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Artificial boundary condition for Klein-Gordon equation by constructing mechanics structure
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作者 Pang Gang Zheng Zijun 《Theoretical & Applied Mechanics Letters》 CSCD 2023年第5期394-398,共5页
An innovative local artificial boundary condition is proposed to numerically solve the Cauchy problem of the Klein-Gordon equation in an unbounded domain.Initially,the equation is considered as the axial wave prop-aga... An innovative local artificial boundary condition is proposed to numerically solve the Cauchy problem of the Klein-Gordon equation in an unbounded domain.Initially,the equation is considered as the axial wave prop-agation in a bar supported on a spring foundation.The numerical model is then truncated by replacing the half-infinitely long bar with an equivalent mechanical structure.The effective frequency-dependent stiffness of the half-infinitely long bar is expressed as the sum of rational terms using Pade approximation.For each term,a corresponding substructure composed of dampers and masses is constructed.Finally,the equivalent mechan-ical structure is obtained by parallelly connecting these substructures.The proposed approach can be easily implemented within a standard finite element framework by incorporating additional mass points and damper elements.Numerical examples show that with just a few extra degrees of freedom,the proposed approach effec-tively suppresses artificial reflections at the truncation boundary and exhibits first-order convergence. 展开更多
关键词 artificial boundary condition Pade approximation Dispersive wave Spring-damper-mass system Klein-Gordon equation
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New artificial boundary condition for saturated soil foundations 被引量:1
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作者 Xu Qiang Chen Jianyun +1 位作者 Li Jing Fan Shuli 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2012年第1期139-147,共9页
Anew artificial boundary model based on multi-directional transmitting and viscous-spring artificial boundary theories is proposed to absorb stress waves in a saturated soil foundation in dynamic analysis. Since shear... Anew artificial boundary model based on multi-directional transmitting and viscous-spring artificial boundary theories is proposed to absorb stress waves in a saturated soil foundation in dynamic analysis. Since shear waves (S-waves) are the same in a saturated soil foundation and a single-phase medium foundation, a tangential visco-elastic boundary condition for a single-phase medium foundation can also be used for saturated soil foundations. Thus, the purpose of the artificial boundary proposed in this paper is primarily to absorb two types of P-waves in a saturated soil foundation. The main idea is that the stress of the P-waves in the saturated soil foundation is decomposed into two types. The first type of stress, δra' is absorbed by the first artificial boundary. The second type of stress, δrb, is balanced by the stress generated by the second artificial boundary. Ultimately, both types of P-waves (fast-P-waves and slow-P-waves) are absorbed by the artificial boundary model proposed in this paper. In particular, note that the fast-P-waves and slow-P-waves are absorbed at the position of the first boundary. Thus, the artificial boundary model proposed herein can simultaneously absorb P-fast waves, P-slow waves and shear waves. Finally, a numerical example is given to examine the proposed artificial boundary model, and the results show that it is very accurate. 展开更多
关键词 multi-directional transmitting artificial boundary viscous-spring artificial boundary saturated soil foundation Biot's equations
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3D viscous-spring artificial boundary in time domain 被引量:61
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作者 刘晶波 杜义欣 +2 位作者 杜修力 王振宇 伍俊 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2006年第1期93-102,共10页
After a brief review of studies on artificial boundaries in dynamic soil-structure interaction, a three-dimensional viscous-spring artificial boundary (VSAB) in the time domain is developed in this paper. First, the... After a brief review of studies on artificial boundaries in dynamic soil-structure interaction, a three-dimensional viscous-spring artificial boundary (VSAB) in the time domain is developed in this paper. First, the 3D VSAB equations in the normal and tangential directions are derived based on the elastic wave motion theory. Secondly, a numerical simulation technique of wave motion equations along with the VSAB condition in the time domain is studied. Finally, numerical examples of some classical elastic wave motion problems are presented and the results are compared with the associated theoretical solutions, demonstrating that high precision and adequate stability can be achieved by using the proposed 3D VSAB. The proposed 3D VSAB can be conveniently incorporated in the general finite element program, which is commonly used to study dynamic soil-structure interaction problems. 展开更多
