scholarly journals A General Method to Compute Numerical Dispersion Error

2021 ◽  
Author(s):  
J. Ruano ◽  
A. Vidal ◽  
J. Rigola ◽  
F. Trias
Keyword(s):  
Numerical Dispersion ◽  
Dispersion Error ◽  
General Method

scholarly journals A Hybrid Smoothed Finite Element Method for Predicting the Sound Field in the Enclosure with High Wave Numbers

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Haitao Wang ◽  
Xiangyang Zeng ◽  
Ye Lei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Sound Field ◽  
Numerical Dispersion ◽  
Computational Accuracy ◽  
Dispersion Error ◽  
High Wave ◽  
Wave Numbers ◽  
Smoothed Finite Element Method ◽  
Element Method

Wave-based methods for acoustic simulations within enclosures suffer the numerical dispersion and then usually have evident dispersion error for problems with high wave numbers. To improve the upper limit of calculating frequency for 3D problems, a hybrid smoothed finite element method (hybrid SFEM) is proposed in this paper. This method employs the smoothing technique to realize the reduction of the numerical dispersion. By constructing a type of mixed smoothing domain, the traditional node-based and face-based smoothing techniques are mixed in the hybrid SFEM to give a more accurate stiffness matrix, which is widely believed to be the ultimate cause for the numerical dispersion error. The numerical examples demonstrate that the hybrid SFEM has better accuracy than the standard FEM and traditional smoothed FEMs under the condition of the same basic elements. Moreover, the hybrid SFEM also has good performance on the computational efficiency. A convergence experiment shows that it costs less time than other comparison methods to achieve the same computational accuracy.

scholarly journals An Artificial Anisotropy Four-Step HIE-FDTD Method With Lower Numerical Dispersion Error

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 199016-199024
Author(s):  
Yong-Dan Kong ◽  
Chu-Bin Zhang ◽  
Hong-Yu Zhang ◽  
Qing-Xin Chu
Keyword(s):  
Fdtd Method ◽  
Numerical Dispersion ◽  
Dispersion Error

Effect of Element Distortion on the Numerical Dispersion of Spectral Element Methods

2011 ◽  
Vol 9 (4) ◽  
pp. 937-958 ◽  
Author(s):  
S.P. Oliveira ◽  
G. Seriani
Keyword(s):  
Finite Element ◽  
Spectral Element ◽  
Accurate Solution ◽  
Error Tolerance ◽  
Numerical Dispersion ◽  
Spectral Element Methods ◽  
Element Mesh ◽  
Dispersion Error ◽  
Numerical Errors ◽  
Double Grid

AbstractSpectral element methods are well established in the field of wave propagation, in particular because they inherit the flexibility of finite element methods and have low numerical dispersion error. The latter is experimentally acknowledged, but has been theoretically shown only in limited cases, such as Cartesian meshes. It is well known that a finite element mesh can contain distorted elements that generate numerical errors for very large distortions. In the present work, we study the effect of element distortion on the numerical dispersion error and determine the distortion range in which an accurate solution is obtained for a given error tolerance. We also discuss a double-grid calculation of the spectral element matrices that preserves accuracy in deformed geometries.

Reduction of Numerical Dispersion Error in 3-D ADI-MRTD Method With the Coarse Mesh

2009 ◽  
Vol 19 (8) ◽  
pp. 485-487 ◽  
Author(s):  
Jaejong Ryu ◽  
Wuseong Lee ◽  
Jugab Lee ◽  
Yeonkwan Moon ◽  
Hachul Kim ◽  
...  
Keyword(s):  
Numerical Dispersion ◽  
Coarse Mesh ◽  
Dispersion Error

Dispersion Error Reduction for Acoustic Problems Using the Finite Element-Least Square Point Interpolation Method

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
L. Y. Yao ◽  
J. W. Zhou ◽  
Z. Zhou ◽  
L. Li
Keyword(s):  
Finite Element ◽  
Interpolation Method ◽  
Local Approximation ◽  
Least Square ◽  
Numerical Dispersion ◽  
Benchmark Problems ◽  
Shape Functions ◽  
Dispersion Error ◽  
Point Interpolation Method ◽  
Point Interpolation

The shape function of the finite element-least square point interpolation method (FE-LSPIM) combines the quadrilateral element for partition of unity and the least square point interpolation method (LSPIM) for local approximation, and inherits the completeness properties of meshfree shape functions and the compatibility properties of FE shape functions, and greatly reduces the numerical dispersion error. This paper derives the formulas and performs the dispersion analysis for the FE-LSPIM. Numerical results for benchmark problems show that, the FE-LSPIM yields considerably better results than the finite element method (FEM) and element-free Galerkin method (EFGM).

scholarly journals An Efficient Numerical Formulation for Wave Propagation in Magnetized Plasma Using PITD Method

Electronics ◽  
2020 ◽  
Vol 9 (10) ◽  
pp. 1575 ◽  
Author(s):  
Zhen Kang ◽  
Ming Huang ◽  
Weilin Li ◽  
Yufeng Wang ◽  
Fang Yang
Keyword(s):  
Wave Propagation ◽  
Time Domain ◽  
Fdtd Method ◽  
Magnetized Plasma ◽  
Numerical Dispersion ◽  
Step Size ◽  
Time Step ◽  
Precise Integration ◽  
Dispersion Error ◽  
Time Step Size

A modified precise-integration time-domain (PITD) formulation is presented to model the wave propagation in magnetized plasma based on the auxiliary differential equation (ADE). The most prominent advantage of this algorithm is using a time-step size which is larger than the maximum value of the Courant–Friedrich–Levy (CFL) condition to achieve the simulation with a satisfying accuracy. In this formulation, Maxwell’s equations in magnetized plasma are obtained by using the auxiliary variables and equations. Then, the spatial derivative is approximated by the second-order finite-difference method only, and the precise integration (PI) scheme is used to solve the resulting ordinary differential equations (ODEs). The numerical stability and dispersion error of this modified method are discussed in detail in magnetized plasma. The stability analysis validates that the simulated time-step size of this method can be chosen much larger than that of the CFL condition in the finite-difference time-domain (FDTD) simulations. According to the numerical dispersion analysis, the range of the relative error in this method is 10−6 to 5×10−4 when the electromagnetic wave frequency is from 1 GHz to 100 GHz. More particularly, it should be emphasized that the numerical dispersion error is almost invariant under different time-step sizes which is similar to the conventional PITD method in the free space. This means that with the increase of the time-step size, the presented method still has a lower computational error in the simulations. Numerical experiments verify that the presented method is reliable and efficient for the magnetized plasma problems. Compared with the formulations based on the FDTD method, e.g., the ADE-FDTD method and the JE convolution FDTD (JEC-FDTD) method, the modified algorithm in this paper can employ a larger time step and has simpler iterative formulas so as to reduce the execution time. Moreover, it is found that the presented method is more accurate than the methods based on the FDTD scheme, especially in the high frequency range, according to the results of the magnetized plasma slab. In conclusion, the presented method is efficient and accurate for simulating the wave propagation in magnetized plasma.

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