共查询到20条相似文献,搜索用时 31 毫秒
1.
Xian Ma Yongxian Wang Xiaoqian Zhu Wei Liu Wenbin Xiao Qiang Lan 《Entropy (Basel, Switzerland)》2021,23(9)
The accuracy and efficiency of sound field calculations highly concern issues of hydroacoustics. Recently, one-dimensional spectral methods have shown high-precision characteristics when solving the sound field but can solve only simplified models of underwater acoustic propagation, thus their application range is small. Therefore, it is necessary to directly calculate the two-dimensional Helmholtz equation of ocean acoustic propagation. Here, we use the Chebyshev–Galerkin and Chebyshev collocation methods to solve the two-dimensional Helmholtz model equation. Then, the Chebyshev collocation method is used to model ocean acoustic propagation because, unlike the Galerkin method, the collocation method does not need stringent boundary conditions. Compared with the mature Kraken program, the Chebyshev collocation method exhibits a higher numerical accuracy. However, the shortcoming of the collocation method is that the computational efficiency cannot satisfy the requirements of real-time applications due to the large number of calculations. Then, we implemented the parallel code of the collocation method, which could effectively improve calculation effectiveness. 相似文献
2.
K.-Y. LEEA.A. RENSHAW 《Journal of sound and vibration》2002,258(4):725-739
The spectral collocation method is used to determine the stability of parametrically excited systems and compared with the traditional transition matrix approach. Results from a series of test problems demonstrate that spectral collocation converges rapidly. In addition, the spectral collocation method preserves the sparsity of the underlying system matrices, a property not shared by the transition matrix approach. As a result, spectral collocation can be used for very large systems and can utilize sparse eigensolvers to reduce computational memory and time. For the large-scale system studied (up to 40 degrees of freedom), the spectral collocation method was on average an order of magnitude faster than the transition matrix approach using Matlab. This computational advantage is implementation specific; in a C implementation of the algorithm, the transition matrix method is faster than the spectral collocation. Overall, the method proves to be simple, efficient, reliable, and generally competitive with the transition matrix method. 相似文献
3.
A least-squares collocation meshless method is employed for solving the radiative heat transfer in absorbing, emitting and scattering media. The least-squares collocation meshless method for radiative transfer is based on the discrete ordinates equation. A moving least-squares approximation is applied to construct the trial functions. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three numerical examples are studied to illustrate the performance of this new solution method. The numerical results are compared with the other benchmark approximate solutions. By comparison, the results show that the least-squares collocation meshless method is efficient, accurate and stable, and can be used for solving the radiative heat transfer in absorbing, emitting and scattering media. 相似文献
4.
We discuss the Crank–Nicolson and Laplace modified alternating direction implicit Legendre and Chebyshev spectral collocation methods for a linear, variable coefficient, parabolic initial-boundary value problem on a rectangular domain with the solution subject to non-zero Dirichlet boundary conditions. The discretization of the problems by the above methods yields matrices which possess banded structures. This along with the use of fast Fourier transforms makes the cost of one step of each of the Chebyshev spectral collocation methods proportional, except for a logarithmic term, to the number of the unknowns. We present the convergence analysis for the Legendre spectral collocation methods in the special case of the heat equation. Using numerical tests, we demonstrate the second order accuracy in time of the Chebyshev spectral collocation methods for general linear variable coefficient parabolic problems. 相似文献
5.
Mustafa Gü lsu Yalç ın Ö ztü rk & Ayşe Anapali 《advances in applied mathematics and mechanics.》2013,5(6):872-884
In this article, we have introduced a Taylor collocation method,
which is based on collocation method for solving fractional Riccati
differential equation. The fractional derivatives are described in
the Caputo sense. This method is based on first taking the truncated
Taylor expansions of the solution function in the fractional Riccati
differential equation and then substituting their matrix forms into
the equation. Using collocation points, the systems of nonlinear
algebraic equation are derived. We further solve the system of
nonlinear algebraic equation using Maple 13 and thus obtain the
coefficients of the generalized Taylor expansion. Illustrative
examples are presented to demonstrate the effectiveness of the
proposed method. 相似文献
6.
Huajun Zhu Songhe Song & Yaming Chen 《advances in applied mathematics and mechanics.》2011,3(6):663-688
In this paper, we develop a multi-symplectic wavelet collocation method for
three-dimensional (3-D) Maxwell's equations. For the multi-symplectic formulation
of the equations, wavelet collocation method based on autocorrelation functions
is applied for spatial discretization and appropriate symplectic scheme is employed
for time integration. Theoretical analysis shows that the proposed method is
multi-symplectic, unconditionally stable and energy-preserving under periodic
boundary conditions. The numerical dispersion relation is investigated. Combined
with splitting scheme, an explicit splitting symplectic wavelet collocation method
is also constructed. Numerical experiments illustrate that the proposed methods are
efficient, have high spatial accuracy and can preserve energy conservation laws exactly. 相似文献
7.
Collocation Methods for a Class of Volterra Integral Functional Equations with Multiple Proportional Delays 下载免费PDF全文
Kai Zhang & Jie Li 《advances in applied mathematics and mechanics.》2012,4(5):575-602
In this paper, we apply the collocation methods to a class of
Volterra integral functional equations with multiple proportional
delays (VIFEMPDs). We shall present the existence, uniqueness and
regularity properties of analytic solutions for this type of equations,
and then analyze the convergence orders of the collocation solutions
and give corresponding error estimates. The numerical results verify
our theoretical analysis. 相似文献
8.