关键词 artificial boundary viscous-spring wave motion time domain numerical simulation soil-structure interaction
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Model test to investigate reasonable reactive artificial boundary in shaking table test with a rigid container 被引量:2
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作者 LEI Ming-feng ZHOU Bo-cheng +3 位作者 LIN Yue-xiang CHEN Fu-dong SHI Cheng-hua PENG Li-min 《Journal of Central South University》 SCIE EI CAS CSCD 2020年第1期210-220,共11页
When conducting dynamic tests of underground structure by a rigid container, reasonable boundary conditions are one of the essential factors related to the accuracy of test results, especially the artificial boundary ... When conducting dynamic tests of underground structure by a rigid container, reasonable boundary conditions are one of the essential factors related to the accuracy of test results, especially the artificial boundary perpendicular to the excitation direction. On the basis of numerous studies, shaking table tests with four different typical boundaries are performed in this study. The tests consider the seismic intensity and seismic wave types. Then, the simulation effects of the four boundary conditions are evaluated from four aspects as follows: the differential rate of peak acceleration, acceleration curve, similarity of Fourier frequency spectra, and uneven soil settlement in rigid containers. Results show that the simulation effects of the boundary conditions are not only affected by the nature of the boundary material but also related to the seismic intensity, types of seismic waves, and filter characteristic of the filling medium in containers. In comparison with the other three types of boundary condition, foamed polyethylene shows the best simulation effect and its effect decreases gradually with the increase in earthquake intensity. Finally, on the basis of existing studies, the evaluation criteria of boundary effect, the principle for the selection of boundary material type and the thickness of boundary material are discussed and summarized, and the corresponding design methods and suggestions are then provided. 展开更多
关键词 shaking table test artificial boundary conditions rigid container
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BOUNDARY ELEMENT ANALYSIS OF CONTACT PROBLEMS USING ARTIFICIAL BOUNDARY NODE APPROACH 被引量:1
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作者 BahattinKANBER IbrahimH.GUZELBEY AhmetERKLIG 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2003年第4期347-354,共8页
An improved version of the regular boundary element method, the artificial boundary node approach, is derived. A simple contact algorithm is designed and implemented into the direct boundary element, regular boundary ... An improved version of the regular boundary element method, the artificial boundary node approach, is derived. A simple contact algorithm is designed and implemented into the direct boundary element, regular boundary element and artificial boundary node approaches. The exisiting and derived approaches are tested using some case studies. The results of the artificial boundary node approach are compared with those of the existing boundary element program, the regular element approach, ANSYS and analytical solution whenever possible. The results show the effectiveness of the artificial boundary node approach for a wider range of boundary offsets. 展开更多
关键词 boundary element method contact problems regular boundary element artificial boundary node
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Artificial boundary conditions for Euler–Bernoulli beam equation 被引量:1
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作者 Shao-Qiang Tang Eduard G.Karpov 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2014年第5期687-692,共6页
In a semi-discretized Euler-Bernoulli beam equa- tion, the non-nearest neighboring interaction and large span of temporal scales for wave propagations pose challenges to the effectiveness and stability for artificial ... In a semi-discretized Euler-Bernoulli beam equa- tion, the non-nearest neighboring interaction and large span of temporal scales for wave propagations pose challenges to the effectiveness and stability for artificial boundary treat- ments. With the discrete equation regarded as an atomic lattice with a three-atom potential, two accurate artificial boundary conditions are first derived here. Reflection co- efficient and numerical tests illustrate the capability of the proposed methods. In particular, the time history treatment gives an exact boundary condition, yet with sensitivity to nu- merical implementations. The ALEX (almost EXact) bound- ary condition is numerically more effective. 展开更多
