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A Compact Explicit Difference Scheme of High Accuracy for Extended Boussinesq Equations
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作者 周俊陶 林建国 谢志华 《China Ocean Engineering》 SCIE EI 2007年第3期507-514,共8页
Presented here is a compact explicit difference scheme of high accuracy for solving the extended Boussinesq equations. For time discretization, a three-stage explicit Runge-Kutta method with TVD property is used at pr... Presented here is a compact explicit difference scheme of high accuracy for solving the extended Boussinesq equations. For time discretization, a three-stage explicit Runge-Kutta method with TVD property is used at predicting stage, a cubic spline function is adopted at correcting stage, which made the time discretization accuracy up to fourth order; For spatial discretization, a three-point explicit compact difference scheme with arbitrary order accuracy is employed. The extended Boussinesq equations derived by Beji and Nadaoka are solved by the proposed scheme. The numerical results agree well with the experimental data. At the same time, the comparisons of the two numerical results between the present scheme and low accuracy difference method are made, which further show the necessity of using high accuracy scheme to solve the extended Boussinesq equations. As a valid sample, the wave propagation on the rectangular step is formulated by the present scheme, the modelled results are in better agreement with the experimental data than those of Kittitanasuan. 展开更多
关键词 high accuracy numerical simulation compact explicit difference scheme extended Boussinesq equations
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Numerical modeling of wave equation by a truncated high-order finite-difference method 被引量:4
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作者 Yang Liu Mrinal K. Sen 《Earthquake Science》 CSCD 2009年第2期205-213,共9页
Finite-difference methods with high-order accuracy have been utilized to improve the precision of numerical solution for partial differential equations. However, the computation cost generally increases linearly with ... Finite-difference methods with high-order accuracy have been utilized to improve the precision of numerical solution for partial differential equations. However, the computation cost generally increases linearly with increased order of accuracy. Upon examination of the finite-difference formulas for the first-order and second-order derivatives, and the staggered finite-difference formulas for the first-order derivative, we examine the variation of finite-difference coefficients with accuracy order and note that there exist some very small coefficients. With the order increasing, the number of these small coefficients increases, however, the values decrease sharply. An error analysis demonstrates that omitting these small coefficients not only maintain approximately the same level of accuracy of finite difference but also reduce computational cost significantly. Moreover, it is easier to truncate for the high-order finite-difference formulas than for the pseudospectral for- mulas. Thus this study proposes a truncated high-order finite-difference method, and then demonstrates the efficiency and applicability of the method with some numerical examples. 展开更多
关键词 finite difference high-order accuracy TRUNCATION EFFICIENCY numerical modeling
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A COUPLING METHOD OF DIFFERENCE WITH HIGH ORDER ACCURACY AND BOUNDARY INTEGRAL EQUATION FOR EVOLUTIONARY EQUATION AND ITS ERROR ESTIMATES
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作者 羊丹平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1991年第9期891-905,共15页
