We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forwa...We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forward scattering dominates. At the same time, this model provides an efficiency gain of an order of magnitude or more over two-way coupled-mode models. This model can be applied to three-dimensional range-dependent problems with a slowly varying bathymetry or internal waves. A numerical example of the latter is demonstrated in this work. Comparisons of both accuracy and efficiency between the present model and a benchmark model are also provided.展开更多
In this paper we consider two problems. The first is connected with the optimal recovery of functions satisfyiog boundary conditions. The second is the characterization of the unique func- tion whose r-th derivative h...In this paper we consider two problems. The first is connected with the optimal recovery of functions satisfyiog boundary conditions. The second is the characterization of the unique func- tion whose r-th derivative has minimum L_∞-norm, taking given values of alternating signs and satis fying boundary conditions.展开更多
To solve large-scale optimization problems,Fragrance coefficient and variant Particle Swarm local search Butterfly Optimization Algorithm(FPSBOA)is proposed.In the position update stage of Butterfly Optimization Algor...To solve large-scale optimization problems,Fragrance coefficient and variant Particle Swarm local search Butterfly Optimization Algorithm(FPSBOA)is proposed.In the position update stage of Butterfly Optimization Algorithm(BOA),the fragrance coefficient is designed to balance the exploration and exploitation of BOA.The variant particle swarm local search strategy is proposed to improve the local search ability of the current optimal butterfly and prevent the algorithm from falling into local optimality.192000-dimensional functions and 201000-dimensional CEC 2010 large-scale functions are used to verify FPSBOA for complex large-scale optimization problems.The experimental results are statistically analyzed by Friedman test and Wilcoxon rank-sum test.All attained results demonstrated that FPSBOA can better solve more challenging scientific and industrial real-world problems with thousands of variables.Finally,four mechanical engineering problems and one ten-dimensional process synthesis and design problem are applied to FPSBOA,which shows FPSBOA has the feasibility and effectiveness in real-world application problems.展开更多
The stability in L∞-norm is considered for the Ritz-Volterra projection and some applications are presented in this paper. As a result, point-wise error estimates are established for the finite element approximation ...The stability in L∞-norm is considered for the Ritz-Volterra projection and some applications are presented in this paper. As a result, point-wise error estimates are established for the finite element approximation for the parabolic integrodifferential equation, Sobolev equations, and a diffusion equation with non-local boundary value problem.展开更多
The numerical quadrature methods for dealing with the problems of singular and near-singular integrals caused by Burton-Miller method are proposed, by which the conventional and fast multipole BEMs (boundary element ...The numerical quadrature methods for dealing with the problems of singular and near-singular integrals caused by Burton-Miller method are proposed, by which the conventional and fast multipole BEMs (boundary element methods) for 3D acoustic problems based on constant elements are improved. To solve the problem of singular integrals, a Hadamard finite-part integral method is presented, which is a simplified combination of the methods proposed by Kirkup and Wolf. The problem of near-singular integrals is overcome by the simple method of polar transformation and the more complex method of PART (Projection and Angular & Radial Transformation). The effectiveness of these methods for solving the singular and near-singular problems is validated through comparing with the results computed by the analytical method and/or the commercial software LMS Virtual.Lab. In addition, the influence of the near-singular integral problem on the computational precisions is analyzed by computing the errors relative to the exact solution. The computational complexities of the conventional and fast multipole BEM are analyzed and compared through numerical computations. A large-scale acoustic scattering problem, whose degree of freedoms is about 340,000, is implemented successfully. The results show that, the near singularity is primarily introduced by the hyper-singular kernel, and has great influences on the precision of the solution. The precision of fast multipole BEM is the same as conventional BEM, but the computational complexities are much lower.展开更多
A numerical method of solving acoustic wave scattering pnblem in fluids is described. Radiation boundary condition (RBC) obtained by factorization method of Helmholtz equation is applied to transforming the exterior b...A numerical method of solving acoustic wave scattering pnblem in fluids is described. Radiation boundary condition (RBC) obtained by factorization method of Helmholtz equation is applied to transforming the exterior boundary value problem in unbounded region into one in a finite region. Combined with RBC and scatterer surface boundary condition, Helmholtz equation is solved numerically by the finite difference method. Computational results for sphere and prolate spheroidal scatterers are in excellent agreement with eigenfunction solutions and much better than the results of OSRC method.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 11774374the Natural Science Foundation of Shandong Province of China under Grant No ZR2016AL10
文摘We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forward scattering dominates. At the same time, this model provides an efficiency gain of an order of magnitude or more over two-way coupled-mode models. This model can be applied to three-dimensional range-dependent problems with a slowly varying bathymetry or internal waves. A numerical example of the latter is demonstrated in this work. Comparisons of both accuracy and efficiency between the present model and a benchmark model are also provided.
