly journals A numerical investigation on impulse-induced nonlinear longitudinal waves in pantographic beams

2021 ◽  
pp. 108128652110108
Author(s):  
Emilio Turco ◽  
Emilio Barchiesi ◽  
Francesco dell’Isola
Keyword(s):  
Numerical Simulations ◽  
Mechanical Response ◽  
Integration Scheme ◽  
Present Contribution ◽  
Longitudinal Waves ◽  
Deformation Regime ◽  
Impulsive Loads ◽  
Unit Cells ◽  
Statics And Dynamics ◽  
Equations Of Motions

This contribution presents the results of a campaign of numerical simulations aimed at better understanding the propagation of longitudinal waves in pantographic beams within the large-deformation regime. Initially, we recall the key features of a Lagrangian discrete spring model, which was introduced in previous works and that was tested extensively as capable of accurately forecasting the mechanical response of structures based on the pantographic motif, both in statics and dynamics. Successively, a stepwise integration scheme used to solve equations of motions is briefly discussed. The key content of the present contribution concerns the thorough presentation of some selected numerical simulations, which focus in particular on the propagation of stretch profiles induced by impulsive loads. The study takes into account different tests, by varying the number of unit cells, i.e., the total length of the system, spring stiffnesses, the shape of the impulse, as well as its properties such as duration and peak amplitude, and boundary conditions. Some conjectures about the form of traveling waves are formulated, to be confirmed by both further numerical simulations and analytical investigations.

scholarly journals On Hydromechanical Interaction during Propagation of Localized Damage in Rocks

Minerals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 162
Author(s):  
A.A. Jameei ◽  
S. Pietruszczak
Keyword(s):  
Numerical Study ◽  
Fluid Pressure ◽  
Implicit Time ◽  
Integration Scheme ◽  
Internal Length ◽  
Element Analysis ◽  
Equivalent Permeability ◽  
Mechanical Coupling ◽  
Splitting Test ◽  
Localized Damage

This paper provides a mathematical description of hydromechanical coupling associated with propagation of localized damage. The framework incorporates an embedded discontinuity approach and addresses the assessment of both hydraulic and mechanical properties in the region intercepted by a fracture. Within this approach, an internal length scale parameter is explicitly employed in the definition of equivalent permeability as well as the tangential stiffness operators. The effect of the progressive evolution of damage on the hydro-mechanical coupling is examined and an evolution law is derived governing the variation of equivalent permeability with the continuing deformation. The framework is verified by a numerical study involving 3D simulation of an axial splitting test carried out on a saturated sample under displacement and fluid pressure-controlled conditions. The finite element analysis incorporates the Polynomial-Pressure-Projection (PPP) stabilization technique and a fully implicit time integration scheme.

Geometrically nonlinear static and dynamic analysis of CNT reinforced laminated composite plates: A finite element study

2021 ◽  
pp. 095440622110089
Author(s):  
Balakrishna Adhikari ◽  
BN Singh
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Dynamic Response ◽  
Integration Scheme ◽  
Static And Dynamic Analysis ◽  
Finite Element Study ◽  
Nonlinear Eigenvalues ◽  
Nonlinear Static ◽  
The Impact ◽  
Element Study

In this paper, a finite element study is conducted using the Green Lagrange strain field based on vonKarman assumptions for the geometric nonlinear static and dynamic response of the laminated functionally graded CNT reinforced (FG-CNTRC) composite plate. The governing equations for determining the nonlinear static and dynamic behavior of the FG-CNTRC plate are derived using the Lagrange equation of motion based on Reddy's higher order theory. Using the direct iteration technique, the nonlinear eigenvalues for analyzing the free vibration response are obtained and the nonlinear dynamic responses of the FG-CNTRC plate are encapsulated based on the nonlinear Newmark integration scheme. The impact of the amplitude of vibration on mode switching phenomena and the consequence of the duration of the pulse on the free vibration regime of the plate are outlined. Also, the effect of time dependent loads is studied on the normal stresses of the plate. Furthermore, the impact on the nonlinear static and dynamic response of the laminated FG-CNTRC plate of various parameters such as span-thickness ratio (b/h ratio), aspect ratio (a/b ratio), different edge constraints, CNT fiber gradation, etc. are also studied.

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