In the present paper, a new numerical method for solving initial-boundary value problems of evolutionary equations is proposed and studied, combining difference method with high accuracy with boundary integral equatio... In the present paper, a new numerical method for solving initial-boundary value problems of evolutionary equations is proposed and studied, combining difference method with high accuracy with boundary integral equation method. The numerical approximate schemes for both problems on a bounded or unbounded domain in R3 are proposed and their prior error estimates are obtained. 展开更多
关键词 difference with high order accuracy boundary finite element evolutionary equation error estimates
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High Order of Accuracy for Poisson Equation Obtained by Grouping of Repeated Richardson Extrapolation with Fourth Order Schemes
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作者 Luciano Pereira da Silva Bruno Benato Rutyna +1 位作者 Aline Roberta Santos Righi Marcio Augusto Villela Pinto 《Computer Modeling in Engineering & Sciences》 SCIE EI 2021年第8期699-715,共17页
In this article,we improve the order of precision of the two-dimensional Poisson equation by combining extrapolation techniques with high order schemes.The high order solutions obtained traditionally generate non-spar... In this article,we improve the order of precision of the two-dimensional Poisson equation by combining extrapolation techniques with high order schemes.The high order solutions obtained traditionally generate non-sparse matrices and the calculation time is very high.We can obtain sparse matrices by applying compact schemes.In this article,we compare compact and exponential finite difference schemes of fourth order.The numerical solutions are calculated in quadruple precision(Real*16 or extended precision)in FORTRAN language,and iteratively obtained until reaching the round-off error magnitude around 1.0E−32.This procedure is performed to ensure that there is no iteration error.The Repeated Richardson Extrapolation(RRE)method combines numerical solutions in different grids,determining higher orders of accuracy.The main contribution of this work is based on a process that initializes with fourth order solutions combining with RRE in order to find solutions of sixth,eighth,and tenth order of precision.The multigrid Full Approximation Scheme(FAS)is also applied to accelerate the convergence and obtain the numerical solutions on the fine grids. 展开更多
关键词 Tenth order accuracy RRE compact scheme exponential scheme MULTIGRID finite difference
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Optimization of a global seventh-order dissipative compact finite-difference scheme by a genetic algorithm
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作者 Yu LIN Yaming CHEN +1 位作者 Chuanfu XU Xiaogang DENG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2018年第11期1679-1690,共12页
A global seventh-order dissipative compact finite-difference scheme is optimized in terms of time stability. The dissipative parameters appearing in the boundary closures are assumed to be different, resulting in an o... A global seventh-order dissipative compact finite-difference scheme is optimized in terms of time stability. The dissipative parameters appearing in the boundary closures are assumed to be different, resulting in an optimization problem with several parameters determined by applying a generic algorithm. The optimized schemes are analyzed carefully from the aspects of the eigenvalue distribution, the ε-pseudospectra, the short time behavior, and the Fourier analysis. Numerical experiments for the Euler equations are used to show the effectiveness of the final recommended scheme. 展开更多
关键词 high-ORDER dissipative compact finite-difference scheme genetic algorithm time stable
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A new alternating group explicit-implicit algorithm with high accuracy for dispersive equation
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作者 张青洁 王文洽 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第9期1221-1230,共10页
