A new absorbing boundary condition (ABC) for frequency dependent finite difference time domain algorithm for the arbitrary dispersive media is presented. The concepts of the digital systems are introduced to the (F...A new absorbing boundary condition (ABC) for frequency dependent finite difference time domain algorithm for the arbitrary dispersive media is presented. The concepts of the digital systems are introduced to the (FD) 2TD method. On the basis of digital filter designing and vector algebra, the absorbing boundary condition under arbitrary angle of incidence are derived. The transient electromagnetic problems in two dimensions and three dimensions are calculated and the validity of the ABC is verified.展开更多
In this paper the explanation of the mechanism of high-frequency oscillation instability resulted from absorbing boundary conditions is further improved. And we analytically prove the proposition that for one dimensio...In this paper the explanation of the mechanism of high-frequency oscillation instability resulted from absorbing boundary conditions is further improved. And we analytically prove the proposition that for one dimensional discrete model of elastic wave motion, the module of reflection factor will be greater than 1 in high frequency band when artificial wave velocity is greater than 1.5 times the ratio of discrete space step to discrete time step. Based on the proof, the frequency band in which instability occurs is discussed in detail, showing such high-frequency waves are meaningless for the numerical simulation of wave motion.展开更多
With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） meth...With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） method. The reflection of the ABC caused by both the truncated error and the phase velocity error is analyzed. Based on the phase velocity estimation and the nonuniform cell, two methods are studied and then adopted to improve the performance of the ABC. A calculation case of a rectangular waveguide which is a typical dispersive transmission line is carried out using the ADI-FDTD method with the improved ABC for evaluation. According to the calculated case, the comparison is given between the reflection coefficients of the ABC with and without the velocity estimation and also the comparison between the reflection coefficients of the ABC with and without the nonuniform processing. The reflection variation of the ABC under different time steps is also analyzed and the acceptable worsening will not obscure the improvement on the absorption. Numerical results obviously show that efficient improvement on the absorbing performance of the ABC is achieved based on these methods for the ADI-FDTD.展开更多
The key problem of finite-difference time-domain (FD-TD) method is the skillful application of special conditions on the boundaries of the computational domain. A new technique named Perfectly Matched Layer(PML) yield...The key problem of finite-difference time-domain (FD-TD) method is the skillful application of special conditions on the boundaries of the computational domain. A new technique named Perfectly Matched Layer(PML) yields a robust Absorbing Boundary Condition(ABC) independent of the angle of incidence and the frequency of outgoing waves. In this paper, the principle of the PML technique is briefly presented. Then some problems in the application and their settlements are discussed emphatically. Finally three numerical tests and a measured result are devoted to examine the accuracy and effectiveness of this approach.展开更多
In this paper,a step approach method in the time domain is developed to calculate the radiated waves from an arbitrary obstacle pulsating with multiple frequencies.The computing scheme is based on the Boundary Integra...In this paper,a step approach method in the time domain is developed to calculate the radiated waves from an arbitrary obstacle pulsating with multiple frequencies.The computing scheme is based on the Boundary Integral Equation and derived in the time domain;thus,the time-harmonic Neumann boundary condition can be imposed.By the present method,the values of the initial conditions are set to zero,and the approach process is carried forward in a loop from the first time step to the last.At each time step,the radiated pressure on each element is updated.After several loops,the correct radiated pressures can be obtained.A sphere pulsating with a monopole frequency in an infinite acoustic domain is calculated first.This result is compared with the analytical solution,and both of them are in good agreement.Then,a complex-shaped radiator is taken as the studied case.The pulsating frequency of this case is multiple,and the waves propagate in half space.It is shown that the present method can treat multiple-frequency pulsation well,even when the radiator is a complex shape,and a robust convergence can be attained quickly.展开更多
