This study is concerned with the numerical approximation of the extended Fisher-Kolmogorov equation with a modified boundary integral method. A key aspect of this formulation is that it relaxes the domain-driven appro...This study is concerned with the numerical approximation of the extended Fisher-Kolmogorov equation with a modified boundary integral method. A key aspect of this formulation is that it relaxes the domain-driven approach of a typical boundary element (BEM) technique. While its discretization keeps faith with the second order accurate BEM formulation, its implementation is element-based. This leads to a local solution of all integral equation and their final assembly into a slender and banded coefficient matrix which is far easier to manipulate numerically. This outcome is much better than working with BEM’s fully populated coefficient matrices resulting from a numerical encounter with the problem domain especially for nonlinear, transient, and heterogeneous problems. Faithful results of high accuracy are achieved when the results obtained herein are compared with those available in literature.展开更多
This work deals with incompressible two-dimensional viscous flow over a semi-infinite plate ac-cording to the approximations resulting from Prandtl boundary layer theory. The governing non-linear coupled partial diffe...This work deals with incompressible two-dimensional viscous flow over a semi-infinite plate ac-cording to the approximations resulting from Prandtl boundary layer theory. The governing non-linear coupled partial differential equations describing laminar flow are converted to a self-simi- lar type third order ordinary differential equation known as the Falkner-Skan equation. For the purposes of a numerical solution, the Falkner-Skan equation is converted to a system of first order ordinary differential equations. These are numerically addressed by the conventional shooting and bisection methods coupled with the Runge-Kutta technique. However the accompanying energy equation lends itself to a hybrid numerical finite element-boundary integral application. An appropriate complementary differential equation as well as the Green second identity paves the way for the integral representation of the energy equation. This is followed by a finite element-type discretization of the problem domain. Based on the quality of the results obtained herein, a strong case is made for a hybrid numerical scheme as a useful approach for the numerical resolution of boundary layer flows and species transport. Thanks to the sparsity of the resulting coefficient matrix, the solution profiles not only agree with those of similar problems in literature but also are in consonance with the physics they represent.展开更多
The Volume-Surface Current Continuity Method (VSCCM) is presented to analyze electromagnetic radiation from microstrip antenna. The microstrip antenna is discretized into small triangular patches on conducting surface...The Volume-Surface Current Continuity Method (VSCCM) is presented to analyze electromagnetic radiation from microstrip antenna. The microstrip antenna is discretized into small triangular patches on conducting surface and tetrahedral volume cells in dielectric region. The Method of Moments (MoM) is applied to solve the integral equation. An equation contains the restriction relation between the volume and surface current coefficient is derived from the current continuity equation at those parts where the conducting surface is in contact with the dielectric material. A simple equivalent strip model is introduced in the treatment of the feeding probe in VSCCM. The VSCCM can reduce the unknowns required to be solved in MoM, as well as the condition number of the matrix equation. Numerical results are given to validate the accuracy and efficiency of this method.展开更多
The hybrid boundary node method （HBNM） is a promising method for solving boundary value problems with the hybrid displacement variational formulation and shape functions from the moving least squares（MLS） approxim...The hybrid boundary node method （HBNM） is a promising method for solving boundary value problems with the hybrid displacement variational formulation and shape functions from the moving least squares（MLS） approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the latter. Following its application in solving potential problems, it is further developed and numerically implemented for 2D solids in this paper. The rigid movement method is employed to solve the hyper-singular integrations. Numerical examples for some 2D solids have been given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method are studied through numerical examples.展开更多
This paper presents a high-order coupled compact integrated RBF(CC IRBF)approximation based domain decomposition(DD)algorithm for the discretisation of second-order differential problems.Several Schwarz DD algorithms,...This paper presents a high-order coupled compact integrated RBF(CC IRBF)approximation based domain decomposition(DD)algorithm for the discretisation of second-order differential problems.Several Schwarz DD algorithms,including one-level additive/multiplicative and two-level additive/multiplicative/hybrid,are employed.The CCIRBF based DD algorithms are analysed with different mesh sizes,numbers of subdomains and overlap sizes for Poisson problems.Our convergence analysis shows that the CCIRBF two-level multiplicative version is the most effective algorithm among various schemes employed here.Especially,the present CCIRBF two-level method converges quite rapidly even when the domain is divided into many subdomains,which shows