In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body...In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.展开更多
The rigid body limit equilibrium method(LEM)and the nonlinear finite element method(NFEM)are often used in the analysis of anti-sliding stability of gravity dam.But LEM cannot reflect the process of progressive instab...The rigid body limit equilibrium method(LEM)and the nonlinear finite element method(NFEM)are often used in the analysis of anti-sliding stability of gravity dam.But LEM cannot reflect the process of progressive instability and mechanical mecha-nism on failure for rock mass while NFEM is difficult to use to solve the displacement discontinuity of weak structural plane.Combining the research with Xiangjiaba Hydropower Station project,the analysis of anti-sliding stability for segment 12#of the dam has been carried out using interface stress element method(ISEM).The results can reflect the most dangerous location,the scope and distribution of failure zone in weak structural plane,and present the process of progressive failure in dam foun-dation as well as the safety coefficient of possible sliding body.These achievements provide an important technical reference for dam foundation treatment measures.The computational results show that ISEM can naturally describe discontinuous de-formation of rock mass such as dislocation,openness and sliding.Besides,this method is characterized by good adaptability,convenient calculation and high compatibility,thus it is regarded as an effective way to make an analysis of anti-sliding stabil-ity of gravity dam.展开更多
In this paper,the electromagnetic scattering from overfilled cavities with inhomogeneous anisotropic media is investigated.To solve the scattering problem,a Petrov-Galerkin finite element interfacemethod on non-body-f...In this paper,the electromagnetic scattering from overfilled cavities with inhomogeneous anisotropic media is investigated.To solve the scattering problem,a Petrov-Galerkin finite element interfacemethod on non-body-fitted grids is presented.We reduce the infinite domain of scattering to a bounded domain problem by introducing a transparent boundary condition.The level set function is used to capture complex boundary and interface geometry that is not aligned with the mesh.Nonbody-fitted grids allow us to save computational costs during mesh generation and significantly reduce the amount of computer memory required.The solution is built by connecting two linear polynomials across the interfaces to satisfy the jump conditions.The proposed method can handle matrix coefficients produced by permittivity and permeability tensors of anisotropic media.The final linear system is sparse,making it more suitable for most iterative methods.Numerical experiments show that the proposed method has good convergence and realizability.Meanwhile,we discover that the absorbing properties of anisotropic media clearly and positively influence the reduction of radar cross section.It has also been demonstrated that the method can achieve second-order accuracy.展开更多
基金supported by the US ARO grants 49308-MA and 56349-MAthe US AFSOR grant FA9550-06-1-024+1 种基金he US NSF grant DMS-0911434the State Key Laboratory of Scientific and Engineering Computing of Chinese Academy of Sciences during a visit by Z.Li between July-August,2008.
文摘In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.
基金supported by the National Natural Science Foundation of China(Grant Nos.51179064,11132003 and 10972072)the National Science and Technology Supporting Plan(Grant No.2008BAB29B03)
文摘The rigid body limit equilibrium method(LEM)and the nonlinear finite element method(NFEM)are often used in the analysis of anti-sliding stability of gravity dam.But LEM cannot reflect the process of progressive instability and mechanical mecha-nism on failure for rock mass while NFEM is difficult to use to solve the displacement discontinuity of weak structural plane.Combining the research with Xiangjiaba Hydropower Station project,the analysis of anti-sliding stability for segment 12#of the dam has been carried out using interface stress element method(ISEM).The results can reflect the most dangerous location,the scope and distribution of failure zone in weak structural plane,and present the process of progressive failure in dam foun-dation as well as the safety coefficient of possible sliding body.These achievements provide an important technical reference for dam foundation treatment measures.The computational results show that ISEM can naturally describe discontinuous de-formation of rock mass such as dislocation,openness and sliding.Besides,this method is characterized by good adaptability,convenient calculation and high compatibility,thus it is regarded as an effective way to make an analysis of anti-sliding stabil-ity of gravity dam.
基金supported by the National Natural Science Foundation of China(No.12271159)the Natural Science Foundation of Hebei Province(No.A2020502003)+2 种基金the Fundamental Research Funds for the Central Universities(No.2021MS115)supported by the National Natural Science Foundation of China(No.12171482)the State Key Laboratory of Petroleum Resources and Prospecting,China University of Petroleum(No.PRP/DX-2307).
文摘In this paper,the electromagnetic scattering from overfilled cavities with inhomogeneous anisotropic media is investigated.To solve the scattering problem,a Petrov-Galerkin finite element interfacemethod on non-body-fitted grids is presented.We reduce the infinite domain of scattering to a bounded domain problem by introducing a transparent boundary condition.The level set function is used to capture complex boundary and interface geometry that is not aligned with the mesh.Nonbody-fitted grids allow us to save computational costs during mesh generation and significantly reduce the amount of computer memory required.The solution is built by connecting two linear polynomials across the interfaces to satisfy the jump conditions.The proposed method can handle matrix coefficients produced by permittivity and permeability tensors of anisotropic media.The final linear system is sparse,making it more suitable for most iterative methods.Numerical experiments show that the proposed method has good convergence and realizability.Meanwhile,we discover that the absorbing properties of anisotropic media clearly and positively influence the reduction of radar cross section.It has also been demonstrated that the method can achieve second-order accuracy.
