This paper investigates the eigenmode optimization problem governed by the scalar Helmholtz equation in continuum system in which the computed eigenmode approaches the prescribed eigenmode in the whole domain.The first variation for the eigenmode optimization problem is evaluated by the quadratic penalty method,the adjoint variable method,and the formula based on sensitivity analysis.A penalty optimization algorithm is proposed,in which the density evolution is accomplished by introducing an artificial time term and solving an additional ordinary differential equation.The validity of the presented algorithm is confirmed by numerical results of the first and second eigenmode optimizations in 1D and 2D problems.
Calibration and identification of the exchange effect between the karst aquifers and the underlying conduit network are important issues in order to gain a better understanding of these hydraulic systems. Based on a coupled continuum pipe-flow(CCPF for short) model describing flows in karst aquifers, this paper is devoted to the identification of an exchange rate function, which models the hydraulic interaction between the fissured volume(matrix) and the conduit, from the Neumann boundary data, i.e., matrix/conduit seepage velocity. The authors formulate this parameter identification problem as a nonlinear operator equation and prove the compactness of the forward mapping. The stable approximate solution is obtained by two classic iterative regularization methods, namely,the Landweber iteration and Levenberg-Marquardt method. Numerical examples on noisefree and noisy data shed light on the appropriateness of the proposed approaches.
This paper proposes a variational binary level set method for shape and topology optimization of structural.First,a topology optimization problem is presented based on the level set method and an algorithm based on binary level set method is proposed to solve such problem.Considering the difficulties of coordination between the various parameters and efficient implementation of the proposed method,we present a fast algorithm by reducing several parameters to only one parameter,which would substantially reduce the complexity of computation and make it easily and quickly to get the optimal solution.The algorithm we constructed does not need to re-initialize and can produce many new holes automatically.Furthermore,the fast algorithm allows us to avoid the update of Lagrange multiplier and easily deal with constraints,such as piecewise constant,volume and length of the interfaces.Finally,we show several optimum design examples to confirm the validity and efficiency of our method.
The paper is concerned with the reconstruction of a defect in the core of a two-dimensional open waveguide from the scattering data. Since only a finite numbers of modes can propagate without attenuation inside the core, the problem is similar to the one-dimensional inverse medium problem. In particular, the inverse problem suffers from a lack of uniqueness and is known to be severely ill-posed. To overcome these difficulties, we consider multi-frequency scattering data. The uniqueness of solution to the inverse problem is established from the far field scattering information over an interval of low frequencies.
We propose a new numerical method for estimating the piecewise constant Robin coefficient in two-dimensional elliptic equation from boundary measurements. The Robin in- verse problem is recast into a minimization of an output least-square formulation. A technique based on determining the discontinuous points of the unknown coefficient is suggested, and we investigate the differentiability of the solution and the objective functional with respect to the discontinuous points. Then we apply the Gauss-Newton method for reconstructing the shape of the unknown Robin coefficient. Numerical examples illustrate its efficiency and stability.
This paper investigates the reduction of backscatter radar cross section(RCS)for a rectangular cavity embedded in the ground plane.The bottom of the cavity is coated by a thin,multilayered radar absorbing material(RAM)with possibly different permittivities.The objective is to minimize the backscatter RCS by the incidence of a plane wave over a single or a set of incident angles.By formulating the scattering problem as a Helmholtz equation with artificial boundary condition,the gradient with respect to the material permittivities is determined efficiently by the adjoint state method,which is integrated into a nonlinear optimization scheme.Numerical example shows the RCS may be significantly reduced.
Numerical oscillation of the total energy can be observed when the Kohn-Sham equation is solved by real-space methods to simulate the translational move of an electronic system.Effectively remove or reduce the unphysical oscillation is crucial not only for the optimization of the geometry of the electronic structure,but also for the study of molecular dynamics.In this paper,we study such unphysical oscillation based on the numerical framework in[G.Bao,G.H.Hu,and D.Liu,An h-adaptive fi-nite element solver for the calculations of the electronic structures,Journal of Computational Physics,Volume 231,Issue 14,Pages 4967-4979,2012],and deliver some numerical methods to constrain such unphysical effect for both pseudopotential and all-electron calculations,including a stabilized cubature strategy for Hamiltonian operator,and an a posteriori error estimator of the finite element methods for Kohn-Sham equation.The numerical results demonstrate the effectiveness of our method on restraining unphysical oscillation of the total energies.
