In this paper,numerical sensitivity analysis with respect to the Reynolds number for the flow past obstacle problem is presented.To carry out such analysis,at each time step,we need to solve the incompressible Navier-...In this paper,numerical sensitivity analysis with respect to the Reynolds number for the flow past obstacle problem is presented.To carry out such analysis,at each time step,we need to solve the incompressible Navier-Stokes equations on irregular domains twice,one for the primary variables;the other is for the sensitivity variables with homogeneous boundary conditions.The Navier-Stokes solver is the augmented immersed interface method for Navier-Stokes equations on irregular domains.One of the most important contribution of this paper is that our analysis can predict the critical Reynolds number at which the vortex shading begins to develop in the wake of the obstacle.Some interesting experiments are shown to illustrate how the critical Reynolds number varies with different geometric settings.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
An augmented method is proposed for solving stationary incompressible Stokes equations with a Dirichlet boundary condition along parts of the boundary.In this approach,the normal derivative of the pressure along the p...An augmented method is proposed for solving stationary incompressible Stokes equations with a Dirichlet boundary condition along parts of the boundary.In this approach,the normal derivative of the pressure along the parts of the boundary is introduced as an additional variable and it is solved by the GMRES iterative method.The dimension of the augmented variable in discretization is the number of grid points along the boundary which is O(N).Each GMRES iteration(or one matrix-vector multiplication)requires three fast Poisson solvers for the pressure and the velocity.In our numerical experiments,only a few iterations are needed.We have also combined the augmented approach for Stokes equations involving interfaces,discontinuities,and singularities.展开更多
The immersed interface technique is incorporated into CIP method to solve one-dimensional hyperbolic equations with piecewise constant coefficients.The proposed method achieves the third order of accuracy in time and ...The immersed interface technique is incorporated into CIP method to solve one-dimensional hyperbolic equations with piecewise constant coefficients.The proposed method achieves the third order of accuracy in time and space in the vicinity of the interface where the coefficients have jump discontinuities,which is the same order of accuracy of the standard CIP scheme.Some numerical tests are given to verify the accuracy of the proposed method.展开更多
基金The first and second authors are partially supported by US-ARO grant 49308-MAUS-AFSOR grant FA9550-06-1-0241+2 种基金The second author is also partially supported by US-NSF grant DMS-0911434the US-NIH grant 096195-01,and CNSF 11071123The third author is partially supported by the Hong Kong RGC Grant HKBU201710。
文摘In this paper,numerical sensitivity analysis with respect to the Reynolds number for the flow past obstacle problem is presented.To carry out such analysis,at each time step,we need to solve the incompressible Navier-Stokes equations on irregular domains twice,one for the primary variables;the other is for the sensitivity variables with homogeneous boundary conditions.The Navier-Stokes solver is the augmented immersed interface method for Navier-Stokes equations on irregular domains.One of the most important contribution of this paper is that our analysis can predict the critical Reynolds number at which the vortex shading begins to develop in the wake of the obstacle.Some interesting experiments are shown to illustrate how the critical Reynolds number varies with different geometric settings.
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.
基金USA NSF-NIH grant#0201094,the USA-ARO under grant number 43751-MAan NSF grant DMS-0412654。
文摘An augmented method is proposed for solving stationary incompressible Stokes equations with a Dirichlet boundary condition along parts of the boundary.In this approach,the normal derivative of the pressure along the parts of the boundary is introduced as an additional variable and it is solved by the GMRES iterative method.The dimension of the augmented variable in discretization is the number of grid points along the boundary which is O(N).Each GMRES iteration(or one matrix-vector multiplication)requires three fast Poisson solvers for the pressure and the velocity.In our numerical experiments,only a few iterations are needed.We have also combined the augmented approach for Stokes equations involving interfaces,discontinuities,and singularities.
基金the Army Research Office under DAAD19-02-1-0394,US-ARO grant 49308-MA,and US-AFSOR grant FA9550-06-1-0241.
文摘The immersed interface technique is incorporated into CIP method to solve one-dimensional hyperbolic equations with piecewise constant coefficients.The proposed method achieves the third order of accuracy in time and space in the vicinity of the interface where the coefficients have jump discontinuities,which is the same order of accuracy of the standard CIP scheme.Some numerical tests are given to verify the accuracy of the proposed method.
