In this paper,the collocation methods are used to solve the boundary integral equations of the first kind on the polygon.By means of Sidi’s periodic transformation and domain decomposition,the errors are proved to po...In this paper,the collocation methods are used to solve the boundary integral equations of the first kind on the polygon.By means of Sidi’s periodic transformation and domain decomposition,the errors are proved to possess the multi-parameter asymptotic expansion at the interior point with the powers h^(3)/_(i)(i=1,...,d),which means that the approximations of higher accuracy and a posteriori estimation of the errors can be obtained by splitting extrapolations.Numerical experiments are carried out to show that the methods are very efficient.展开更多
The entrance region flow of a Herschel-Bulkley fluid in an annular cylinder has been investigated numerically without making prior assumptions on the form of velocity profile within the boundary layer region. This vel...The entrance region flow of a Herschel-Bulkley fluid in an annular cylinder has been investigated numerically without making prior assumptions on the form of velocity profile within the boundary layer region. This velocity distribution is determined as part of the procedure by cross sectional integration of the momentum differential equation for a given distance z from the channel entrance. Using the macroscopic mass and momentum balance equation, the entrance length at each cross section of the entrance region of the annuli and pressure distribution have been calculated for specific values of Herschel-Bulkley number and various values of aspect ratio and flow behavior index. The effects of non-Newtonian characteristics and channel width on the velocity profile, pressure distribution and the entrance length have been discussed.展开更多
The uniqueness of solution of field point, inside a convex region due to singular source(s) with kernel function decreasing with distance increasing, outside-region-distribution(s) such that the boundary condition exp...The uniqueness of solution of field point, inside a convex region due to singular source(s) with kernel function decreasing with distance increasing, outside-region-distribution(s) such that the boundary condition expressed by the response of the source(s) is satisfied, is proved by using the condition of kernel function decreasing with distance increasing anal an integral inequality. Examples of part of these singular sources such as Kelvin's point force, Point-Ring-Couple (PRC) etc. are given. The proof of uniqueness of solution of field point in a twisted shaft of revolution due to PRC distribution is given as an example of application.展开更多
We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions.Standard finite or boundary element methods require the number of degrees of free...We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions.Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy.Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem,we propose a novel Galerkin boundary element method,with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon.Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.展开更多
This paper presents mechanical quadrature methods for solving first-kind boundary integral equations on polygonal regions, which possesses high accuracy O(h0^3)and low computing complexities. Moreover, the multivariat...This paper presents mechanical quadrature methods for solving first-kind boundary integral equations on polygonal regions, which possesses high accuracy O(h0^3)and low computing complexities. Moreover, the multivariate asymptotic expansion of the error with hi^3(i = 1,…,d) power is shown. Using the multi-parameter asymptotic expansion, we not only get a high precisioin approximation solution by means of the splitting extrapolation, but also derive a posteriori estimation.展开更多
文摘In this paper,the collocation methods are used to solve the boundary integral equations of the first kind on the polygon.By means of Sidi’s periodic transformation and domain decomposition,the errors are proved to possess the multi-parameter asymptotic expansion at the interior point with the powers h^(3)/_(i)(i=1,...,d),which means that the approximations of higher accuracy and a posteriori estimation of the errors can be obtained by splitting extrapolations.Numerical experiments are carried out to show that the methods are very efficient.
文摘The entrance region flow of a Herschel-Bulkley fluid in an annular cylinder has been investigated numerically without making prior assumptions on the form of velocity profile within the boundary layer region. This velocity distribution is determined as part of the procedure by cross sectional integration of the momentum differential equation for a given distance z from the channel entrance. Using the macroscopic mass and momentum balance equation, the entrance length at each cross section of the entrance region of the annuli and pressure distribution have been calculated for specific values of Herschel-Bulkley number and various values of aspect ratio and flow behavior index. The effects of non-Newtonian characteristics and channel width on the velocity profile, pressure distribution and the entrance length have been discussed.
文摘The uniqueness of solution of field point, inside a convex region due to singular source(s) with kernel function decreasing with distance increasing, outside-region-distribution(s) such that the boundary condition expressed by the response of the source(s) is satisfied, is proved by using the condition of kernel function decreasing with distance increasing anal an integral inequality. Examples of part of these singular sources such as Kelvin's point force, Point-Ring-Couple (PRC) etc. are given. The proof of uniqueness of solution of field point in a twisted shaft of revolution due to PRC distribution is given as an example of application.
文摘We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions.Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy.Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem,we propose a novel Galerkin boundary element method,with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon.Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.
文摘This paper presents mechanical quadrature methods for solving first-kind boundary integral equations on polygonal regions, which possesses high accuracy O(h0^3)and low computing complexities. Moreover, the multivariate asymptotic expansion of the error with hi^3(i = 1,…,d) power is shown. Using the multi-parameter asymptotic expansion, we not only get a high precisioin approximation solution by means of the splitting extrapolation, but also derive a posteriori estimation.
