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
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
A new numerical method based on locally modified Cartesian meshes is proposed for solving a coupled system of a fluid flow and a porous media flow.The fluid flow is modeled by the Stokes equations while the porous med...A new numerical method based on locally modified Cartesian meshes is proposed for solving a coupled system of a fluid flow and a porous media flow.The fluid flow is modeled by the Stokes equations while the porous media flow is modeled by Darcy’s law.The method is based on a Robin-Robin domain decomposition method with a Cartesian mesh with local modifications near the interface.Some computational examples are presented and discussed.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
This work is concerned with the numerical simulations on the Gierer-Meinhardt activator-inhibitor models. We consider the case when the inhibitor timeconstant τ is non-zero. In this case, oscillations and pulse split...This work is concerned with the numerical simulations on the Gierer-Meinhardt activator-inhibitor models. We consider the case when the inhibitor timeconstant τ is non-zero. In this case, oscillations and pulse splitting are observed numerically.Numerical experiments are carried out to investigate the dynamical behaviorsand instabilities of the spike patterns. The numerical schemes used are based upon anefficient moving mesh finite element method which distributes more grid points nearthe localized spike regions.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
We consider two player electromagnetic evasion-pursuit games where each player must incorporate significant uncertainty into their design strategies to disguise their intension and confuse their opponent.In this paper...We consider two player electromagnetic evasion-pursuit games where each player must incorporate significant uncertainty into their design strategies to disguise their intension and confuse their opponent.In this paper,the evader is allowed to make dynamic changes to his strategies in response to the dynamic input with uncertainty from the interrogator.The problem is formulated in two different ways;one is based on the evolution of the probability density function of the intensity of reflected signal and leads to a controlled forward Kolmogorov or Fokker-Planck equation.The other formulation is based on the evolution of expected value of the intensity of reflected signal and leads to controlled backward Kolmogorov equations.In addition,a number of numerical results are presented to illustrate the usefulness of the proposed approach in exploring problems of control in a general dynamic game setting.展开更多
We consider the problem of detecting cardiac artery occlusions using stenosis driven viscoelastic(VE)waves propagated through biotissue to body surface sensors.We investigate possible statistical model formulations(o...We consider the problem of detecting cardiac artery occlusions using stenosis driven viscoelastic(VE)waves propagated through biotissue to body surface sensors.We investigate possible statistical model formulations(ordinary least squares(OLS),generalized least squares(GLS))and post analysis techniques(residual plots)to ascertain uncertainty in estimates as well as validity of the statistical models as part of a methodology for stenosis detection using viscoelastic waves.展开更多
The ability to reliably detect coronary artery disease based on the acousticnoises produced by a stenosis can provide a simple, non-invasive technique for diagnosis.Current research exploits the shear wave fields in b...The ability to reliably detect coronary artery disease based on the acousticnoises produced by a stenosis can provide a simple, non-invasive technique for diagnosis.Current research exploits the shear wave fields in body tissue to detect andanalyze coronary stenoses. The methods and ideas outlined in earlier efforts [6] includinga mathematical model utilizing an internal strain variable approximation tothe quasi-linear viscoelastic constitutive equation proposed by Fung in [19] is extendedhere. As an initial investigation, a homogeneous two-dimensional viscoelastic geometryis considered. Being uniform in θ, this geometry behaves as a one dimensionalmodel, and the results generated from it are compared to the one dimensional resultsfrom [6]. To allow for different assumptions on the elastic response, several variationsof the model are considered. A statistical significance test is employed to determine ifthe more complex models are significant improvements. After calibrating the modelwith a comparison to previous findings, more complicated geometries are considered.Simulations involving a heterogeneous geometrywith a uniformring running throughthe original medium, a θ-dependent model which considers a rigid partial occlusionformed along the inner radius of the geometry, and a model which combines the ringand occlusion are presented.展开更多
