In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be r...In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.展开更多
For a class of two-point boundary value problems, by virtue of onedimensional projection interpolation, it is proved that the nodal recovery derivative obtained by Yuan＇s element energy projection （EEP） method has ...For a class of two-point boundary value problems, by virtue of onedimensional projection interpolation, it is proved that the nodal recovery derivative obtained by Yuan＇s element energy projection （EEP） method has the accuracy O（h^min{2k,k＋4}） The theoretical analysis coincides the reported numerical results.展开更多
Combining the radial point interpolation method （RPIM）, the dual reciprocity method （DRM） and the hybrid boundary node method （HBNM）, a dual reciprocity hybrid radial boundary node method （DHRBNM） is proposed ...Combining the radial point interpolation method （RPIM）, the dual reciprocity method （DRM） and the hybrid boundary node method （HBNM）, a dual reciprocity hybrid radial boundary node method （DHRBNM） is proposed for linear elasticity. Compared to DHBNM, RPIM is exploited to replace the moving least square （MLS） in DHRBNM, and it gets rid of the deficiency of MLS approximation, in which shape functions lack the delta function property, the boundary condition can not be applied easily and directly and it＇s computational expense is high. Besides, different approximate functions are discussed in DRM to get the interpolation property, in which the accuracy and efficiency for different basis functions are compared. Then RPIM is also applied in DRM to replace the conical function interpolation, which can greatly improve the accuracy of the present method. To demonstrate the effectiveness of the present method, DHBNM is applied for comparison, and some numerical examples of 2-D elasticity problems show that the present method is much more effective than DHBNM.展开更多
A novel extended traction boundary element-free method is proposed to analyze the crack problems of two-dimensional infinite magnetoelectroelastic solid.An extended traction boundary integral equation only involving C...A novel extended traction boundary element-free method is proposed to analyze the crack problems of two-dimensional infinite magnetoelectroelastic solid.An extended traction boundary integral equation only involving Cauchy singularity is firstly derived.Then,the extended dislocation densities on the crack surface are expressed as the combination of a characteristic term and unknown weight functions,and the radial point interpolation method is adopted to approximate the unknown weight functions.The numerical scheme of the extended traction boundary element-free method is further established,and an effective numerical procedure is used to evaluate the Cauchy singular integrals.Finally,the stress intensity factor,electric displacement intensity factor and magnetic induction intensity factor are computed for some selected crack problems that contain straight,curved and branched cracks,and good numerical results are obtained.At the same time,the fracture properties of these crack problems are discussed.展开更多
For a class of two-point boundary value problems, using projection type interpolation we proved there are κ + 1, κ u-ultraconvergence points in each element for k degree finite element solution and its derivative, r...For a class of two-point boundary value problems, using projection type interpolation we proved there are κ + 1, κ u-ultraconvergence points in each element for k degree finite element solution and its derivative, respectively. The computing formulars are given.展开更多
基金supported by the National Natural Science Foundation of China (No.12172154)the 111 Project (No.B14044)+1 种基金the Natural Science Foundation of Gansu Province (No.23JRRA1035)the Natural Science Foundation of Anhui University of Finance and Economics (No.ACKYC20043).
文摘In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.
基金Project supported by the National Natural Science Foundation of China (Nos. 10571046, 10371038)
文摘For a class of two-point boundary value problems, by virtue of onedimensional projection interpolation, it is proved that the nodal recovery derivative obtained by Yuan＇s element energy projection （EEP） method has the accuracy O（h^min{2k,k＋4}） The theoretical analysis coincides the reported numerical results.
基金Project supported by the National Basic Research Program of China (No. 2010CB732006)the CAS/SAFEA International Partnership Program for Creative Research Teams (No. KZCX2-YW-T12)the National Natural Science Foundation of China (No. 11002154)
文摘Combining the radial point interpolation method （RPIM）, the dual reciprocity method （DRM） and the hybrid boundary node method （HBNM）, a dual reciprocity hybrid radial boundary node method （DHRBNM） is proposed for linear elasticity. Compared to DHBNM, RPIM is exploited to replace the moving least square （MLS） in DHRBNM, and it gets rid of the deficiency of MLS approximation, in which shape functions lack the delta function property, the boundary condition can not be applied easily and directly and it＇s computational expense is high. Besides, different approximate functions are discussed in DRM to get the interpolation property, in which the accuracy and efficiency for different basis functions are compared. Then RPIM is also applied in DRM to replace the conical function interpolation, which can greatly improve the accuracy of the present method. To demonstrate the effectiveness of the present method, DHBNM is applied for comparison, and some numerical examples of 2-D elasticity problems show that the present method is much more effective than DHBNM.
基金supported by the National Natural Science Foundation of China (10772123,11072160)Natural Science Foundation for Outstanding Young People of Hebei Province (A2009001624),China
文摘A novel extended traction boundary element-free method is proposed to analyze the crack problems of two-dimensional infinite magnetoelectroelastic solid.An extended traction boundary integral equation only involving Cauchy singularity is firstly derived.Then,the extended dislocation densities on the crack surface are expressed as the combination of a characteristic term and unknown weight functions,and the radial point interpolation method is adopted to approximate the unknown weight functions.The numerical scheme of the extended traction boundary element-free method is further established,and an effective numerical procedure is used to evaluate the Cauchy singular integrals.Finally,the stress intensity factor,electric displacement intensity factor and magnetic induction intensity factor are computed for some selected crack problems that contain straight,curved and branched cracks,and good numerical results are obtained.At the same time,the fracture properties of these crack problems are discussed.
文摘For a class of two-point boundary value problems, using projection type interpolation we proved there are κ + 1, κ u-ultraconvergence points in each element for k degree finite element solution and its derivative, respectively. The computing formulars are given.