关键词 Euler-Bernoulli beam. artificial boundary con- dition - Wave propagation
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Comparison of perfectly matched layer and multi-transmitting formula artificial boundary condition based on hybrid finite element formulation
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作者 李宁 谢礼立 翟长海 《Acta Seismologica Sinica(English Edition)》 CSCD 2007年第6期684-695,共12页
The theory of perfectly matched layer (PML) artificial boundary condition (ABC), which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The co... The theory of perfectly matched layer (PML) artificial boundary condition (ABC), which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The construction process of PML boundary based on elastodynamic partial differential equation (PDE) system is developed. Combining with velocity-stress hybrid finite element formulation, the applicability of PML boundary is investigated and the numerical reflection of PML boundary is estimated. The reflectivity of PML and multi-transmitting formula (MTF) boundary is then compared based on body wave and surface wave simulations. The results show that although PML boundary yields some reflection, its absorption performance is superior to MTF boundary in the numerical simulations of near-fault wave propagation, especially in comer and large angle grazing incidence situations. The PML boundary does not arise any unstable phenomenon and the stability of PML boundary is better than MTF boundary in hybrid finite element method. For a specified problem and analysis tolerance, the computational efficiency of PML boundary is only a little lower than MTF boundary. 展开更多
关键词 perfectly matched layer multi-transmitting formula elastodynamic wave artificial boundary hybrid finite element
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A survey on artificial boundary method Dedicated to Professor Shi Zhong-Ci on the Occasion of his 80th Birthday 被引量:3
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作者 HAN HouDe WU XiaoNan 《Science China Mathematics》 SCIE 2013年第12期2439-2488,共50页
The artificial boundary method is one of the most popular and effective numerical methods tor solving partial differential equations on unbounded domains, with more than thirty years development. The artificiM boundar... The artificial boundary method is one of the most popular and effective numerical methods tor solving partial differential equations on unbounded domains, with more than thirty years development. The artificiM boundary method has reached maturity in recent years. It has been applied to various problems in scientific and engineering computations, and the theoretical issues such as the convergence and error estimates of the artificial boundary method have been solved gradually. This paper reviews the development and discusses different forms of the artificial boundary method. 展开更多
关键词 artificial boundary method global artificial boundary condition local artificial boundary condi-tion discrete artificial boundary condition implicit artificial boundary condition nonlinear artificial boundarycondition
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THE APPROXIMATIONS OF THE EXACT BOUNDARY CONDITION AT AN ARTIFICIAL BOUNDARY FOR LINEARIZED INCOMPRESSIBLE VISCOUS FLOWS 被引量:2
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作者 Wei-zhu Bao (Department of Applied Mathematics, Tsinghua University, Beijing 100084, P.R. China) 《Journal of Computational Mathematics》 SCIE CSCD 1998年第3期239-256,共18页
We consider the linearized incompressible Navier-Stokes (Oseen) equations in a flat channel. A sequence of approximations to the exact boundary condition at an artificial boundary is derived. Then the original problem... We consider the linearized incompressible Navier-Stokes (Oseen) equations in a flat channel. A sequence of approximations to the exact boundary condition at an artificial boundary is derived. Then the original problem is reduced to a boundary value problem in a bounded domain, which is well-posed. A finite element approximation on the bounded domain is given, furthermore the error estimate of the finite element approximation is obtained. Numerical example shows that our artificial boundary conditions are very effective. 展开更多
关键词 Oseen equations artificial boundary artificial boundary condition finite element approximation error estimate
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Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain 被引量:1
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作者 Wei Zhang Jiang Yang +1 位作者 Jiwei Zhang Qiang Du 《Communications in Computational Physics》 SCIE 2017年第1期16-39,共24页
