In this paper we propose a novel two-stage method to solve the threedimensional Poisson equation in an arbitrary bounded domain enclosed by a smooth boundary.The solution is decomposed into a particular solution and a...In this paper we propose a novel two-stage method to solve the threedimensional Poisson equation in an arbitrary bounded domain enclosed by a smooth boundary.The solution is decomposed into a particular solution and a homogeneous solution.In the first stage a multiple-scale polynomial method(MSPM)is used to approximate the forcing term and then the formula of Tsai et al.[Tsai,Cheng,and Chen(2009)]is used to obtain the corresponding closed-form solution for each polynomial term.Then in the second stage we use a multiple/scale/direction Trefftz method(MSDTM)to find the solution of Laplace equation,of which the directions are uniformly distributed on a unit circle 1,and the scales are determined a priori by the collocation points on boundary.Two examples of 3D data interpolation,and several numerical examples of direct and inverse Cauchy problems in complex domain confirm the efficiency of the MSPM and the MSDTM.展开更多
This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method(LKM)with the dual reciprocity method(DRM).Firstly,the temporal derivative is discretized by...This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method(LKM)with the dual reciprocity method(DRM).Firstly,the temporal derivative is discretized by a finite difference scheme,and thus the governing equation of transient heat transfer is transformed into a non-homogeneous modified Helmholtz equation.Secondly,the solution of the non-homogeneous modified Helmholtz equation is decomposed into a particular solution and a homogeneous solution.And then,the DRM and LKM are used to solve the particular solution of the non-homogeneous equation and the homogeneous solution of the modified Helmholtz equation,respectively.The LKM is a recently proposed local radial basis function collocationmethod with themerits of being simple,accurate,and free ofmesh and integration.Compared with the traditional domain-type and boundary-type schemes,the present coupling algorithm could be treated as a really good alternative for the analysis of transient heat conduction on high-dimensional and complicated domains.Numerical experiments,including two-and three-dimensional heat transfer models,demonstrated the effectiveness and accuracy of the new methodology.展开更多
This paper presents a novel approach called the boundary integrated neural networks(BINNs)for analyzing acoustic radiation and scattering.The method introduces fundamental solutions of the time-harmonic wave equation ...This paper presents a novel approach called the boundary integrated neural networks(BINNs)for analyzing acoustic radiation and scattering.The method introduces fundamental solutions of the time-harmonic wave equation to encode the boundary integral equations(BIEs)within the neural networks,replacing the conventional use of the governing equation in physics-informed neural networks(PINNs).This approach offers several advantages.First,the input data for the neural networks in the BINNs only require the coordinates of“boundary”collocation points,making it highly suitable for analyzing acoustic fields in unbounded domains.Second,the loss function of the BINNs is not a composite form and has a fast convergence.Third,the BINNs achieve comparable precision to the PINNs using fewer collocation points and hidden layers/neurons.Finally,the semianalytic characteristic of the BIEs contributes to the higher precision of the BINNs.Numerical examples are presented to demonstrate the performance of the proposed method,and a MATLAB code implementation is provided as supplementary material.展开更多
This paper proposes a semi‐analytical and local meshless collocation method,the loca-lized method of fundamental solutions(LMFS),to address three‐dimensional(3D)acoustic inverse problems in complex domains.The propo...This paper proposes a semi‐analytical and local meshless collocation method,the loca-lized method of fundamental solutions(LMFS),to address three‐dimensional(3D)acoustic inverse problems in complex domains.The proposed approach is a recently developed numerical scheme with the potential of being mathematically simple,nu-merically accurate,and requiring less computational time and storage.In LMFS,an overdetermined sparse linear system is constructed by using the known data at the nodes on the accessible boundary and by making the remaining nodes satisfy the governing equation.In the numerical procedure,the pseudoinverse of a matrix is solved via the truncated singular value decomposition,and thus the regularization techniques are not needed in solving the resulting linear system with a well‐conditioned matrix.Numerical experiments,involving complicated geometry and the high noise level,confirm the ef-fectiveness and performance of the LMFS for solving 3D acoustic inverse problems.展开更多
