The boundary element method(BEM)is a popular method for solving acoustic wave propagation problems,especially those in exterior domains,owing to its ease in handling radiation conditions at infinity.However,BEM models...The boundary element method(BEM)is a popular method for solving acoustic wave propagation problems,especially those in exterior domains,owing to its ease in handling radiation conditions at infinity.However,BEM models must meet the requirement of 6–10 elements per wavelength,using the conventional constant,linear,or quadratic elements.Therefore,a large storage size of memory and long solution time are often needed in solving higher-frequency problems.In this work,we propose two new types of enriched elements based on conventional constant boundary elements to improve the computational efficiency of the 2D acoustic BEM.The first one uses a plane wave expansion,which can be used to model scattering problems.The second one uses a special plane wave expansion,which can be used tomodel radiation problems.Five examples are investigated to showthe advantages of the enriched elements.Compared with the conventional constant elements,the new enriched elements can deliver results with the same accuracy and in less computational time.This improvement in the computational efficiency is more evident at higher frequencies(with the nondimensional wave numbers exceeding 100).The paper concludes with the potential of our proposed enriched elements and plans for their further improvement.展开更多
This paper describes formulation and implementation of the fast multipole boundary element method (FMBEM) for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the...This paper describes formulation and implementation of the fast multipole boundary element method (FMBEM) for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the FMBEM are described in details. They are moment calculation, moment to moment translation, moment to local translation, and local to local translation. A data structure for the quad-tree construction is proposed which can facilitate implementation. An analytical moment expression is derived, which is more accurate, stable, and efficient than direct numerical computation. Numerical examples are presented to demonstrate the accuracy and efficiency of the FMBEM, and radiation of a 2D vibration rail mode is simulated using the FMBEM.展开更多
The physical objective of solving for eigen-modes of a 1D quasiperiodic structure in photonics has been achieved. This was achieved thru considering this structure as a 1D projection or cut of a 2D periodic structure....The physical objective of solving for eigen-modes of a 1D quasiperiodic structure in photonics has been achieved. This was achieved thru considering this structure as a 1D projection or cut of a 2D periodic structure. And the problem is solved in a manner similar to 2D periodic photonic structures. A mechanical analogy (quasiperiodic orbits) helps to bring conceptual clarity.展开更多
This paper proposes an eigenfunction expansion method to solve twodimensional (2D) elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial diffe...This paper proposes an eigenfunction expansion method to solve twodimensional (2D) elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.展开更多
A scheme of boundary element method for moving contact of two-dimensional elastic bodies using conforming discretization is presented. Both the displacement and the traction boundary conditions are satisfied on the co...A scheme of boundary element method for moving contact of two-dimensional elastic bodies using conforming discretization is presented. Both the displacement and the traction boundary conditions are satisfied on the contacting region in the sense of discretization. An algorithm to deal with the moving of the contact boundary on a larger possible contact region is presented. The algorithm is generalized to rolling contact problem as well. Some numerical examples of moving and rolling contact of 2D elastic bodies with or without friction, including the bodies with a hole-type defect, are given to show the effectiveness and the accuracy of the presented schemes.展开更多
This paper studies the eigenfunction expansion method to solve the two dimensional (2D) elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problem...This paper studies the eigenfunction expansion method to solve the two dimensional (2D) elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.展开更多
In the present paper on the one hand we apply the central limit theorem to the solution of the sign problem of a path integral of two-interacting particles in potential and give an expression for the sign solved propa...In the present paper on the one hand we apply the central limit theorem to the solution of the sign problem of a path integral of two-interacting particles in potential and give an expression for the sign solved propagator (SSP) derived from that solution and on the other hand we perform the angular decomposition of the path integrals of the 2D and 3D Helium atoms. Finally, we combine those two results and derive the SSPs of the 2D and 3D Helium atoms.展开更多
针对二维矩形条带装箱问题提出了一种启发式布局算法,即底部左齐择优匹配算法(lowest-level left a lignbest fit,简称LLABF).LLABF算法遵循最佳匹配优先原则,该原则综合考虑完全匹配优先、宽度匹配优先、高度匹配优先、组合宽度匹配优...针对二维矩形条带装箱问题提出了一种启发式布局算法,即底部左齐择优匹配算法(lowest-level left a lignbest fit,简称LLABF).LLABF算法遵循最佳匹配优先原则,该原则综合考虑完全匹配优先、宽度匹配优先、高度匹配优先、组合宽度匹配优先及可装入优先等启发式规则.与BL(bottom-left),IBL(improved-bottom-left)与BLF(bottom-left-fill)等启发算法不同的是,LLABF能够在矩形装入过程中自动选择与可装区域匹配的下一个待装矩形.计算结果表明,LLABF结合遗传算法(genetic algorithm,简称GA)解决二维条带装箱问题更加有效.展开更多
基金the National Natural Science Foundation of China(https://www.nsfc.gov.cn/,Project No.11972179)the Natural Science Foundation of Guangdong Province(http://gdstc.gd.gov.cn/,No.2020A1515010685)the Department of Education of Guangdong Province(http://edu.gd.gov.cn/,No.2020ZDZX2008).