基金Partially supported by Ministry of Science under Project MM--414.
文摘In this paper we consider two problems. The first is connected with the optimal recovery of functions satisfyiog boundary conditions. The second is the characterization of the unique func- tion whose r-th derivative has minimum L_∞-norm, taking given values of alternating signs and satis fying boundary conditions.
基金funded by the National Natural Science Foundation of China(No.72104069)the Science and Technology Department of Henan Province,China(No.182102310886 and 162102110109)the Postgraduate Meritocracy Scheme,hina(No.SYL19060145).
文摘To solve large-scale optimization problems,Fragrance coefficient and variant Particle Swarm local search Butterfly Optimization Algorithm(FPSBOA)is proposed.In the position update stage of Butterfly Optimization Algorithm(BOA),the fragrance coefficient is designed to balance the exploration and exploitation of BOA.The variant particle swarm local search strategy is proposed to improve the local search ability of the current optimal butterfly and prevent the algorithm from falling into local optimality.192000-dimensional functions and 201000-dimensional CEC 2010 large-scale functions are used to verify FPSBOA for complex large-scale optimization problems.The experimental results are statistically analyzed by Friedman test and Wilcoxon rank-sum test.All attained results demonstrated that FPSBOA can better solve more challenging scientific and industrial real-world problems with thousands of variables.Finally,four mechanical engineering problems and one ten-dimensional process synthesis and design problem are applied to FPSBOA,which shows FPSBOA has the feasibility and effectiveness in real-world application problems.
文摘The stability in L∞-norm is considered for the Ritz-Volterra projection and some applications are presented in this paper. As a result, point-wise error estimates are established for the finite element approximation for the parabolic integrodifferential equation, Sobolev equations, and a diffusion equation with non-local boundary value problem.
基金supported by the National Natural Science Foundation of China(11304344,11404364)the Project of Hubei Provincial Department of Education(D20141803)+1 种基金the Natural Science Foundation of Hubei Province(2014CFB378)the Doctoral Scientific Research Foundation of Hubei University of Automotive Technology(BK201604)
文摘The numerical quadrature methods for dealing with the problems of singular and near-singular integrals caused by Burton-Miller method are proposed, by which the conventional and fast multipole BEMs (boundary element methods) for 3D acoustic problems based on constant elements are improved. To solve the problem of singular integrals, a Hadamard finite-part integral method is presented, which is a simplified combination of the methods proposed by Kirkup and Wolf. The problem of near-singular integrals is overcome by the simple method of polar transformation and the more complex method of PART (Projection and Angular & Radial Transformation). The effectiveness of these methods for solving the singular and near-singular problems is validated through comparing with the results computed by the analytical method and/or the commercial software LMS Virtual.Lab. In addition, the influence of the near-singular integral problem on the computational precisions is analyzed by computing the errors relative to the exact solution. The computational complexities of the conventional and fast multipole BEM are analyzed and compared through numerical computations. A large-scale acoustic scattering problem, whose degree of freedoms is about 340,000, is implemented successfully. The results show that, the near singularity is primarily introduced by the hyper-singular kernel, and has great influences on the precision of the solution. The precision of fast multipole BEM is the same as conventional BEM, but the computational complexities are much lower.
基金The Project is supported by the National Natural Science Foundation of China.
文摘A numerical method of solving acoustic wave scattering pnblem in fluids is described. Radiation boundary condition (RBC) obtained by factorization method of Helmholtz equation is applied to transforming the exterior boundary value problem in unbounded region into one in a finite region. Combined with RBC and scatterer surface boundary condition, Helmholtz equation is solved numerically by the finite difference method. Computational results for sphere and prolate spheroidal scatterers are in excellent agreement with eigenfunction solutions and much better than the results of OSRC method.