With the development of numerical methods the numerical computations require higher and higher accuracy. This paper is devoted to the high-order local absorbing boundary conditions （ABCs） for heat equation. We prove...With the development of numerical methods the numerical computations require higher and higher accuracy. This paper is devoted to the high-order local absorbing boundary conditions （ABCs） for heat equation. We proved that the coupled system yields a stable problem between the obtained high-order local ABCs and the partial differential equation in the computational domain. This method has been used widely in wave propagation models only recently. We extend the spirit of the methodology to parabolic ones, which will become a basis to design the local ABCs for a class of nonlinear PDEs. Some numerical tests show that the new treatment is very efficient and tractable.展开更多
The performances of absorbing boundary conditions （ABCs） in four widely used finite difference time domain （FDTD） methods, i.e. explicit, implicit, explicit staggered-time, and Chebyshev methods, for solving the t...The performances of absorbing boundary conditions （ABCs） in four widely used finite difference time domain （FDTD） methods, i.e. explicit, implicit, explicit staggered-time, and Chebyshev methods, for solving the time-dependent Schrodinger equation are assessed and compared. The computation efficiency for each approach is also evaluated. A typical evolution problem of a single Gaussian wave packet is chosen to demonstrate the performances of the four methods combined with ABCs. It is found that ABCs perfectly eliminate reflection in implicit and explicit staggered-time methods. However, small reflection still exists in explicit and Chebyshev methods even though ABCs are applied.展开更多
In this paper, equivalent surface impedance boundary condition （ESIBC）, which takes fractal parameters （D, G） into SIBC, is implemented in the 4-component 2-D compact finite difference frequency domain （2-D CFDFD...In this paper, equivalent surface impedance boundary condition （ESIBC）, which takes fractal parameters （D, G） into SIBC, is implemented in the 4-component 2-D compact finite difference frequency domain （2-D CFDFD） method to an- alyze the propagation characteristics of lossy circular waveguide with fractal rough surface based on Weierstrass-Mandelbrot （W-M） function. Fractal parameters’ effects on attenuation constant are presented in the 3 mm lossy circular waveguide, and the attenuation constants of the first three modes vary monotonically with scaling constant （G） and decrease as the fractal dimension （D） increasing.展开更多
We propose a hierarchy of novel absorbing boundary conditions for the onedimensional stationary Schr¨odinger equation with general(linear and nonlinear)potential.The accuracy of the new absorbing boundary conditi...We propose a hierarchy of novel absorbing boundary conditions for the onedimensional stationary Schr¨odinger equation with general(linear and nonlinear)potential.The accuracy of the new absorbing boundary conditions is investigated numerically for the computation of energies and ground-states for linear and nonlinear Schr¨odinger equations.It turns out that these absorbing boundary conditions and their variants lead to a higher accuracy than the usual Dirichlet boundary condition.Finally,we give the extension of these ABCs to N-dimensional stationary Schr¨odinger equations.展开更多
In this paper we study numerical issues related to the Schr ¨odinger equationwith sinusoidal potentials at infinity. An exact absorbing boundary condition in a formof Dirichlet-to-Neumann mapping is derived. This...In this paper we study numerical issues related to the Schr ¨odinger equationwith sinusoidal potentials at infinity. An exact absorbing boundary condition in a formof Dirichlet-to-Neumann mapping is derived. This boundary condition is based on ananalytical expression of the logarithmic derivative of the Floquet solution toMathieu’sequation, which is completely new to the author’s knowledge. The implementationof this exact boundary condition is discussed, and a fast evaluation method is used toreduce the computation burden arising from the involved half-order derivative operator.Some numerical tests are given to showthe performance of the proposed absorbingboundary conditions.展开更多
大体积混凝土结构被广泛应用于土木、水利等领域的重大工程中,而混凝土抗拉强度低的力学特性决定了其易产生裂纹,因此,发展高效的检测方法,识别大体积混凝土结构中的裂纹信息十分必要.论文提出了一种新的方法,通过提取响应信号频谱中特...大体积混凝土结构被广泛应用于土木、水利等领域的重大工程中,而混凝土抗拉强度低的力学特性决定了其易产生裂纹,因此,发展高效的检测方法,识别大体积混凝土结构中的裂纹信息十分必要.论文提出了一种新的方法,通过提取响应信号频谱中特定频率的幅值特征,基于BP人工神经网络建立幅值特征与裂纹信息间的映射关系,从而有效识别出裂纹信息.首先采用扩展有限元法(eXtended Finite Element Methods, XFEM)和人工吸收边界模型,分别模拟了单裂纹和双裂纹情形下,大量不同裂纹信息下特定位置传感器的响应,分析其频谱曲线并提取特征,建立频谱特征—裂尖位置数据集,以训练人工神经网络,测试集的反演效果显示,该方法具有较好的准确度,可有效识别出裂纹信息.展开更多
文摘A new absorbing boundary condition (ABC) for frequency dependent finite difference time domain algorithm for the arbitrary dispersive media is presented. The concepts of the digital systems are introduced to the (FD) 2TD method. On the basis of digital filter designing and vector algebra, the absorbing boundary condition under arbitrary angle of incidence are derived. The transient electromagnetic problems in two dimensions and three dimensions are calculated and the validity of the ABC is verified.