In this paper, a new alternating group explicit-implicit (nAGEI) scheme for dispersive equations with a periodic boundary condition is derived. This new unconditionally stable scheme has a fourth-order truncation er... In this paper, a new alternating group explicit-implicit (nAGEI) scheme for dispersive equations with a periodic boundary condition is derived. This new unconditionally stable scheme has a fourth-order truncation error in space and a convergence ratio faster than some known alternating methods such as ASEI and AGE. Comparison in accuracy with the AGEI and AGE methods is presented in the numerical experiment. 展开更多
关键词 Dispersive equation finite difference alternating group explicit-implicitmethod (nAGEI) high accuracy unconditional stability parallel computation.
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A High-Order Compact Scheme with Square-Conservativity
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作者 季仲贞 李京 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 1998年第4期150-154,共5页
In order to improve the accuracy of forecasts of atmospheric and oceanic phenomena which possess a wide range of space and time scales, it is crucial to design the high-order and stable schemes. On the basis of the ex... In order to improve the accuracy of forecasts of atmospheric and oceanic phenomena which possess a wide range of space and time scales, it is crucial to design the high-order and stable schemes. On the basis of the explicit square-conservative scheme, a high-order compact explicit square-conservative scheme is proposed in this paper. This scheme not only keeps the square-conservative characteristics, but also is of high accuracy. The numerical example shows that this scheme has less computing errors and better computational stability, and it could be considered to be tested and used in many atmospheric and oceanic problems. 展开更多
关键词 Square conservative scheme compact difference high accuracy scheme
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含新型间断探测器的混合WCNS格式在间断无粘可压流的应用
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作者 张昊 邓小刚 《国防科技大学学报》 EI CAS CSCD 北大核心 2024年第1期1-11,共11页
为了让高精度数值格式在含间断和小尺度涡等复杂结构的超声速无粘可压缩流动情况下,仍能鲁棒地捕捉激波并快速得到流场高保真的模拟结果,研究了以子模板导数组合为基础的光滑度量算法,构造了精度与鲁棒性兼顾的新型间断探测器,使间断识... 为了让高精度数值格式在含间断和小尺度涡等复杂结构的超声速无粘可压缩流动情况下,仍能鲁棒地捕捉激波并快速得到流场高保真的模拟结果,研究了以子模板导数组合为基础的光滑度量算法,构造了精度与鲁棒性兼顾的新型间断探测器,使间断识别对小尺度涡也具有高分辨率;研究了混合加权紧致非线性格式(weighted compact nonlinear scheme, WCNS)方法,对流场中的光滑与间断区域分别使用线性与非线性加权格式求解,从而克服单一非线性格式在光滑区分辨率难以达到设计精度的问题。数值实验表明,使用新型间断探测器的混合WCNS格式对一维、二维Euler方程模拟结果良好,并且相比于在全流场使用局部特征分解的原始WCNS方法有计算效率的提高。 展开更多
关键词 激波捕捉 问题单元识别 有限差分法 高精度格式 双曲守恒律 无粘流动
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一类椭圆型Dirichlet边值问题的高精度Richardson外推法 被引量:1
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作者 李曹杰 张海湘 杨雪花 《湖南工业大学学报》 2024年第1期91-97,104,共8页
针对椭圆型偏微分方程,先建立四阶和六阶精度的紧致差分格式,在此基础上用Richardson外推法,得到其六阶和八阶精度的外推差分格式。并通过两个Poisson方程算例,验算已建立的差分格式。数值算例结果表明,基于紧致差分格式的Richardson外... 针对椭圆型偏微分方程,先建立四阶和六阶精度的紧致差分格式,在此基础上用Richardson外推法,得到其六阶和八阶精度的外推差分格式。并通过两个Poisson方程算例,验算已建立的差分格式。数值算例结果表明,基于紧致差分格式的Richardson外推法能够得到有效的、健壮的高精度数值解。 展开更多
关键词 计算数学 椭圆型偏微分方程 紧致差分格式 RICHARDSON外推法 高阶精度
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带间断非线性定常对流扩散方程的高精度解法
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作者 陈雪钦 王晓峰 晏云 《莆田学院学报》 2024年第5期33-38,共6页
针对一类带有间断系数的非线性定常对流扩散方程,提出了一种高精度的紧致有限差分方法;该方法在内点处采用的是三点四阶的差分格式,在边界点与间断点处采用的是两点三阶的差分格式;给出的数值算例表明这种新的方法整体求解精度可以达到... 针对一类带有间断系数的非线性定常对流扩散方程,提出了一种高精度的紧致有限差分方法;该方法在内点处采用的是三点四阶的差分格式,在边界点与间断点处采用的是两点三阶的差分格式;给出的数值算例表明这种新的方法整体求解精度可以达到四阶。 展开更多
关键词 非线性对流项 对流扩散方程 高精度 间断 定常 有限差分
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Analysis on Sixth-Order Compact Approximations with Richardson Extrapolation for 2D Poisson Equation
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作者 Ruxin Dai Pengpeng Lin 《Journal of Applied Mathematics and Physics》 2018年第6期1139-1159,共21页
