A numerical resolution of the Gelfand-Levitan equation

The Gelfand-Levitan equation is the main equation in inverse scatterring theory; a new numerical method for solving this equation is presented, based on a predictor-corrector scheme.     

Homogenization of the Maxwell Equations: Case II. Nonlinear Conductivity

The Maxwell equations with uniformly monotone nonlinear electric conductivity in a heterogeneous medium, which may be non-periodic, are homogenized by two-scale convergence. We introduce a new set of function spaces appropriate for the nonlinear Maxwell system. New compactness results, of two-scale type, are proved for these function spaces. We prove existence of a unique solution for the heterogeneous system as well as for the homogenized system. We also prove that the solutions of the heterogeneous system converge weakly to the solution of the homogenized system. Furthermore, we prove corrector results, important for numerical implementations.     

A fully hydrodynamic model for three‐dimensional,free‐surface flows

The hydrostatic pressure assumption has been widely used in studying water movements in rivers, lakes, estuaries, and oceans. While this assumption is valid in many cases and has been successfully used in numerous studies, there are many cases where this assumption is questionable. This paper presents a three‐dimensional, hydrodynamic model for free‐surface flows without using the hydrostatic pressure assumption. The model includes two predictor–corrector steps. In the first predictor–corrector step, the model uses hydrostatic pressure at the previous time step as an initial estimate of the total pressure field at the new time step. Based on the estimated pressure field, an intermediate velocity field is calculated, which is then corrected by adding the non‐hydrostatic component of the pressure to the estimated pressure field. A Poisson equation for non‐hydrostatic pressure is solved before the second intermediate velocity field is calculated. The final velocity field is found after the free surface at the new time step is computed by solving a free‐surface correction equation. The numerical method was validated with several analytical solutions and laboratory experiments. Model results agree reasonably well with analytical solutions and laboratory results. Model simulations suggest that the numerical method presented is suitable for fully hydrodynamic simulations of three‐dimensional, free‐surface flows. Copyright © 2003 John Wiley & Sons, Ltd.     

无光焦度校正器和单一反射镜组成的光学系统

从三级像差理论出发分析了由两透镜无光焦度校正器和单一反射镜组成的光学系统，讨论两透镜无光焦度校正器放置在单一反射镜前和后组成的光学系统的各种消像差条件。并给出求解两透镜无光焦度校正器参量的计算公式。     

Time-reversible always stable predictor-corrector method for molecular dynamics of polarizable molecules

An improved method for classic molecular dynamics of polarizable molecules is proposed. The method uses a predictor, one evaluation of the electrostatic field per integration step, and relaxation (damping). The self-consistent solution is approximated with error of the second order (with respect to the timestep). The time reversibility (long-time energy conservation) error is of the (2n - 1)th order, where n is the predictor length. The method is easy to implement, efficient, accurate, and suitable for any model of polarizability.     

环形光斑的波前传感器与波前校正器优化布局

针对自适应光学系统常遇到的环形光斑，仿真研究了波前传感器子孔径的六种环形布局，得出了环形布局的指导原则，并将环形布局与传统的方形布局进行了比较，认为环形布局更适合于环形光斑．     

Pressure segregation methods based on a discrete pressure Poisson equation. An algebraic approach

In this paper, we introduce some pressure segregation methods obtained from a non‐standard version of the discrete monolithic system, where the continuity equation has been replaced by a pressure Poisson equation obtained at the discrete level. In these methods it is the velocity instead of the pressure the extrapolated unknown. Moreover, predictor–corrector schemes are suggested, again motivated by the new monolithic system. Key implementation aspects are discussed, and a complete stability analysis is performed. We end with a set of numerical examples in order to compare these methods with classical pressure‐correction schemes. Copyright © 2007 John Wiley & Sons, Ltd.     

A numerical method for the one‐dimensional sine‐Gordon equation

A numerical method based on a predictor–corrector (P‐C) scheme arising from the use of rational approximants of order 3 to the matrix‐exponential term in a three‐time level recurrence relation is applied successfully to the one‐dimensional sine‐Gordon equation, already known from the bibliography. In this P‐C scheme a modification in the corrector (MPC) has been proposed according to which the already evaluated corrected values are considered. The method, which uses as predictor an explicit finite‐difference scheme arising from the second order rational approximant and as corrector an implicit one, has been tested numerically on the single and the soliton doublets. Both the predictor and the corrector schemes are analyzed for local truncation error and stability. From the investigation of the numerical results and the comparison of them with other ones known from the bibliography it has been derived that the proposed P‐C/MPC schemes at least coincide in terms of accuracy with them. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

Asymptotic approximation of the solution of Stokes equations in a domain with highly oscillating boundary

We consider a viscous incompressible flow in an infinite horizontal domain bounded at the bottom by a smooth wall and at the top by a rough wall. The latter is assumed to consist in a plane wall covered with periodically distributed asperities which size depends on a small parameter, and with a fixed height. We assume that the flow is governed by the stationary Stokes equations. Using a boundary layer corrector we derive and analyze a first order asymptotic approximation of the flow.      

双透镜无光焦度校正板和单一反射镜的研究

对双透镜无光焦度校正板和单一反射镜组成的光学系统进行了研究,利用三级像差理论分析了消像差条件,并得出了一组被证明是正确的公式.根据该公式可以求出光学系统的初始结构参量.对于在球面镜反射系统中,基于像差特性分析,得出了系统的最佳结构和双透镜无光焦度校正板中单透镜光焦度的最佳选择.