基金Basic Scientific Research-related Project from Institute of Engineering Mechanics (01180001 and 2007C01)
文摘In this paper the explanation of the mechanism of high-frequency oscillation instability resulted from absorbing boundary conditions is further improved. And we analytically prove the proposition that for one dimensional discrete model of elastic wave motion, the module of reflection factor will be greater than 1 in high frequency band when artificial wave velocity is greater than 1.5 times the ratio of discrete space step to discrete time step. Based on the proof, the frequency band in which instability occurs is discussed in detail, showing such high-frequency waves are meaningless for the numerical simulation of wave motion.
基金The National Natural Science Foundation of China(No.60702027)the Free Research Fund of the National Mobile Communications Research Laboratory of Southeast University (No.2008B07)the National Basic Research Program of China(973 Program)(No.2007CB310603)
文摘With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） method. The reflection of the ABC caused by both the truncated error and the phase velocity error is analyzed. Based on the phase velocity estimation and the nonuniform cell, two methods are studied and then adopted to improve the performance of the ABC. A calculation case of a rectangular waveguide which is a typical dispersive transmission line is carried out using the ADI-FDTD method with the improved ABC for evaluation. According to the calculated case, the comparison is given between the reflection coefficients of the ABC with and without the velocity estimation and also the comparison between the reflection coefficients of the ABC with and without the nonuniform processing. The reflection variation of the ABC under different time steps is also analyzed and the acceptable worsening will not obscure the improvement on the absorption. Numerical results obviously show that efficient improvement on the absorbing performance of the ABC is achieved based on these methods for the ADI-FDTD.
基金Supported by the National Natural Science Foundation of China
文摘The key problem of finite-difference time-domain (FD-TD) method is the skillful application of special conditions on the boundaries of the computational domain. A new technique named Perfectly Matched Layer(PML) yields a robust Absorbing Boundary Condition(ABC) independent of the angle of incidence and the frequency of outgoing waves. In this paper, the principle of the PML technique is briefly presented. Then some problems in the application and their settlements are discussed emphatically. Finally three numerical tests and a measured result are devoted to examine the accuracy and effectiveness of this approach.
文摘In this paper,a step approach method in the time domain is developed to calculate the radiated waves from an arbitrary obstacle pulsating with multiple frequencies.The computing scheme is based on the Boundary Integral Equation and derived in the time domain;thus,the time-harmonic Neumann boundary condition can be imposed.By the present method,the values of the initial conditions are set to zero,and the approach process is carried forward in a loop from the first time step to the last.At each time step,the radiated pressure on each element is updated.After several loops,the correct radiated pressures can be obtained.A sphere pulsating with a monopole frequency in an infinite acoustic domain is calculated first.This result is compared with the analytical solution,and both of them are in good agreement.Then,a complex-shaped radiator is taken as the studied case.The pulsating frequency of this case is multiple,and the waves propagate in half space.It is shown that the present method can treat multiple-frequency pulsation well,even when the radiator is a complex shape,and a robust convergence can be attained quickly.