great promise for either serial or parallel computing.For practical tests,we then incorporate the CCIRBF into serial and parallel two-level multiplicative Schwarz.Several numerical examples,including those governed by Poisson and Navier-Stokes equations are analysed to demonstrate the accuracy and efficiency of the serial and parallel algorithms implemented with the CCIRBF.Numerical results show:(i)the CCIRBF-Serial and-Parallel algorithms have the capability to reach almost the same solution accuracy level of the CCIRBF-Single domain,which is ideal in terms of computational calculations;(ii)the CCIRBF-Serial and-Parallel algorithms are highly accurate in comparison with standard finite difference,compact finite difference and some other schemes;(iii)the proposed CCIRBF-Serial and-Parallel algorithms may be used as alternatives to solve large-size problems which the CCIRBF-Single domain may not be able to deal with.The ability of producing stable and highly accurate results of the proposed serial and parallel schemes is believed to be the contribution of the coarse mesh of the two-level domain decomposition and the CCIRBF approximation.It is noted that the focus of this paper is on the derivation of highly accurate serial and parallel algorithms for second-order differential problems.The scope of this work does not cover a thorough analysis of computational time.展开更多
Torsional guided waves have been widely utilized to inspect the surface corrosion in pipelines due to their simple displacement behaviors and the ability of longrange transmission.Especially,the torsional mode T(0,1),...Torsional guided waves have been widely utilized to inspect the surface corrosion in pipelines due to their simple displacement behaviors and the ability of longrange transmission.Especially,the torsional mode T(0,1),which is the first order of torsional guided waves,plays the irreplaceable position and role,mainly because of its non-dispersion characteristic property.However,one of the most pressing challenges faced in modern quality inspection is to detect the surface defects in pipelines with a high level of accuracy.Taking into account this situation,a quantitative reconstruction method using the torsional guided wave T(0,1)is proposed in this paper.The methodology for defect reconstruction consists of three steps.First,the reflection coefficients of the guided wave T(0,1)scattered by different sizes of axisymmetric defects are calculated using the developed hybrid finite element method(HFEM).Then,applying the boundary integral equation(BIE)and Born approximation,the Fourier transform of the surface defect profile can be analytically derived as the correlative product of reflection coefficients of the torsional guided wave T(0,1)and the fundamental solution of the intact pipeline in the frequency domain.Finally,reconstruction of defects is precisely performed by the inverse Fourier transform of the product in the frequency domain.Numerical experiments show that the proposed approach is suitable for the detection of surface defects with arbitrary shapes.Meanwhile,the effects of the depth and width of surface defects on the accuracy of defect reconstruction are investigated.It is noted that the reconstructive error is less than 10%,providing that the defect depth is no more than one half of the pipe thickness.展开更多
文摘This study is concerned with the numerical approximation of the extended Fisher-Kolmogorov equation with a modified boundary integral method. A key aspect of this formulation is that it relaxes the domain-driven approach of a typical boundary element (BEM) technique. While its discretization keeps faith with the second order accurate BEM formulation, its implementation is element-based. This leads to a local solution of all integral equation and their final assembly into a slender and banded coefficient matrix which is far easier to manipulate numerically. This outcome is much better than working with BEM’s fully populated coefficient matrices resulting from a numerical encounter with the problem domain especially for nonlinear, transient, and heterogeneous problems. Faithful results of high accuracy are achieved when the results obtained herein are compared with those available in literature.
文摘This work deals with incompressible two-dimensional viscous flow over a semi-infinite plate ac-cording to the approximations resulting from Prandtl boundary layer theory. The governing non-linear coupled partial differential equations describing laminar flow are converted to a self-simi- lar type third order ordinary differential equation known as the Falkner-Skan equation. For the purposes of a numerical solution, the Falkner-Skan equation is converted to a system of first order ordinary differential equations. These are numerically addressed by the conventional shooting and bisection methods coupled with the Runge-Kutta technique. However the accompanying energy equation lends itself to a hybrid numerical finite element-boundary integral application. An appropriate complementary differential equation as well as the Green second identity paves the way for the integral representation of the energy equation. This is followed by a finite element-type discretization of the problem domain. Based on the quality of the results obtained herein, a strong case is made for a hybrid numerical scheme as a useful approach for the numerical resolution of boundary layer flows and species transport. Thanks to the sparsity of the resulting coefficient matrix, the solution profiles not only agree with those of similar problems in literature but also are in consonance with the physics they represent.