The electromagnetic backscattering of a crosscut of a cruise missile coated by a thin homogeneous layer made of radar absorbent material is modeled using a finite element method.Based on the radar cross section and a ...The electromagnetic backscattering of a crosscut of a cruise missile coated by a thin homogeneous layer made of radar absorbent material is modeled using a finite element method.Based on the radar cross section and a reflection coefficient,optimization problems are formulated for evaders and interrogators leading to optimal material parameters for the coating and optimal monostatic radar operating frequencies,respectively.Optimal coating materials are constructed for several radar frequencies.Tuning only dielectric permittivity gives a narrow frequency range of high absorption while also tuning magnetic permeability widens it significantly.However the coating layers considered do not provide substantial reduction of backscattering in the entire frequency range from 0.2 to 1.6 GHz.Computational experiments also demonstrate that the reflection coefficient based on a simple planar geometry can predict well the strength of radar cross section in the sector of interest with a substantially reduced computational burden.展开更多
This paper compares two models predicting elastic and viscoelastic properties of large arteries.Models compared include a Kelvin(standard linear)model and an extended 2-term exponential linear viscoelastic model.Mode...This paper compares two models predicting elastic and viscoelastic properties of large arteries.Models compared include a Kelvin(standard linear)model and an extended 2-term exponential linear viscoelastic model.Models were validated against in-vitro data from the ovine thoracic descending aorta and the carotid artery.Measurements of blood pressure data were used as an input to predict vessel cross-sectional area.Material properties were predicted by estimating a set of model parameters that minimize the difference between computed and measured values of the cross-sectional area.The model comparison was carried out using generalized analysis of variance type statistical tests.For the thoracic descending aorta,results suggest that the extended 2-term exponential model does not improve the ability to predict the observed cross-sectional area data,while for the carotid artery the extended model does statistically provide an improved fit to the data.This is in agreement with the fact that the aorta displays more complex nonlinear viscoelastic dynamics,while the stiffer carotid artery mainly displays simpler linear viscoelastic dynamics.展开更多
We study multi-parameter regularization(multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regu...We study multi-parameter regularization(multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters from the viewpoint of augmented Tikhonov regularization, and derive a new parameter choice strategy called the balanced discrepancy principle. A priori and a posteriori error estimates are provided to theoretically justify the principles, and numerical algorithms for efficiently implementing the principles are also provided. Numerical results on deblurring are presented to illustrate the feasibility of the balanced discrepancy principle.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supported in part by the US-NIH grant R01GM096195supported by the US AFSOR grant FA9550-09-1-0520the NCSU Innovation Seed grant.
文摘A new numerical method based on locally modified Cartesian meshes is proposed for solving a coupled system of a fluid flow and a porous media flow.The fluid flow is modeled by the Stokes equations while the porous media flow is modeled by Darcy’s law.The method is based on a Robin-Robin domain decomposition method with a Cartesian mesh with local modifications near the interface.Some computational examples are presented and discussed.
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.
文摘This work is concerned with the numerical simulations on the Gierer-Meinhardt activator-inhibitor models. We consider the case when the inhibitor timeconstant τ is non-zero. In this case, oscillations and pulse splitting are observed numerically.Numerical experiments are carried out to investigate the dynamical behaviorsand instabilities of the spike patterns. The numerical schemes used are based upon anefficient moving mesh finite element method which distributes more grid points nearthe localized spike regions.
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 U.S.Air Force Office of Scientific Research under grant number FA9550-09-1-0226。
文摘We consider two player electromagnetic evasion-pursuit games where each player must incorporate significant uncertainty into their design strategies to disguise their intension and confuse their opponent.In this paper,the evader is allowed to make dynamic changes to his strategies in response to the dynamic input with uncertainty from the interrogator.The problem is formulated in two different ways;one is based on the evolution of the probability density function of the intensity of reflected signal and leads to a controlled forward Kolmogorov or Fokker-Planck equation.The other formulation is based on the evolution of expected value of the intensity of reflected signal and leads to controlled backward Kolmogorov equations.In addition,a number of numerical results are presented to illustrate the usefulness of the proposed approach in exploring problems of control in a general dynamic game setting.
基金was supported in part by the U.S.Air Force Office of Scientific Research under grant AFOSR-FA9550-08-1-0147in part by the National Institute of Allergy and Infectious Disease under grant NIAID 9R01AI071915-05。
文摘We consider the problem of detecting cardiac artery occlusions using stenosis driven viscoelastic(VE)waves propagated through biotissue to body surface sensors.We investigate possible statistical model formulations(ordinary least squares(OLS),generalized least squares(GLS))and post analysis techniques(residual plots)to ascertain uncertainty in estimates as well as validity of the statistical models as part of a methodology for stenosis detection using viscoelastic waves.