文摘With the development of numerical methods the numerical computations require higher and higher accuracy. This paper is devoted to the high-order local absorbing boundary conditions （ABCs） for heat equation. We proved that the coupled system yields a stable problem between the obtained high-order local ABCs and the partial differential equation in the computational domain. This method has been used widely in wave propagation models only recently. We extend the spirit of the methodology to parabolic ones, which will become a basis to design the local ABCs for a class of nonlinear PDEs. Some numerical tests show that the new treatment is very efficient and tractable.
基金supported by the State Key Development Program for Basic Research of China (No. 2006CB932404)
文摘The performances of absorbing boundary conditions （ABCs） in four widely used finite difference time domain （FDTD） methods, i.e. explicit, implicit, explicit staggered-time, and Chebyshev methods, for solving the time-dependent Schrodinger equation are assessed and compared. The computation efficiency for each approach is also evaluated. A typical evolution problem of a single Gaussian wave packet is chosen to demonstrate the performances of the four methods combined with ABCs. It is found that ABCs perfectly eliminate reflection in implicit and explicit staggered-time methods. However, small reflection still exists in explicit and Chebyshev methods even though ABCs are applied.
文摘In this paper, equivalent surface impedance boundary condition （ESIBC）, which takes fractal parameters （D, G） into SIBC, is implemented in the 4-component 2-D compact finite difference frequency domain （2-D CFDFD） method to an- alyze the propagation characteristics of lossy circular waveguide with fractal rough surface based on Weierstrass-Mandelbrot （W-M） function. Fractal parameters’ effects on attenuation constant are presented in the 3 mm lossy circular waveguide, and the attenuation constants of the first three modes vary monotonically with scaling constant （G） and decrease as the fractal dimension （D） increasing.
基金supported by the French ANR fundings under the project MicroWave NT09_460489.
文摘We propose a hierarchy of novel absorbing boundary conditions for the onedimensional stationary Schr¨odinger equation with general(linear and nonlinear)potential.The accuracy of the new absorbing boundary conditions is investigated numerically for the computation of energies and ground-states for linear and nonlinear Schr¨odinger equations.It turns out that these absorbing boundary conditions and their variants lead to a higher accuracy than the usual Dirichlet boundary condition.Finally,we give the extension of these ABCs to N-dimensional stationary Schr¨odinger equations.
基金the National Natural Science Foundation of China underGrant No. 10401020.
文摘In this paper we study numerical issues related to the Schr ¨odinger equationwith sinusoidal potentials at infinity. An exact absorbing boundary condition in a formof Dirichlet-to-Neumann mapping is derived. This boundary condition is based on ananalytical expression of the logarithmic derivative of the Floquet solution toMathieu’sequation, which is completely new to the author’s knowledge. The implementationof this exact boundary condition is discussed, and a fast evaluation method is used toreduce the computation burden arising from the involved half-order derivative operator.Some numerical tests are given to showthe performance of the proposed absorbingboundary conditions.
文摘大体积混凝土结构被广泛应用于土木、水利等领域的重大工程中,而混凝土抗拉强度低的力学特性决定了其易产生裂纹,因此,发展高效的检测方法,识别大体积混凝土结构中的裂纹信息十分必要.论文提出了一种新的方法,通过提取响应信号频谱中特定频率的幅值特征,基于BP人工神经网络建立幅值特征与裂纹信息间的映射关系,从而有效识别出裂纹信息.首先采用扩展有限元法(eXtended Finite Element Methods, XFEM)和人工吸收边界模型,分别模拟了单裂纹和双裂纹情形下,大量不同裂纹信息下特定位置传感器的响应,分析其频谱曲线并提取特征,建立频谱特征—裂尖位置数据集,以训练人工神经网络,测试集的反演效果显示,该方法具有较好的准确度,可有效识别出裂纹信息.