This paper is concerned with numerical approximations of a nonlocal heat equation define on an infinite domain.Two classes of artificial boundary conditions(ABCs)are designed,namely,nonlocal analog Dirichlet-to-Neuman... This paper is concerned with numerical approximations of a nonlocal heat equation define on an infinite domain.Two classes of artificial boundary conditions(ABCs)are designed,namely,nonlocal analog Dirichlet-to-Neumann-type ABCs(global in time)and high-order Pad´e approximate ABCs(local in time).These ABCs reformulate the original problem into an initial-boundary-value(IBV)problem on a bounded domain.For the global ABCs,we adopt a fast evolution to enhance computational efficiency and reduce memory storage.High order fully discrete schemes,both second-order in time and space,are given to discretize two reduced problems.Extensive numerical experiments are carried out to show the accuracy and efficiency of the proposed methods. 展开更多
关键词 artificial boundary conditions nonlocal models Pad´e approximation nonlocal heat equations artificial boundary method
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Mixed Finite Element Method and Higher-Order Local Artificial Boundary Conditions for Exterior 3-D Poisson Equation
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作者 韩厚德 郑春雄 《Tsinghua Science and Technology》 SCIE EI CAS 2002年第3期228-234,共7页
The mixed finite element method is used to solve the exterior Poisson equations with higher-order local artificial boundary conditions in 3-D space. New unknowns are introduced to reduce the order of the derivatives ... The mixed finite element method is used to solve the exterior Poisson equations with higher-order local artificial boundary conditions in 3-D space. New unknowns are introduced to reduce the order of the derivatives of the unknown to two. The result is an equivalent mixed variational problem which was solved using bilinear finite elements. The primary advantage is that special finite elements are not needed on the adjacent layer of the artificial boundary for the higher-order derivatives. Error estimates are obtained for some local artificial boundary conditions with prescibed orders. A numerical example demonstrates the effectiveness of this method. 展开更多
关键词 artificial boundary high-order artificial boundary condition mixed finite element method
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ARTIFICIAL BOUNDARY METHOD FOR BURGERS' EQUATION USING NONLINEAR BOUNDARY CONDITIONS 被引量:4
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作者 Hou-de Han Xiao-nan Wu Zhen-li Xu 《Journal of Computational Mathematics》 SCIE EI CSCD 2006年第3期295-304,共10页
This paper discusses the numerical solution of Burgers' equation on unbounded domains. Two artificial boundaries are introduced and boundary conditions are obtained on the artificial boundaries, which are in nonlinea... This paper discusses the numerical solution of Burgers' equation on unbounded domains. Two artificial boundaries are introduced and boundary conditions are obtained on the artificial boundaries, which are in nonlinear forms. Then the original problem is reduced to an equivalent problem on a bounded domain. Finite difference method is applied to the reduced problem, and some numerical examples are given to show the effectiveness of the new approach. 展开更多
关键词 Burgers' equation Unbounded domain artificial boundary condition.
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APPROXIMATION, STABILITY AND FAST EVALUATION OF EXACT ARTIFICIAL BOUNDARY CONDITION FOR THE ONE-DIMENSIONAL HEAT EQUATION 被引量:3
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作者 Chunxiong Zheng 《Journal of Computational Mathematics》 SCIE EI CSCD 2007年第6期730-745,共16页
In this paper we consider the numerical solution of the one-dimensional heat equation on unbounded domains. First an exact semi-discrete artificial boundary condition is derived by discretizing the time variable with ... In this paper we consider the numerical solution of the one-dimensional heat equation on unbounded domains. First an exact semi-discrete artificial boundary condition is derived by discretizing the time variable with the Crank-Nicolson method. The semi-discretized heat equation equipped with this boundary condition is then proved to be unconditionally stable, and its solution is shown to have second-order accuracy. In order to reduce the computational cost, we develop a new fast evaluation method for the convolution operation involved in the exact semi-discrete artificial boundary condition. A great advantage of this method is that the unconditional stability held by the semi-discretized heat equation is preserved. An error estimate is also given to show the dependence of numerical errors on the time step and the approximation accuracy of the convolution kernel. Finally, a simple numerical example is presented to validate the theoretical results. 展开更多
关键词 Heat equation artificial boundary conditions Fast evaluation Unbounded domains.