By using Richardson extrapolation and fourth-order compact finite difference scheme on different scale grids, a sixth-order solution is computed on the coarse grid. Other three techniques are applied to obtain a sixth... By using Richardson extrapolation and fourth-order compact finite difference scheme on different scale grids, a sixth-order solution is computed on the coarse grid. Other three techniques are applied to obtain a sixth-order solution on the fine grid, and thus give out three kinds of Richardson extrapolation-based sixth order compact computation methods. By carefully analyzing the truncation errors respectively on 2D Poisson equation, we compare the accuracy of these three sixth order methods theoretically. Numerical results for two test problems are discussed. 展开更多
关键词 RICHARDSON EXTRAPOLATION Sixth-Order Solutions high Order compact finite Difference Scheme TRUNCATION Error ANALYSIS 2D Poisson Equation
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时间-空间高阶精度矩形交错网格隐式有限差分声波正演模拟 被引量:4
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作者 王静 刘洋 周泓宇 《地球物理学报》 SCIE EI CAS CSCD 北大核心 2023年第1期368-382,共15页
有限差分方法因其操作简单、计算消耗低而成为地震勘探领域中最为常用的数值模拟方法之一,然而用离散的显式差分算子数值逼近地震波动方程中的连续导数容易导致数值频散,并且基于正方形网格离散形式的有限差分方法对不同地质模型的适应... 有限差分方法因其操作简单、计算消耗低而成为地震勘探领域中最为常用的数值模拟方法之一,然而用离散的显式差分算子数值逼近地震波动方程中的连续导数容易导致数值频散,并且基于正方形网格离散形式的有限差分方法对不同地质模型的适应性较低.针对一阶变密度声波方程的数值模拟,本文发展了一种适用于矩形网格离散形式的时间高阶空间隐式有限差分格式,可以有效压制时间和空间频散,同时灵活的网格剖分增强了其应用的广泛性.基于本文矩形交错网格时间高阶空间隐式有限差分格式的时空域频散关系和变量替换的思想,首先采用泰勒级数展开方法求解不同方向的非轴上时间差分系数及轴上空间差分系数,使本文差分格式可以获得任意偶数阶时间和空间精度.为了进一步提高本文差分格式在更大波数区域的空间模拟精度,我们采用线性优化方法来求取新的轴上空间差分系数用于一阶变密度声波方程的波场迭代求解中.频散、稳定性分析及数值模拟算例表明:相比于传统十字形空间域隐式有限差分格式,本文矩形交错网格时间高阶空间隐式有限差分格式在精度、稳定性和效率方面均具有优势. 展开更多
关键词 矩形交错网格 隐式有限差分 线性优化算法 时间、空间高阶精度
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A New Fourth Order Difference Approximation for the Solution of Three-dimensional Non-linear Biharmonic Equations Using Coupled Approach
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作者 Ranjan Kumar Mohanty Mahinder Kumar Jain Biranchi Narayan Mishra 《American Journal of Computational Mathematics》 2011年第4期318-327,共10页
This paper deals with a new higher order compact difference scheme, which is, O(h4) using coupled approach on the 19-point 3D stencil for the solution of three dimensional nonlinear biharmonic equations. At each inter... This paper deals with a new higher order compact difference scheme, which is, O(h4) using coupled approach on the 19-point 3D stencil for the solution of three dimensional nonlinear biharmonic equations. At each internal grid point, the solution u(x,y,z) and its Laplacian Δ4u are obtained. The resulting stencil algo-rithm is presented and hence this new algorithm can be easily incorporated to solve many problems. The present discretization allows us to use the Dirichlet boundary conditions only and there is no need to discretize the derivative boundary conditions near the boundary. We also show that special treatment is required to handle the boundary conditions. Convergence analysis for a model problem is briefly discussed. The method is tested on three problems and compares very favourably with the corresponding second order approximation which we also discuss using coupled approach. 展开更多
关键词 THREE-DIMENSIONAL NON-LINEAR BIHARMONIC Equation finite Differences Fourth Order accuracy compact Discretization Block-Block-Tridiagonal Tangential Derivatives Laplacian Stream Function REYNOLDS Number
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Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media using Compact High Order Schemes 被引量:2
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作者 Steven Britt Semyon Tsynkov Eli Turkel 《Communications in Computational Physics》 SCIE 2011年第3期520-541,共22页