基金the U.S.Air Force Office of Scientific Research under grant AFOSR-FA9550-04-1-0220 and in part by The David and Lucille Packard Foundation.
文摘The ability to reliably detect coronary artery disease based on the acousticnoises produced by a stenosis can provide a simple, non-invasive technique for diagnosis.Current research exploits the shear wave fields in body tissue to detect andanalyze coronary stenoses. The methods and ideas outlined in earlier efforts [6] includinga mathematical model utilizing an internal strain variable approximation tothe quasi-linear viscoelastic constitutive equation proposed by Fung in [19] is extendedhere. As an initial investigation, a homogeneous two-dimensional viscoelastic geometryis considered. Being uniform in θ, this geometry behaves as a one dimensionalmodel, and the results generated from it are compared to the one dimensional resultsfrom [6]. To allow for different assumptions on the elastic response, several variationsof the model are considered. A statistical significance test is employed to determine ifthe more complex models are significant improvements. After calibrating the modelwith a comparison to previous findings, more complicated geometries are considered.Simulations involving a heterogeneous geometrywith a uniformring running throughthe original medium, a θ-dependent model which considers a rigid partial occlusionformed along the inner radius of the geometry, and a model which combines the ringand occlusion are presented.
基金supported in part by the U.S.Air Force Offices of Scientific Research under grant AFOSR FA9550-04-1-0220。
文摘The electromagnetic backscattering of a crosscut of a cruise missile coated by a thin homogeneous layer made of radar absorbent material is modeled using a finite element method.Based on the radar cross section and a reflection coefficient,optimization problems are formulated for evaders and interrogators leading to optimal material parameters for the coating and optimal monostatic radar operating frequencies,respectively.Optimal coating materials are constructed for several radar frequencies.Tuning only dielectric permittivity gives a narrow frequency range of high absorption while also tuning magnetic permeability widens it significantly.However the coating layers considered do not provide substantial reduction of backscattering in the entire frequency range from 0.2 to 1.6 GHz.Computational experiments also demonstrate that the reflection coefficient based on a simple planar geometry can predict well the strength of radar cross section in the sector of interest with a substantially reduced computational burden.
基金supported in part(DVJ)by the Consejo Nacional de Ciencias y Tecnologia de Mexico(CONACYT)in part(HTB)by the US Air Force Office of Scientific Research under grant AFOSR-FA9550-08-1-0147+3 种基金by the National Institute of Al-lergy and Infectious Disease under grant NIAID 9R01AI071915-05in part(MAH)by the National Science Foundation under grant DMS-0636590by the National Insti-tutes of Health under grant NIH-AG-15768in part(MSO)by the National Science Foundation under grant DMS-0616597。
文摘This paper compares two models predicting elastic and viscoelastic properties of large arteries.Models compared include a Kelvin(standard linear)model and an extended 2-term exponential linear viscoelastic model.Models were validated against in-vitro data from the ovine thoracic descending aorta and the carotid artery.Measurements of blood pressure data were used as an input to predict vessel cross-sectional area.Material properties were predicted by estimating a set of model parameters that minimize the difference between computed and measured values of the cross-sectional area.The model comparison was carried out using generalized analysis of variance type statistical tests.For the thoracic descending aorta,results suggest that the extended 2-term exponential model does not improve the ability to predict the observed cross-sectional area data,while for the carotid artery the extended model does statistically provide an improved fit to the data.This is in agreement with the fact that the aorta displays more complex nonlinear viscoelastic dynamics,while the stiffer carotid artery mainly displays simpler linear viscoelastic dynamics.
基金supported by the Army Research Office under DAAD19-02-1-0394,US-ARO grant 49308MA and US-AFSOR grant FA9550-06-1-0241
文摘We study multi-parameter regularization(multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters from the viewpoint of augmented Tikhonov regularization, and derive a new parameter choice strategy called the balanced discrepancy principle. A priori and a posteriori error estimates are provided to theoretically justify the principles, and numerical algorithms for efficiently implementing the principles are also provided. Numerical results on deblurring are presented to illustrate the feasibility of the balanced discrepancy principle.