This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semi...This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semianalytical collocation methods and localization strategies.Based on these basic concepts,five different formulations of localized collocation methods are introduced,including the localized radial basis function collocation method(LRBFCM)and the generalized finite difference method(GFDM),the localized method of fundamental solutions(LMFS),the localized radial Trefftz collocation method(LRTCM),and the localized collocation Trefftz method(LCTM).Then,several additional schemes,such as the generalized reciprocity method,Laplace and Fourier transformations,and Krylov deferred correction,are introduced to enable the application of the LCM to large-scale engineering and scientific computing for solving inhomogeneous,nonisotropic and time-dependent partial differential equations.Several typical benchmark examples are presented to show the recent developments and applications on the LCM solution of some selected boundary value problems,such as numerical wave flume,potential-based inverse electrocardiography,wave propagation analysis and 2D phononic crystals,elasticity and in-plane crack problems,heat conduction problems in heterogeneous material and nonlinear time-dependent Burgers’equations.Finally,some conclusions and outlooks of the LCMs are summarized.展开更多
This paper documents the first attempt to apply a localized method of fundamental solutions(LMFS)to the acoustic analysis of car cavity containing soundabsorbing materials.The LMFS is a recently developed meshless app...This paper documents the first attempt to apply a localized method of fundamental solutions(LMFS)to the acoustic analysis of car cavity containing soundabsorbing materials.The LMFS is a recently developed meshless approach with the merits of being mathematically simple,numerically accurate,and requiring less computer time and storage.Compared with the traditional method of fundamental solutions(MFS)with a full interpolation matrix,the LMFS can obtain a sparse banded linear algebraic system,and can circumvent the perplexing issue of fictitious boundary encountered in the MFS for complex solution domains.In the LMFS,only circular or spherical fictitious boundary is involved.Based on these advantages,the method can be regarded as a competitive alternative to the standard method,especially for high-dimensional and large-scale problems.Three benchmark numerical examples are provided to verify the effectiveness and performance of the present method for the solution of car cavity acoustic problems with impedance conditions.展开更多
The direct preparation of a kind of fluorinating reagent 1[F-TEDA-N(SO_(2)Ph)_(2)]was realized in high yield via the complexation of N-fluorobenzenesulfonimide(NFSI)with 1-(chloromethyl)-1,4-diazabicyclo[2.2.2]octan-1...The direct preparation of a kind of fluorinating reagent 1[F-TEDA-N(SO_(2)Ph)_(2)]was realized in high yield via the complexation of N-fluorobenzenesulfonimide(NFSI)with 1-(chloromethyl)-1,4-diazabicyclo[2.2.2]octan-1-ium N',N'-bis-(benzenesulfonylimide)salt.In its fluorination to oxindoles,the fluorinating products 6 were afforded in moderate to high yields.展开更多
With the increase in car ownership,traffic noise pollution has increased considerably and is one of the most severe types of noise pollution that affects living standards.Noise reduction by sound barriers is a common ...With the increase in car ownership,traffic noise pollution has increased considerably and is one of the most severe types of noise pollution that affects living standards.Noise reduction by sound barriers is a common protective measure used in this country and abroad.The acoustic performance of a sound barrier is highly dependent on its shape and material.In this paper,a semianalytical meshless Burton-Miller‐type singular boundary method is proposed to analyze the acoustic performance of various shapes of sound barriers,and the distribution of sound‐absorbing materials on the surface of sound barriers is optimized by combining a solid isotropic material with a penalization method.The acoustic effect of the sound‐absorbing material is simplified as the acoustical impedance boundary condition.The objective of optimization is to minimize the sound pressure in a given reference plane.The volume of the sound‐absorbing material is used as a constraint.The density of the nodes covered with the sound‐absorbing material is used as the design variable.The method of moving asymptotes was used to update the design variables.This model completely avoids the mesh discretization process in the finite element method and requires only boundary nodes.In addition,the approach also does not require the singular integral calculation in the boundary element method.The method is illustrated and validated using numerical examples to demonstrate its accuracy and efficiency.展开更多
基金The work described in this paper was supported by the Thousand Talents Plan of China(Grant No.A1211010)the Fundamental Research Funds for the Central Universities(Grant nos.2017B656X14,2017B05714)+1 种基金the Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.KYCX17_0487)the Natural Science Foundation of Shandong Province of China(Grant No.ZR2017BA003).