文摘The boundary element method(BEM)is a popular method for solving acoustic wave propagation problems,especially those in exterior domains,owing to its ease in handling radiation conditions at infinity.However,BEM models must meet the requirement of 6–10 elements per wavelength,using the conventional constant,linear,or quadratic elements.Therefore,a large storage size of memory and long solution time are often needed in solving higher-frequency problems.In this work,we propose two new types of enriched elements based on conventional constant boundary elements to improve the computational efficiency of the 2D acoustic BEM.The first one uses a plane wave expansion,which can be used to model scattering problems.The second one uses a special plane wave expansion,which can be used tomodel radiation problems.Five examples are investigated to showthe advantages of the enriched elements.Compared with the conventional constant elements,the new enriched elements can deliver results with the same accuracy and in less computational time.This improvement in the computational efficiency is more evident at higher frequencies(with the nondimensional wave numbers exceeding 100).The paper concludes with the potential of our proposed enriched elements and plans for their further improvement.
基金Project supported by the National Natural Science Foundation of China(No.11074170)the State Key Laboratory Foundation of Shanghai Jiao Tong University(No.MSVMS201105)
文摘This paper describes formulation and implementation of the fast multipole boundary element method (FMBEM) for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the FMBEM are described in details. They are moment calculation, moment to moment translation, moment to local translation, and local to local translation. A data structure for the quad-tree construction is proposed which can facilitate implementation. An analytical moment expression is derived, which is more accurate, stable, and efficient than direct numerical computation. Numerical examples are presented to demonstrate the accuracy and efficiency of the FMBEM, and radiation of a 2D vibration rail mode is simulated using the FMBEM.
文摘The physical objective of solving for eigen-modes of a 1D quasiperiodic structure in photonics has been achieved. This was achieved thru considering this structure as a 1D projection or cut of a 2D periodic structure. And the problem is solved in a manner similar to 2D periodic photonic structures. A mechanical analogy (quasiperiodic orbits) helps to bring conceptual clarity.
基金Project supported by the National Natural Science Foundation of China (No. 10962004)the Special-ized Research Fund for the Doctoral Program of Higher Education of China (No. 20070126002)+1 种基金the Chunhui Program of Ministry of Education of China (No. Z2009-1-01010)the Natural Science Foundation of Inner Mongolia (No. 2009BS0101)
文摘This paper proposes an eigenfunction expansion method to solve twodimensional (2D) elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.
基金The project supported by the National Natural Science Foundation of China (19772025)
文摘A scheme of boundary element method for moving contact of two-dimensional elastic bodies using conforming discretization is presented. Both the displacement and the traction boundary conditions are satisfied on the contacting region in the sense of discretization. An algorithm to deal with the moving of the contact boundary on a larger possible contact region is presented. The algorithm is generalized to rolling contact problem as well. Some numerical examples of moving and rolling contact of 2D elastic bodies with or without friction, including the bodies with a hole-type defect, are given to show the effectiveness and the accuracy of the presented schemes.
基金supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20070126002)the National Natural Science Foundation of China (No. 10962004)
文摘This paper studies the eigenfunction expansion method to solve the two dimensional (2D) elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.
文摘In the present paper on the one hand we apply the central limit theorem to the solution of the sign problem of a path integral of two-interacting particles in potential and give an expression for the sign solved propagator (SSP) derived from that solution and on the other hand we perform the angular decomposition of the path integrals of the 2D and 3D Helium atoms. Finally, we combine those two results and derive the SSPs of the 2D and 3D Helium atoms.
文摘针对二维矩形条带装箱问题提出了一种启发式布局算法,即底部左齐择优匹配算法(lowest-level left a lignbest fit,简称LLABF).LLABF算法遵循最佳匹配优先原则,该原则综合考虑完全匹配优先、宽度匹配优先、高度匹配优先、组合宽度匹配优先及可装入优先等启发式规则.与BL(bottom-left),IBL(improved-bottom-left)与BLF(bottom-left-fill)等启发算法不同的是,LLABF能够在矩形装入过程中自动选择与可装区域匹配的下一个待装矩形.计算结果表明,LLABF结合遗传算法(genetic algorithm,简称GA)解决二维条带装箱问题更加有效.