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
There are a number of interesting applications where modeling elastic and/or viscoelastic materials is fundamental,including uses in civil engineering,the food industry,land mine detection and ultrasonic imaging.Here ...There are a number of interesting applications where modeling elastic and/or viscoelastic materials is fundamental,including uses in civil engineering,the food industry,land mine detection and ultrasonic imaging.Here we provide an overview of the subject for both elastic and viscoelastic materials in order to understand the behavior of these materials.We begin with a brief introduction of some basic terminology and relationships in continuum mechanics,and a review of equations of motion in a continuum in both Lagrangian and Eulerian forms.To complete the set of equations,we then proceed to present and discuss a number of specific forms for the constitutive relationships between stress and strain proposed in the literature for both elastic and viscoelastic materials.In addition,we discuss some applications for these constitutive equations.Finally,we give a computational example describing the motion of soil experiencing dynamic loading by incorporating a specific form of constitutive equation into the equation of motion.展开更多
In this work, we propose an efficient numerical method for computing the electrostatic interaction between two like-charged spherical particles which is governed by the nonlinear Poisson-Boltzmann equation. The nonlin...In this work, we propose an efficient numerical method for computing the electrostatic interaction between two like-charged spherical particles which is governed by the nonlinear Poisson-Boltzmann equation. The nonlinear problem is solved by a monotone iterative method which leads to a sequence of linearized equations. A modified central finite difference scheme is developed to solve the linearized equations on an exterior irregular domain using a uniform Cartesian grid. With uniform grids, the method is simple, and as a consequence, multigrid solvers can be employed to speed up the convergence. Numerical experiments on cases with two isolated spheres and two spheres confined in a charged cylindrical pore are carried out using the proposed method. Our numerical schemes are found efficient and the numerical results are found in good agreement with the previous published results.展开更多
We propose a variant modified skew-normal splitting iterative method to solve a class of large sparse non-Hermitian positive definite linear systems.Applying the preconditioning technique we also construct the precond...We propose a variant modified skew-normal splitting iterative method to solve a class of large sparse non-Hermitian positive definite linear systems.Applying the preconditioning technique we also construct the preconditioned version of the proposed method.Theoretical analysis shows that the proposed method is unconditionally convergent even when the real part and the imaginary part of the coefficient matrix are non-symmetric.Meanwhile,when the real part and the imaginary part of the coefficient matrix are symmetric positive definite,we prove that the preconditioned variant modified skew-normal splitting iterative method will also unconditionally converge.Numerical experiments are presented to illustrate the efficiency of the proposed method and show better performance of it when compared with some other methods.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This research was supported in part by the Air Force Office of Scientific Research under grant number FA9550-09-1-0226The efforts of ZRK were supported in part by the Department of Education with a GAANN Fellowship under grant number P200A070386。
文摘There are a number of interesting applications where modeling elastic and/or viscoelastic materials is fundamental,including uses in civil engineering,the food industry,land mine detection and ultrasonic imaging.Here we provide an overview of the subject for both elastic and viscoelastic materials in order to understand the behavior of these materials.We begin with a brief introduction of some basic terminology and relationships in continuum mechanics,and a review of equations of motion in a continuum in both Lagrangian and Eulerian forms.To complete the set of equations,we then proceed to present and discuss a number of specific forms for the constitutive relationships between stress and strain proposed in the literature for both elastic and viscoelastic materials.In addition,we discuss some applications for these constitutive equations.Finally,we give a computational example describing the motion of soil experiencing dynamic loading by incorporating a specific form of constitutive equation into the equation of motion.
基金The research of the first author is supported by the Hong Kong Baptist University. The research of the second author is partially supported by a USA-AR0 grant 43751-MA and USA- NFS grants DMS0201094 and DMS-0412654. The third author is partially supported by CERG Grants of Hong Kong Research Grant Council, FRG grants of Hong Kong Baptist University, and an NSAF Grant (#10476032) of National Science Foundation of Chian.
文摘In this work, we propose an efficient numerical method for computing the electrostatic interaction between two like-charged spherical particles which is governed by the nonlinear Poisson-Boltzmann equation. The nonlinear problem is solved by a monotone iterative method which leads to a sequence of linearized equations. A modified central finite difference scheme is developed to solve the linearized equations on an exterior irregular domain using a uniform Cartesian grid. With uniform grids, the method is simple, and as a consequence, multigrid solvers can be employed to speed up the convergence. Numerical experiments on cases with two isolated spheres and two spheres confined in a charged cylindrical pore are carried out using the proposed method. Our numerical schemes are found efficient and the numerical results are found in good agreement with the previous published results.
基金R.Li is funded by the China Scholarship Council(File No.201808330668)the National Natural Science Foundation of China(Grant No.11701221)+1 种基金J.-F.Yin is funded by the National Natural Science Foundation of China(Grant No.11971354)Z.Li is partially supported by a Simon’s grant 63372.
文摘We propose a variant modified skew-normal splitting iterative method to solve a class of large sparse non-Hermitian positive definite linear systems.Applying the preconditioning technique we also construct the preconditioned version of the proposed method.Theoretical analysis shows that the proposed method is unconditionally convergent even when the real part and the imaginary part of the coefficient matrix are non-symmetric.Meanwhile,when the real part and the imaginary part of the coefficient matrix are symmetric positive definite,we prove that the preconditioned variant modified skew-normal splitting iterative method will also unconditionally converge.Numerical experiments are presented to illustrate the efficiency of the proposed method and show better performance of it when compared with some other methods.