文摘In this paper we propose a novel two-stage method to solve the threedimensional Poisson equation in an arbitrary bounded domain enclosed by a smooth boundary.The solution is decomposed into a particular solution and a homogeneous solution.In the first stage a multiple-scale polynomial method(MSPM)is used to approximate the forcing term and then the formula of Tsai et al.[Tsai,Cheng,and Chen(2009)]is used to obtain the corresponding closed-form solution for each polynomial term.Then in the second stage we use a multiple/scale/direction Trefftz method(MSDTM)to find the solution of Laplace equation,of which the directions are uniformly distributed on a unit circle 1,and the scales are determined a priori by the collocation points on boundary.Two examples of 3D data interpolation,and several numerical examples of direct and inverse Cauchy problems in complex domain confirm the efficiency of the MSPM and the MSDTM.
基金supported by the NationalNatural Science Foundation of China (No.11802151)the Natural Science Foundation of Shandong Province of China (No.ZR2019BA008)the China Postdoctoral Science Foundation (No.2019M652315).
文摘This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method(LKM)with the dual reciprocity method(DRM).Firstly,the temporal derivative is discretized by a finite difference scheme,and thus the governing equation of transient heat transfer is transformed into a non-homogeneous modified Helmholtz equation.Secondly,the solution of the non-homogeneous modified Helmholtz equation is decomposed into a particular solution and a homogeneous solution.And then,the DRM and LKM are used to solve the particular solution of the non-homogeneous equation and the homogeneous solution of the modified Helmholtz equation,respectively.The LKM is a recently proposed local radial basis function collocationmethod with themerits of being simple,accurate,and free ofmesh and integration.Compared with the traditional domain-type and boundary-type schemes,the present coupling algorithm could be treated as a really good alternative for the analysis of transient heat conduction on high-dimensional and complicated domains.Numerical experiments,including two-and three-dimensional heat transfer models,demonstrated the effectiveness and accuracy of the new methodology.
基金Natural Science Foundation of Shandong Province of China,Grant/Award Numbers:ZR2022YQ06,ZR2021JQ02Development Plan of Youth Innovation Team in Colleges and Universities of Shandong Province,Grant/Award Number:2022KJ140+2 种基金National Natural Science Foundation of China,Grant/Award Number:12372199Fund of the Key Laboratory of Road Construction Technology and Equipment,Chang'an University,Grant/Award Number:300102253502Water Affairs Technology Project of Nanjing,Grant/Award Number:202203。
文摘This paper presents a novel approach called the boundary integrated neural networks(BINNs)for analyzing acoustic radiation and scattering.The method introduces fundamental solutions of the time-harmonic wave equation to encode the boundary integral equations(BIEs)within the neural networks,replacing the conventional use of the governing equation in physics-informed neural networks(PINNs).This approach offers several advantages.First,the input data for the neural networks in the BINNs only require the coordinates of“boundary”collocation points,making it highly suitable for analyzing acoustic fields in unbounded domains.Second,the loss function of the BINNs is not a composite form and has a fast convergence.Third,the BINNs achieve comparable precision to the PINNs using fewer collocation points and hidden layers/neurons.Finally,the semianalytic characteristic of the BIEs contributes to the higher precision of the BINNs.Numerical examples are presented to demonstrate the performance of the proposed method,and a MATLAB code implementation is provided as supplementary material.
基金National Natural Science Foundation of China,Grant/Award Number:11802151Natural Science Foundation of Shandong Province of China,Grant/Award Number:ZR2019BA008+1 种基金supported by the National Natural Science Foundation of China(No.11802151)the Natural Science Foundation of Shandong Province of China(No.ZR2019BA008).
文摘This paper proposes a semi‐analytical and local meshless collocation method,the loca-lized method of fundamental solutions(LMFS),to address three‐dimensional(3D)acoustic inverse problems in complex domains.The proposed approach is a recently developed numerical scheme with the potential of being mathematically simple,nu-merically accurate,and requiring less computational time and storage.In LMFS,an overdetermined sparse linear system is constructed by using the known data at the nodes on the accessible boundary and by making the remaining nodes satisfy the governing equation.In the numerical procedure,the pseudoinverse of a matrix is solved via the truncated singular value decomposition,and thus the regularization techniques are not needed in solving the resulting linear system with a well‐conditioned matrix.Numerical experiments,involving complicated geometry and the high noise level,confirm the ef-fectiveness and performance of the LMFS for solving 3D acoustic inverse problems.