In many problems,one wishes to solve the Helmholtz equation with variable coefficients within the Laplacian-like term and use a high order accurate method(e.g.,fourth order accurate)to alleviate the points-per-wavelen... In many problems,one wishes to solve the Helmholtz equation with variable coefficients within the Laplacian-like term and use a high order accurate method(e.g.,fourth order accurate)to alleviate the points-per-wavelength constraint by reducing the dispersion errors.The variation of coefficients in the equation may be due to an inhomogeneous medium and/or non-Cartesian coordinates.This renders existing fourth order finite difference methods inapplicable.We develop a new compact scheme that is provably fourth order accurate even for these problems.We present numerical results that corroborate the fourth order convergence rate for several model problems. 展开更多
关键词 Helmholtz equation variable coefficients high order accuracy compact finite differences
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求解扩散方程的一种高精度隐式差分方法 被引量:19
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作者 葛永斌 田振夫 +1 位作者 詹咏 吴文权 《上海理工大学学报》 EI CAS 北大核心 2005年第2期107-110,119,共5页
利用一阶微商和二阶微商的四阶紧致差分逼近公式,推导出了数值求解一维扩散方程的两种新的高精度隐式紧致差分格式,其截断误差分别为O(τ2+h4)和O(τ4+h4).通过Fourier分析方法证明了格式O(τ2+h4)是无条件稳定的,而格式O(τ4+h4)是无... 利用一阶微商和二阶微商的四阶紧致差分逼近公式,推导出了数值求解一维扩散方程的两种新的高精度隐式紧致差分格式,其截断误差分别为O(τ2+h4)和O(τ4+h4).通过Fourier分析方法证明了格式O(τ2+h4)是无条件稳定的,而格式O(τ4+h4)是无条件不稳定的.并且由于每一时间层上只用到了3个网格点,所以差分方程可采用追赶法直接进行求解. 展开更多
关键词 扩散方程 紧致隐格式 高精度 差分方法
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含源项非定常对流扩散方程的高精度紧致隐式差分方法 被引量:25
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作者 葛永斌 田振夫 吴文权 《水动力学研究与进展(A辑)》 CSCD 北大核心 2006年第5期619-625,共7页
提出了数值求解含源项非定常对流扩散方程的一种高精度紧致隐式差分方法,其空间为四阶精度,时间为二阶精度。由于每一时间层上只用到了三个网格点,所以差分方程为三对角型的,可采用追赶法进行求解。数值实验结果验证了本文方法的精确性... 提出了数值求解含源项非定常对流扩散方程的一种高精度紧致隐式差分方法,其空间为四阶精度,时间为二阶精度。由于每一时间层上只用到了三个网格点,所以差分方程为三对角型的,可采用追赶法进行求解。数值实验结果验证了本文方法的精确性和可靠性。 展开更多
关键词 非定常对流扩散方程 紧致隐格式 高精度 差分方法
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三维泊松方程的高精度多重网格解法 被引量:18
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作者 葛永斌 田振夫 马红磊 《应用数学》 CSCD 北大核心 2006年第2期313-318,共6页
利用对称网格点泰勒展开式中各阶导数项明显的对称性,得到了数值求解三维泊松方程的四阶和六阶精度的紧致差分格式,其推导过程简便直接.为了克服传统迭代法在求解高维问题时计算量大、收敛速度慢的缺陷,采用了多重网格加速技术,设计了... 利用对称网格点泰勒展开式中各阶导数项明显的对称性,得到了数值求解三维泊松方程的四阶和六阶精度的紧致差分格式,其推导过程简便直接.为了克服传统迭代法在求解高维问题时计算量大、收敛速度慢的缺陷,采用了多重网格加速技术,设计了相应的多重网格算法,求解了三维泊松方程的Dirichlet边值问题.数值实验结果表明,本文所提出的高精度紧致格式达到了期望的精度并且多重网格方法的加速效果是非常显著的. 展开更多
关键词 泊松方程 有限差分法 高阶紧致格式 多重网格
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求解波动方程的高精度紧致隐式差分方法 被引量:6
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作者 葛永斌 朱琳 田振夫 《宁夏大学学报(自然科学版)》 CAS 北大核心 2005年第4期297-299,315,共4页
基于二阶微商的二阶中心差商和四阶紧致差商逼近公式及其加权平均思想,推导出了数值求解一维波动方程的2种精度分别为0(τ2+h4)和O(τ4+h4)的三层隐式紧致差分格式,以及与之相匹配的第一个时间步的同阶离散格式,并采用Fourier方法分析... 基于二阶微商的二阶中心差商和四阶紧致差商逼近公式及其加权平均思想,推导出了数值求解一维波动方程的2种精度分别为0(τ2+h4)和O(τ4+h4)的三层隐式紧致差分格式,以及与之相匹配的第一个时间步的同阶离散格式,并采用Fourier方法分析了格式的稳定性.由于每一时间层上最多只用到了3个网格点,所以可采用追赶法直接求解差分方程.数值实验结果验证了所得方法的精确性和可靠性. 展开更多
关键词 波动方程 紧致隐格式 高精度 差分方法
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求解变系数对流扩散反应方程的指数型高精度紧致差分方法 被引量:7
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作者 田芳 葛永斌 《工程数学学报》 CSCD 北大核心 2017年第3期283-296,共14页
本文给出了一种数值求解变系数对流扩散反应方程的指数型高精度紧致差分方法.我们首先将模型方程变形,借助常系数对流扩散方程的指数型高精度紧致差分格式,采用残量修正法得到变系数对流扩散反应方程的指数型高精度紧致差分格式;并从理... 本文给出了一种数值求解变系数对流扩散反应方程的指数型高精度紧致差分方法.我们首先将模型方程变形,借助常系数对流扩散方程的指数型高精度紧致差分格式,采用残量修正法得到变系数对流扩散反应方程的指数型高精度紧致差分格式;并从理论上分析了当Pelect数很大时,本文格式达到四阶计算精度时网格步长的限制条件;离散得到的代数方程组可采用追赶法直接求解.数值实验结果与理论分析完全吻合,表明了本文格式对于边界层问题或大梯度变化的物理量求解问题具有的高精度和鲁棒性的优点. 展开更多
关键词 对流扩散反应方程 指数型有限差分格式 高精度紧致差分格式 对流占优 边界层
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基于紧致差分格式的高效时域有限差分算法 被引量:5
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作者 况晓静 王道平 +3 位作者 张量 吴先良 沈晶 沈勐 《计算物理》 CSCD 北大核心 2014年第1期91-95,共5页
探讨一种基于紧致差分格式的高效时域有限差分算法(high-order compact-FDTD),该方法不仅提高计算精度,而且网格结点少、内存使用率和CPU时间大为降低.利用紧致格式FDTD方法实现无耗波导系统及光子晶体光纤中电磁波传播的数值模拟.通过... 探讨一种基于紧致差分格式的高效时域有限差分算法(high-order compact-FDTD),该方法不仅提高计算精度,而且网格结点少、内存使用率和CPU时间大为降低.利用紧致格式FDTD方法实现无耗波导系统及光子晶体光纤中电磁波传播的数值模拟.通过计算实例验证算法的高效性. 展开更多
关键词 电磁场与微波技术 时域有限差分法 高阶紧致差分格式 数值模拟
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