基金Supported by Natural Science Foundation of Fujian Province of China (2011J01348)the Science and Technique Major Program of Fujian Province (2010HZ-0004-1)
文摘The Volume-Surface Current Continuity Method (VSCCM) is presented to analyze electromagnetic radiation from microstrip antenna. The microstrip antenna is discretized into small triangular patches on conducting surface and tetrahedral volume cells in dielectric region. The Method of Moments (MoM) is applied to solve the integral equation. An equation contains the restriction relation between the volume and surface current coefficient is derived from the current continuity equation at those parts where the conducting surface is in contact with the dielectric material. A simple equivalent strip model is introduced in the treatment of the feeding probe in VSCCM. The VSCCM can reduce the unknowns required to be solved in MoM, as well as the condition number of the matrix equation. Numerical results are given to validate the accuracy and efficiency of this method.
基金Project supported by the Key Lab of Geomechanics, Chinese Academy of Sciences (No.Z110202).
文摘The hybrid boundary node method （HBNM） is a promising method for solving boundary value problems with the hybrid displacement variational formulation and shape functions from the moving least squares（MLS） approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the latter. Following its application in solving potential problems, it is further developed and numerically implemented for 2D solids in this paper. The rigid movement method is employed to solve the hyper-singular integrations. Numerical examples for some 2D solids have been given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method are studied through numerical examples.
文摘This paper presents a high-order coupled compact integrated RBF(CC IRBF)approximation based domain decomposition(DD)algorithm for the discretisation of second-order differential problems.Several Schwarz DD algorithms,including one-level additive/multiplicative and two-level additive/multiplicative/hybrid,are employed.The CCIRBF based DD algorithms are analysed with different mesh sizes,numbers of subdomains and overlap sizes for Poisson problems.Our convergence analysis shows that the CCIRBF two-level multiplicative version is the most effective algorithm among various schemes employed here.Especially,the present CCIRBF two-level method converges quite rapidly even when the domain is divided into many subdomains,which shows great promise for either serial or parallel computing.For practical tests,we then incorporate the CCIRBF into serial and parallel two-level multiplicative Schwarz.Several numerical examples,including those governed by Poisson and Navier-Stokes equations are analysed to demonstrate the accuracy and efficiency of the serial and parallel algorithms implemented with the CCIRBF.Numerical results show:(i)the CCIRBF-Serial and-Parallel algorithms have the capability to reach almost the same solution accuracy level of the CCIRBF-Single domain,which is ideal in terms of computational calculations;(ii)the CCIRBF-Serial and-Parallel algorithms are highly accurate in comparison with standard finite difference,compact finite difference and some other schemes;(iii)the proposed CCIRBF-Serial and-Parallel algorithms may be used as alternatives to solve large-size problems which the CCIRBF-Single domain may not be able to deal with.The ability of producing stable and highly accurate results of the proposed serial and parallel schemes is believed to be the contribution of the coarse mesh of the two-level domain decomposition and the CCIRBF approximation.It is noted that the focus of this paper is on the derivation of highly accurate serial and parallel algorithms for second-order differential problems.The scope of this work does not cover a thorough analysis of computational time.
基金Project supported by the National Natural Science Foundation of China(Nos.11502108 and 1611530686)the State Key Laboratory of Mechanics and Control of Mechanical Structures at Nanjing University of Aeronautics and Astronautics(NUAA)(No.MCMS-E-0520K02)and the Key Laboratory of Impact and Safety Engineering,Ministry of Education,Ningbo University(No.CJ201904)。
文摘Torsional guided waves have been widely utilized to inspect the surface corrosion in pipelines due to their simple displacement behaviors and the ability of longrange transmission.Especially,the torsional mode T(0,1),which is the first order of torsional guided waves,plays the irreplaceable position and role,mainly because of its non-dispersion characteristic property.However,one of the most pressing challenges faced in modern quality inspection is to detect the surface defects in pipelines with a high level of accuracy.Taking into account this situation,a quantitative reconstruction method using the torsional guided wave T(0,1)is proposed in this paper.The methodology for defect reconstruction consists of three steps.First,the reflection coefficients of the guided wave T(0,1)scattered by different sizes of axisymmetric defects are calculated using the developed hybrid finite element method(HFEM).Then,applying the boundary integral equation(BIE)and Born approximation,the Fourier transform of the surface defect profile can be analytically derived as the correlative product of reflection coefficients of the torsional guided wave T(0,1)and the fundamental solution of the intact pipeline in the frequency domain.Finally,reconstruction of defects is precisely performed by the inverse Fourier transform of the product in the frequency domain.Numerical experiments show that the proposed approach is suitable for the detection of surface defects with arbitrary shapes.Meanwhile,the effects of the depth and width of surface defects on the accuracy of defect reconstruction are investigated.It is noted that the reconstructive error is less than 10%,providing that the defect depth is no more than one half of the pipe thickness.