基金supported by the National Natural Science Foundation of China(Grant Nos.12122205 and 11772119)the Six Talent Peaks Project in Jiangsu Province of China(Grant No.2019-KTHY-009).
文摘This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semianalytical collocation methods and localization strategies.Based on these basic concepts,five different formulations of localized collocation methods are introduced,including the localized radial basis function collocation method(LRBFCM)and the generalized finite difference method(GFDM),the localized method of fundamental solutions(LMFS),the localized radial Trefftz collocation method(LRTCM),and the localized collocation Trefftz method(LCTM).Then,several additional schemes,such as the generalized reciprocity method,Laplace and Fourier transformations,and Krylov deferred correction,are introduced to enable the application of the LCM to large-scale engineering and scientific computing for solving inhomogeneous,nonisotropic and time-dependent partial differential equations.Several typical benchmark examples are presented to show the recent developments and applications on the LCM solution of some selected boundary value problems,such as numerical wave flume,potential-based inverse electrocardiography,wave propagation analysis and 2D phononic crystals,elasticity and in-plane crack problems,heat conduction problems in heterogeneous material and nonlinear time-dependent Burgers’equations.Finally,some conclusions and outlooks of the LCMs are summarized.
基金the National Natural Science Foundation of China(No.11802151)the Natural Science Foundation of Shandong Province of China(No.ZR2019BA008).
文摘This paper documents the first attempt to apply a localized method of fundamental solutions(LMFS)to the acoustic analysis of car cavity containing soundabsorbing materials.The LMFS is a recently developed meshless approach with the merits of being mathematically simple,numerically accurate,and requiring less computer time and storage.Compared with the traditional method of fundamental solutions(MFS)with a full interpolation matrix,the LMFS can obtain a sparse banded linear algebraic system,and can circumvent the perplexing issue of fictitious boundary encountered in the MFS for complex solution domains.In the LMFS,only circular or spherical fictitious boundary is involved.Based on these advantages,the method can be regarded as a competitive alternative to the standard method,especially for high-dimensional and large-scale problems.Three benchmark numerical examples are provided to verify the effectiveness and performance of the present method for the solution of car cavity acoustic problems with impedance conditions.
基金the National Natural Science Foundation of China(No.21372077)for their financial supports.
文摘The direct preparation of a kind of fluorinating reagent 1[F-TEDA-N(SO_(2)Ph)_(2)]was realized in high yield via the complexation of N-fluorobenzenesulfonimide(NFSI)with 1-(chloromethyl)-1,4-diazabicyclo[2.2.2]octan-1-ium N',N'-bis-(benzenesulfonylimide)salt.In its fluorination to oxindoles,the fluorinating products 6 were afforded in moderate to high yields.
基金The Natural Science Foundation of Shandong Province of China,Grant/Award Number:ZR2023YQ005The DAAD-K.C.Wong Postdoctoral Fellowships。
文摘With the increase in car ownership,traffic noise pollution has increased considerably and is one of the most severe types of noise pollution that affects living standards.Noise reduction by sound barriers is a common protective measure used in this country and abroad.The acoustic performance of a sound barrier is highly dependent on its shape and material.In this paper,a semianalytical meshless Burton-Miller‐type singular boundary method is proposed to analyze the acoustic performance of various shapes of sound barriers,and the distribution of sound‐absorbing materials on the surface of sound barriers is optimized by combining a solid isotropic material with a penalization method.The acoustic effect of the sound‐absorbing material is simplified as the acoustical impedance boundary condition.The objective of optimization is to minimize the sound pressure in a given reference plane.The volume of the sound‐absorbing material is used as a constraint.The density of the nodes covered with the sound‐absorbing material is used as the design variable.The method of moving asymptotes was used to update the design variables.This model completely avoids the mesh discretization process in the finite element method and requires only boundary nodes.In addition,the approach also does not require the singular integral calculation in the boundary element method.The method is illustrated and validated using numerical examples to demonstrate its accuracy and efficiency.
