Numerical simulation and convergence analysis for a system of nonlinear singularly perturbed differential equations arising in population dynamics

In this article, we consider a system of nonlinear singularly perturbed differential equations with two different parameters. To solve this system, we develop a weighted monotone hybrid scheme on a nonuniform mesh. The proposed scheme is a combination of the midpoint scheme and the upwind scheme involving the weight parameters. The weight parameters enable the method to switch automatically from the midpoint scheme to the upwind scheme as the nodal points start moving from the inner region to the outer region. The nonuniform mesh in particular the adaptive grid is constructed using the idea of equidistributing a positive monitor function involving the solution gradient. The method is shown to be second order convergent with respect to the small parameters. Numerical experiments are presented to show the robustness of the proposed scheme and indicate that the estimate is optimal.     

A simplified adaptive Cartesian grid system for solving the 2D shallow water equations

This paper presents a new simplified grid system that provides local refinement and dynamic adaptation for solving the 2D shallow water equations (SWEs). Local refinement is realized by simply specifying different subdivision levels to the cells on a background uniform coarse grid that covers the computational domain. On such a non‐uniform grid, the structured property of a regular Cartesian mesh is maintained and neighbor information is determined by simple algebraic relationships, i.e. data structure becomes unnecessary. Dynamic grid adaptation is achieved by changing the subdivision level of a background cell. Therefore, grid generation and adaptation is greatly simplified and straightforward to implement. The new adaptive grid‐based SWE solver is tested by applying it to simulate three idealized test cases and promising results are obtained. The new grid system offers a simplified alternative to the existing approaches for providing adaptive mesh refinement in computational fluid dynamics. Copyright © 2011 John Wiley & Sons, Ltd.     

Residual‐based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods

In this paper, we present a finite element method with a residual‐based artificial viscosity for simulation of turbulent compressible flow, with adaptive mesh refinement based on a posteriori error estimation with sensitivity information from an associated dual problem. The artificial viscosity acts as a numerical stabilization, as shock capturing, and as turbulence capturing for large eddy simulation of turbulent flow. The adaptive method resolves parts of the flow indicated by the a posteriori error estimates but leaves shocks and turbulence under‐resolved in a large eddy simulation. The method is tested for examples in 2D and 3D and is validated against experimental data. Copyright © 2012 John Wiley & Sons, Ltd.     

Moving boundary truncated grid method: Multidimensional quantum dynamics

The moving boundary truncated grid (TG) method is used to study wave packet dynamics of multidimensional quantum systems. As time evolves, appropriate Eulerian grid points required for propagating a wave packet are activated and deactivated with no advance information about the dynamics. This method is applied to the Henon-Heiles potential and wave packet barrier scattering in two, three, and four dimensions. Computational results demonstrate that the TG method not only leads to a great reduction in the number of grid points needed to perform accurate calculations but also is computationally more efficient than the full grid calculations.     

Accurate prediction of relative binding affinities of a series of HIV-1 protease inhibitors using semi-empirical quantum mechanical charge

A major challenge in computer-aided drug design is the accurate estimation of ligand binding affinity. Here, a new approach that combines the adaptive steered molecular dynamics (ASMD) and partial atomic charges calculated by semi-empirical quantum mechanics (SQMPC), namely ASMD-SQMPC, is suggested to predict the ligand binding affinities, with 24 HIV-1 protease inhibitors as testing examples. In the ASMD-SQMPC, the relative binding free energy (ΔG) is reflected by the average maximum potential of mean force (<PMF>_max) between bound and unbound states. The correlation coefficient (R²) between the <PMF>_max and experimentally determined ΔG is 0.86, showing a significant improvement compared with the conventional ASMD (R² = 0.52). Therefore, this study provides an efficient approach to predict the relative ΔG and reveals the significance of precise partial atomic charges in the theoretical simulations.     

模式偏置波前传感器理论模拟及实验验证

将模式偏置法与全息多重存储法波前传感器原理联系起来,通过研究模式偏置波前传感器的输出响应特性,间接得到全息模式波前传感器的运行规律.对模式偏置波前传感器进行理论分析与总结,并建立简化模型,针对若干阶Zernike像差,通过数值模拟对理论结果进行验证.模拟结果显示:传感器输出信号与各种类型待测像差系数有不同的变化关系,这...     

基于自适应侧抑制网络的红外弱小目标检测

 为了提高远距离红外弱小目标的检测效率,提出了一种基于自适应侧抑制网络的复杂背景下的红外弱小目标检测方法。该方法建立了改进的侧抑制网络数学模型,利用各向异性滤波来自适应地确定侧抑制网络的抑制系数,不需要人为干预,实现了侧抑制网络与各向异性高斯滤波的有机结合。同时,在各向异性高斯滤波器两轴确定方面进行了改进,两轴分别采用对比度尺度模型和强度尺度传播模型来独立确定。通过与传统弱小目标检测方法的对比实验,验证了方法的有效性。     

Parallel multigrid method for finite element simulations of complex flow problems on locally refined meshes

We present a parallel multigrid solver on locally refined meshes for solving very complex three‐dimensional flow problems. Besides describing the parallel implementation in detail, we prove the smoothing property of the suggested iteration for a simple model problem. For demonstration of the efficiency and feasibility of the solver, we show a chemically reactive flow simulation for a Methane burner using detailed chemical reaction modeling. Further, we give the results of an ocean flow simulation. All described methods are implemented in the finite element toolbox Gascoigne. Copyright © 2010 John Wiley & Sons, Ltd.