Elliptic interface problems with multi-domains and triple junction points have wide applications in engineering and science. However, the corner singularity makes it a chal- lenging problem for most existing methods. ...Elliptic interface problems with multi-domains and triple junction points have wide applications in engineering and science. However, the corner singularity makes it a chal- lenging problem for most existing methods. An accurate and efficient method is desired. In this paper, an efficient non-traditional finite element method with non-body-fitting grids is proposed to solve the elliptic interface problems with multi-domains and triple junctions. The resulting linear system of equations is positive definite if the matrix coefficients for the elliptic equations in the domains are positive definite. Numerical experiments show that this method is about second order accurate in the L~ norm for piecewise smooth solutions. Corner singularity can be handled in a way such that the accuracy does not degenerate. The triple junction is carefully resolved and it does not need to be placed on the grid, giving our method the potential to treat moving interface problems without regenerating mesh.展开更多
We propose a non-traditional finite element method with non-body-fitting grids to solve the matrix coefficient elliptic equations with sharp-edged interfaces. All possible situations that the interface cuts the grid a...We propose a non-traditional finite element method with non-body-fitting grids to solve the matrix coefficient elliptic equations with sharp-edged interfaces. All possible situations that the interface cuts the grid are considered. Both Diriehlet and Neumann boundary conditions are discussed. The coefficient matrix data can be given only on the grids, rather than an analytical function. Extensive numerical experiments show that this method is second order accurate in the L∞ norm.展开更多
针对一维带有不连续系数和奇异源项的椭圆型方程,采用匹配界面和边界(MIB,matched interface and boundary)方法进行求解.该方法对微分方程和跳跃条件的离散是分别进行的,通过在界面附近构造虚拟点达到提高差分格式整体精度的目的,文中...针对一维带有不连续系数和奇异源项的椭圆型方程,采用匹配界面和边界(MIB,matched interface and boundary)方法进行求解.该方法对微分方程和跳跃条件的离散是分别进行的,通过在界面附近构造虚拟点达到提高差分格式整体精度的目的,文中对Neumann边界也给出了处理办法.通过数值算例对文中构造的差分方法进行了验证,并与文献中的浸入界面方法进行了对比,数值结果证明了方法的有效性和可行性.展开更多
Three systems of balance equations and jump conditions as well as generalized Clausius\|Duhem inequalities for nonlocal polar thermomechanical continua are naturally and systematically derived under the consideration ...Three systems of balance equations and jump conditions as well as generalized Clausius\|Duhem inequalities for nonlocal polar thermomechanical continua are naturally and systematically derived under the consideration of Euler angles as angular coordinates and the negligence of conservation law of microinertia as well as the introduction of some new definitions. These results are more general than those balance equations and jump conditions as well as generalized Clausius\|Duhem inequalities proposed by Eringen for nonlocal micropolar thermomechanical continua and more suitable to treat the problems of finite deformations.展开更多
Based on the general conservation laws in continuum mechanics, the Eulerian and Lagrangian descriptions of the jump conditions of shock waves in 3-dimensional solids were presented respectively. The implication of the...Based on the general conservation laws in continuum mechanics, the Eulerian and Lagrangian descriptions of the jump conditions of shock waves in 3-dimensional solids were presented respectively. The implication of the jump conditions and their relations between each other, particularly the relation between the mass conservation and the displacement continuity, were discussed. Meanwhile the shock wave response curves in 3- dimensional solids, i.e. the Hugoniot curves were analysed, which provide the foundation for studying the coupling effects of shock waves in 3-dimensional solids.展开更多
文摘Elliptic interface problems with multi-domains and triple junction points have wide applications in engineering and science. However, the corner singularity makes it a chal- lenging problem for most existing methods. An accurate and efficient method is desired. In this paper, an efficient non-traditional finite element method with non-body-fitting grids is proposed to solve the elliptic interface problems with multi-domains and triple junctions. The resulting linear system of equations is positive definite if the matrix coefficients for the elliptic equations in the domains are positive definite. Numerical experiments show that this method is about second order accurate in the L~ norm for piecewise smooth solutions. Corner singularity can be handled in a way such that the accuracy does not degenerate. The triple junction is carefully resolved and it does not need to be placed on the grid, giving our method the potential to treat moving interface problems without regenerating mesh.
文摘We propose a non-traditional finite element method with non-body-fitting grids to solve the matrix coefficient elliptic equations with sharp-edged interfaces. All possible situations that the interface cuts the grid are considered. Both Diriehlet and Neumann boundary conditions are discussed. The coefficient matrix data can be given only on the grids, rather than an analytical function. Extensive numerical experiments show that this method is second order accurate in the L∞ norm.
文摘针对一维带有不连续系数和奇异源项的椭圆型方程,采用匹配界面和边界(MIB,matched interface and boundary)方法进行求解.该方法对微分方程和跳跃条件的离散是分别进行的,通过在界面附近构造虚拟点达到提高差分格式整体精度的目的,文中对Neumann边界也给出了处理办法.通过数值算例对文中构造的差分方法进行了验证,并与文献中的浸入界面方法进行了对比,数值结果证明了方法的有效性和可行性.
文摘Three systems of balance equations and jump conditions as well as generalized Clausius\|Duhem inequalities for nonlocal polar thermomechanical continua are naturally and systematically derived under the consideration of Euler angles as angular coordinates and the negligence of conservation law of microinertia as well as the introduction of some new definitions. These results are more general than those balance equations and jump conditions as well as generalized Clausius\|Duhem inequalities proposed by Eringen for nonlocal micropolar thermomechanical continua and more suitable to treat the problems of finite deformations.
基金Project supported by the National Natural Science Foundation of China (No.10272097) and the Foundation of National Key Laboratory of Ballistics (No.51453040101zk0103)
文摘Based on the general conservation laws in continuum mechanics, the Eulerian and Lagrangian descriptions of the jump conditions of shock waves in 3-dimensional solids were presented respectively. The implication of the jump conditions and their relations between each other, particularly the relation between the mass conservation and the displacement continuity, were discussed. Meanwhile the shock wave response curves in 3- dimensional solids, i.e. the Hugoniot curves were analysed, which provide the foundation for studying the coupling effects of shock waves in 3-dimensional solids.
