1 Embedded Spatial Discretization Methods to Itera-tive Splitting Methods

2011 ◽  
pp. 109-115
Keyword(s):  
Splitting Methods ◽  
Spatial Discretization ◽  
Discretization Methods

A New Global Spatial Discretization Method for Calculating Dynamic Responses of Two-Dimensional Continuous Systems With Application to a Rectangular Kirchhoff Plate

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
K. Wu ◽  
W. D. Zhu
Keyword(s):  
Boundary Conditions ◽  
Continuous System ◽  
Dynamic Responses ◽  
Kirchhoff Plate ◽  
Continuous Systems ◽  
Discretization Method ◽  
Two Dimensional ◽  
Spatial Discretization ◽  
Arbitrary Boundary ◽  
Discretization Methods

A new global spatial discretization method (NGSDM) is developed to accurately calculate natural frequencies and dynamic responses of two-dimensional (2D) continuous systems such as membranes and Kirchhoff plates. The transverse displacement of a 2D continuous system is separated into a 2D internal term and a 2D boundary-induced term; the latter is interpolated from one-dimensional (1D) boundary functions that are further divided into 1D internal terms and 1D boundary-induced terms. The 2D and 1D internal terms are chosen to satisfy prescribed boundary conditions, and the 2D and 1D boundary-induced terms use additional degrees-of-freedom (DOFs) at boundaries to ensure satisfaction of all the boundary conditions. A general formulation of the method that can achieve uniform convergence is established for a 2D continuous system with an arbitrary domain shape and arbitrary boundary conditions, and it is elaborated in detail for a general rectangular Kirchhoff plate. An example of a rectangular Kirchhoff plate that has three simply supported boundaries and one free boundary with an attached Euler–Bernoulli beam is investigated using the developed method and results are compared with those from other global and local spatial discretization methods. Advantages of the new method over local spatial discretization methods are much fewer DOFs and much less computational effort, and those over the assumed modes method (AMM) are better numerical property, a faster calculation speed, and much higher accuracy in calculation of bending moments and transverse shearing forces that are related to high-order spatial derivatives of the displacement of the plate with an edge beam.

Spatial Discretization Methods for Air Gap Permeance Calculations in Double Salient Traction Motors

2012 ◽  
Vol 48 (6) ◽  
pp. 2165-2172 ◽  
Author(s):  
Esin Ilhan ◽  
Maarten F. J. Kremers ◽  
Emilia T. Motoasca ◽  
Johan J. H. Paulides ◽  
Elena A. Lomonova
Keyword(s):  
Air Gap ◽  
Spatial Discretization ◽  
Discretization Methods ◽  
Traction Motors

scholarly journals A Full Space-Time Convergence Order Analysis of Operator Splittings for Linear Dissipative Evolution Equations

2016 ◽  
Vol 19 (5) ◽  
pp. 1302-1316 ◽  
Author(s):  
Eskil Hansen ◽  
Erik Henningsson
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Experiments ◽  
Evolution Equations ◽  
Diffusion Problem ◽  
Splitting Methods ◽  
Spatial Discretization ◽  
Order Analysis ◽  
Convergence Results ◽  
Convergence Orders

AbstractThe Douglas-Rachford and Peaceman-Rachford splitting methods are common choices for temporal discretizations of evolution equations. In this paper we combine these methods with spatial discretizations fulfilling some easily verifiable criteria. In the setting of linear dissipative evolution equations we prove optimal convergence orders, simultaneously in time and space. We apply our abstract results to dimension splitting of a 2D diffusion problem, where a finite element method is used for spatial discretization. To conclude, the convergence results are illustrated with numerical experiments.

scholarly journals Dynamics of Structures with Distributed Gyroscopes: Modal Discretization Versus Spatial Discretization

2019 ◽  
Vol 10 (1) ◽  
pp. 160
Author(s):  
Xiao-Dong Yang ◽  
Bao-Yin Xie ◽  
Wei Zhang ◽  
Quan Hu
Keyword(s):  
Numerical Methods ◽  
Natural Frequencies ◽  
Computational Time ◽  
Discretization Method ◽  
Spatial Discretization ◽  
Gyroscopic Effect ◽  
Discretization Methods ◽  
Irregular Structures ◽  
Complex Modes ◽  
Base Structure

In this study, two discretization numerical methods, modal discretization and spatial discretization methods, were proposed and compared when applied to the gyroscopic structures. If the distributed gyroscopes are attached, the general numerical methods should be modified to derive the natural frequencies and complex modes due to the gyroscopic effect. The modal discretization method can be used for cases where the modal functions of the base structure can be expressed in explicit forms, while the spatial discretization method can be used in irregular structures without modal functions, but cost more computational time. The convergence and efficiency of both modal and spatial discretization techniques are illustrated by an example of a beam with uniformly distributed gyroscopes. The investigation of this paper may provide useful techniques to study structures with distributed inertial components.

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