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FINITE ELEMENT-ARTIFICIAL TRANSMITTING BOUNDARY METHOD FOR WAVE SCATTERING FROM IRREGULAR CYLINDER 被引量:1
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作者 杨吉生 徐立军 +1 位作者 邢昌玉 杨光 《Transactions of Tianjin University》 EI CAS 1997年第2期36-39,共4页
The finite element artificial transmitting boundary method is employed here to treat the near field scattering of a cylindrical wave from an irregular cylinder. A comparison is made between this method and the analy... The finite element artificial transmitting boundary method is employed here to treat the near field scattering of a cylindrical wave from an irregular cylinder. A comparison is made between this method and the analytical one. And then examples are given to demonstrate the solution of several problems of the irregular object scattering. The method can not only produce clear physical pictures, but can efficiently handle many complicated scattering problems. 展开更多
关键词 finite elements artificial transmitting boundary SCATTERING
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THE GLOBAL ARTIFICIAL BOUNDARY CONDITIONS FOR NUMERICAL SIMULATIONS OF THE 3D FLOW AROUND A SUBMERGED BODY 被引量:1
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作者 Hou-de Han Xin Wen (Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China) 《Journal of Computational Mathematics》 SCIE CSCD 2003年第4期435-450,共16页
We consider the numerical approximations of the three-dimensional steady potential flow around a body moving in a liquid of finite constant depth at constant speed and distance below a free surface in a channel. One v... We consider the numerical approximations of the three-dimensional steady potential flow around a body moving in a liquid of finite constant depth at constant speed and distance below a free surface in a channel. One vertical side is introduced as the upstream artificial boundary and two vertical sides are introduced as the downstream artificial boundaries. On the artificial boundaries, a sequence of high-order global artificial boundary conditions are given. Then the original problem is reduced to a problem defined on a finite computational domain, which is equivalent to a variational problem. After solving the variational problem by the finite element method, we obtain the numerical approximation of the original problem. The numerical examples show that the artificial boundary conditions given in this paper are very effective. 展开更多
关键词 Ship wave Potential flow Global artificial boundary condition Finite element method.
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ARTIFICIAL BOUNDARY METHOD FOR THE THREE-DIMENSIONAL EXTERIOR PROBLEM OF ELASTICITY 被引量:1
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作者 Hou-de Han Chun-xiong Zheng 《Journal of Computational Mathematics》 SCIE EI CSCD 2005年第6期603-618,共16页
The exact boundary condition on a spherical artificial boundary is derived for the three-dimensional exterior problem of linear elasticity in this paper. After this boundary condition is imposed on the artificial boun... The exact boundary condition on a spherical artificial boundary is derived for the three-dimensional exterior problem of linear elasticity in this paper. After this boundary condition is imposed on the artificial boundary, a reduced problem only defined in a bounded domain is obtained. A series of approximate problems with increasing accuracy can be derived if one truncates the series term in the variational formulation, which is equivalent to the reduced problem. An error estimate is presented to show how the error depends on the finite element discretization and the accuracy of the approximate problem. In the end, a numerical example is given to demonstrate the performance of the proposed method. 展开更多
关键词 artificial boundary method unbounded domains ELASTICITY
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Split Local Artificial Boundary Conditions for the Two-Dimensional Sine-Gordon Equation on R^(2) 被引量:1
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作者 Houde Han Zhiwen Zhang 《Communications in Computational Physics》 SCIE 2011年第10期1161-1183,共23页
In this paper the numerical solution of the two-dimensional sine-Gordon equation is studied.Split local artificial boundary conditions are obtained by the operator splitting method.Then the original problem is reduced... In this paper the numerical solution of the two-dimensional sine-Gordon equation is studied.Split local artificial boundary conditions are obtained by the operator splitting method.Then the original problem is reduced to an initial boundary value problem on a bounded computational domain,which can be solved by the finite differencemethod.Several numerical examples are provided to demonstrate the effectiveness and accuracy of the proposed method,and some interesting propagation and collision behaviors of the solitary wave solutions are observed. 展开更多