A stochastic collocation method is proposed to investigate the secondary bifurcation of a two-dimensional aeroelastic system with structural nonlinearity represented by cubic restoring forces, and uncertainties expressed by random parameters in the cubic stiffness coefficient and in the initial pitch angle. The accuracy of the stochastic collocation method is improved by incorporating higher order schemes, such as piecewise cubic interpolation and piecewise cubic spline interpolation, instead of a piecewise linear interpolation formula. For an aeroelastic problem with the uncertainty expressed by a time dependent combination of five random variables, an efficient collocation method is developed using a sparse grid approach with a dimension adaptive strategy. Numerical simulations are carried out to demonstrate the effectiveness of the proposed method for long term computation and discontinuous problems. 相似文献
9.
In this paper, we combine Carrera's Unified Formulation and a radial basis function collocation technique for predicting the static deformations and free vibration behavior of thin and thick isotropic and cross-ply laminated plates. Through numerical experiments, the capability and efficiency of this collocation technique for static and vibration problems are demonstrated, and the numerical accuracy and convergence are thoughtfully examined. 相似文献
10.
提出了一种基于工艺参数扰动的随机点匹配时延评估算法.该算法通过Cholesky分解将具有强相关性的工艺随机扰动转化为独立随机变量,并结合随机点匹配方法和多项式混沌理论对耦合随机互连线模型进行时延分析.最后,利用数值计算方法给出互连时延的有限维表达式.仿真实验结果表明,该算法与HSPICE仿真时延的相对误差不超过2%,且相比于HSPICE显著降低了电路模拟时间.
关键词:
工艺参数扰动
随机互连模型
随机点匹配方法
多项式混沌理论 相似文献
11.
We analyze a least-squares asymmetric radial basis function
collocation method for solving the modified Helmholtz equations. In
the theoretical part, we proved the convergence of the proposed
method providing that the collocation points are sufficiently dense.
For numerical verification, direct solver and a subspace selection
process for the trial space (the so-called adaptive greedy
algorithm) is employed, respectively, for small and large scale
problems. 相似文献
12.
13.
本文用Fourier拟谱配点方法求解有广泛应用的以对数核为主部的第一类边界积分方程,文中通过对积分算子的象征作拟谱插值来建立近似方程,利用快速Fourier变换将计算切换到频率空间进行。本文计算结果表明,用上述拟谱配点方法计算的数值精度较Galerkin配点法更为满意。 相似文献
14.
15.
In this article, Sinc collocation method is considered to obtain the numerical
solution of integral algebraic equation of index-1 by reducing it to an explicit system
of algebraic equation. It is shown that Sinc collocation solution can produce an error
of order $\mathcal{O}(√Ne^{−k√N})$. Moreover, Sinc method is applied to several examples to
illustrate the accuracy and implementation of the method. 相似文献
16.
提出一种求解二维功能梯度材料(FGMs)稳态热传导问题的重心Lagrange插值配点法.基于Chebyshev节点构造二维重心Lagrange插值函数及其偏导数,然后基于配点法将其直接代入FGMs热传导问题的控制方程和边界条件,得到系统离散方程.重心Lagrange插值配点法是一种真正的无网格方法,很好地融合了重心Lagrange插值和配点格式的优势,具有高效、稳定、高精度和易于数值实现的优点.采用重心Lagrange插值配点法分别对指数型、二次型和三角型FGMs热传导问题进行数值模拟.结果表明:该方法具有较高的计算效率和计算精度,对材料梯度参数的变化不敏感.可以进一步拓展到FGMs瞬态问题和FGMs的热力耦合分析. 相似文献
17.
将Chebyshev谱配置法和基于非均匀网格的高阶FD-q差分格式运用于磁流体方腔槽道流整体线性稳定性研究,比较两类数值方法的优缺点.Chebyshev谱配置法收敛快且精度高,但需要构造非常庞大的满矩阵,存储量和计算开销巨大;高阶FD-q差分格式采用了基于Kosloff-Tal-Ezer变换的Chebyshev谱配置点作为离散网格,在保持较高网格收敛精度的同时,差分格式可以采用稀疏矩阵进行存储,显著降低了存储量和计算开销.相比传统的谱配置法,基于非均匀网格的高阶FD-q差分格式计算效率得到显著的提升,将高阶FD-q差分格式运用于非正则模线性最优瞬态增长的计算,计算效果良好. 相似文献
18.
In recent years, there has been a growing interest in analyzing and quantifying the effects of random inputs in the solution of ordinary/partial differential equations. To this end, the spectral stochastic finite element method (SSFEM) is the most popular method due to its fast convergence rate. Recently, the stochastic sparse grid collocation method has emerged as an attractive alternative to SSFEM. It approximates the solution in the stochastic space using Lagrange polynomial interpolation. The collocation method requires only repetitive calls to an existing deterministic solver, similar to the Monte Carlo method. However, both the SSFEM and current sparse grid collocation methods utilize global polynomials in the stochastic space. Thus when there are steep gradients or finite discontinuities in the stochastic space, these methods converge very slowly or even fail to converge. In this paper, we develop an adaptive sparse grid collocation strategy using piecewise multi-linear hierarchical basis functions. Hierarchical surplus is used as an error indicator to automatically detect the discontinuity region in the stochastic space and adaptively refine the collocation points in this region. Numerical examples, especially for problems related to long-term integration and stochastic discontinuity, are presented. Comparisons with Monte Carlo and multi-element based random domain decomposition methods are also given to show the efficiency and accuracy of the proposed method. 相似文献
19.
In this article the Legendre multiwavelet basis with aid of collocation method has been applied to give approximate solution for fractional delay systems. The properties of Legendre multiwavelet are presented. These properties together with the collocation method are then utilized to reduce the problem to the solution of algebraic system. Numerical results and comparison with exact solutions in the cases when we have exact solution are given in test examples in order to demonstrate the applicability and efficiency of the method. 相似文献