关键词 Sine-Gordon equation operator splitting method artificial boundary condition SOLITON unbounded domain
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Exact Artificial Boundary Condition for the Poisson Equation in the Simulation of the 2D Schrodinger-Poisson System 被引量:1
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作者 Norbert J.Mauser Yong Zhang 《Communications in Computational Physics》 SCIE 2014年第8期764-780,共17页
We study the computation of ground states and time dependent solutions of the Schr¨odinger-Poisson system(SPS)on a bounded domain in 2D(i.e.in two space dimensions).On a disc-shaped domain,we derive exact artific... We study the computation of ground states and time dependent solutions of the Schr¨odinger-Poisson system(SPS)on a bounded domain in 2D(i.e.in two space dimensions).On a disc-shaped domain,we derive exact artificial boundary conditions for the Poisson potential based on truncated Fourier series expansion inθ,and propose a second order finite difference scheme to solve the r-variable ODEs of the Fourier coefficients.The Poisson potential can be solved within O(M NlogN)arithmetic operations where M,N are the number of grid points in r-direction and the Fourier bases.Combined with the Poisson solver,a backward Euler and a semi-implicit/leap-frog method are proposed to compute the ground state and dynamics respectively.Numerical results are shown to confirm the accuracy and efficiency.Also we make it clear that backward Euler sine pseudospectral(BESP)method in[33]can not be applied to 2D SPS simulation. 展开更多
关键词 2D Schrodinger-Poisson system exact artificial boundary condition backward Euler scheme semi-implicit/leap-frog scheme backward Euler sine pseudospectral method.
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Artificial Boundary Method for Calculating Ship Wave Resistance
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作者 文新 韩厚德 《Tsinghua Science and Technology》 SCIE EI CAS 2003年第5期526-532,共7页
The calculation of wave resistance for a ship moving at constant speed near a free surface is considered. This wave resistance is calculated with a linearized steady potential model. To deal with the unboundedness of... The calculation of wave resistance for a ship moving at constant speed near a free surface is considered. This wave resistance is calculated with a linearized steady potential model. To deal with the unboundedness of the physical domain in the potential flow problem, we introduce one vertical side as an artificial upstream boundary and two vertical sides as the artificial downstream boundaries. On the artificial boundaries, a sequence of high-order global artificial boundary conditions are given. Then the potential flow problem is reduced to a problem defined on a finite computational domain, which is equivalent to a variational problem. The solution of the variational problem by the finite element method gives the numerical approximation of the potential flow around the ship, which was used to calculate the wave resistance. The numerical examples show the accuracy and efficiency of the proposed numerical scheme. 展开更多
关键词 ship wave potential flow global artificial boundary condition finite element method
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THE ELLIPSOID ARTIFICIAL BOUNDARY METHOD FOR THREE-DIMENSIONAL UNBOUNDED DOMAINS
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作者 Hongying Huang Dehao Yu 《Journal of Computational Mathematics》 SCIE CSCD 2009年第2期196-214,共19页
The artificial boundary method is applied to solve three-dimensional exterior problems. Two kind of rotating ellipsoids are chosen as the artificial boundaries and the exact artificial boundary conditions are derived ... The artificial boundary method is applied to solve three-dimensional exterior problems. Two kind of rotating ellipsoids are chosen as the artificial boundaries and the exact artificial boundary conditions are derived explicitly in terms of an infinite series. Then the well-posedness of the coupled variational problem is obtained. It is found that error estimates derived depend on the mesh size, truncation term and the location of the artificial boundary. Three numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method. 展开更多
关键词 artificial boundary method Exterior harmonic problem Finite element method Natural boundary reduction Oblate ellipsoid Prolate ellipsoid.
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