Gradient Recovery Based Two-Grid Finite Element Method for Parabolic Integro-Differential Optimal Control Problems

In this paper, the optimal control problem of parabolic integro-differential equations is solved by gradient recovery based two-grid finite element method. Piecewise linear functions are used to approximate state and co-state variables, and piecewise constant function is used to approximate control variables. Generally, the optimal conditions for the problem are solved iteratively until the control variable reaches error tolerance. In order to calculate all the variables individually and parallelly, we introduce a gradient recovery based two-grid method. First, we solve the small scaled optimal control problem on coarse grids. Next, we use the gradient recovery technique to recover the gradients of state and co-state variables. Finally, using the recovered variables, we solve the large scaled optimal control problem for all variables independently. Moreover, we estimate priori error for the proposed scheme, and use an example to validate the theoretical results.

Local and parallel finite element algorithms based on two-grid discretization for steady Navier-Stokes equations

Local and parallel finite element algorithms based on two-grid discretization for Navier-Stokes equations in two dimension are presented. Its basis is a coarse finite element space on the global domain and a fine finite element space on the subdomain. The local algorithm consists of finding a solution for a given nonlinear problem in the coarse finite element space and a solution for a linear problem in the fine finite element space, then droping the coarse solution of the region near the boundary. By overlapping domain decomposition, the parallel algorithms are obtained. This paper analyzes the error of these algorithms and gets some error estimates which are better than those of the standard finite element method. The numerical experiments are given too. By analyzing and comparing these results, it is shown that these algorithms are correct and high efficient.

Two-grid methods for semi-linear elliptic interface problems by immersed finite element methods

In this paper,two-grid immersed finite element (IFE) algorithms are proposed and analyzed for semi-linear interface problems with discontinuous diffusion coefficients in two dimension.Because of the advantages of finite element (FE) formulation and the simple structure of Cartesian grids,the IFE discretization is used in this paper.Two-grid schemes are formulated to linearize the FE equations.It is theoretically and numerically illustrated that the coarse space can be selected as coarse as H =O(h^1/4)(or H =O(h^1/8)),and the asymptotically optimal approximation can be achieved as the nonlinear schemes.As a result,we can settle a great majority of nonlinear equations as easy as linearized problems.In order to estimate the present two-grid algorithms,we derive the optimal error estimates of the IFE solution in the L^p norm.Numerical experiments are given to verify the theorems and indicate that the present two-grid algorithms can greatly improve the computing efficiency.

OPTIMAL ERROR ESTIMATES OF A DECOUPLED SCHEME BASED ON TWO-GRID FINITE ELEMENT FOR MIXED NAVIER-STOKES/DARCY MODEL

Although the two-grid finite element decoupled scheme for mixed Navier-Stokes/ Darcy model in literatures has given the numerical results of optimal convergence order, the theoretical analysis only obtain the optimal error order for the porous media flow and a non-optimal error order for the fluid flow. In this article, we give a more rigorous of the error analysis for the fluid flow and obtain the optimal error estimates of the velocity and the pressure.

A two-grid algorithm based on Newton iteration for the stream function form of the Navier-Stokes equations

In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems （with same stiffness matrix but different right-hand side） on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. Furthermore, the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.

Modified two-grid method for solving coupled Navier-Stokes/Darcy model based on Newton iteration

A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is given, which shows that the same order of accuracy can be achieved as solving the system directly in the fine mesh when h = H2. Both theoretical analysis and numerical experiments illustrate the efficiency of the algorithm for solving the coupled problem.

DEM-CFD simulation of modular PB-FHR core with two-grid method

For designing and optimizing the reactor core of modular pebble-bed fluoride salt-cooled high-temperature reactor(PB-FHR),it is of importance to simulate the coupled fluid and particle flow due to strong coolantpebble interactions.Computational fluid dynamics and discrete element method(DEM) coupling approach can be used to track particles individually while it requires a fluid cell being greater than the pebble diameter.However,the large size of pebbles makes the fluid grid too coarse to capture the complicated flow pattern.To solve this problem,a two-grid approach is proposed to calculate interphase momentum transfer between pebbles and coolant without the constraint on the shape and size of fluid meshes.The solid velocity,fluid velocity,fluid pressure and void fraction are mapped between hexahedral coarse particle grid and tine fluid grid.Then the total interphase force can be calculated independently to speed up computation.To evaluate suitability of this two-grid approach,the pressure drop and minimum fluidization velocity of a fluidized bed were predicted,and movements of the pebbles in complex flow field were studied experimentally and numerically.The spouting fluid through a central inlet pipe of a scaled visible PB-FHR core facility was set up to provide the complex flow field.Water was chosen as Liquid to simulate the molten salt coolant,and polypropylene balls were used to simulate the pebble fuels.Results show that the pebble flow pattern captured from experiment agrees well with the simulation from two-grid approach,hence the applicability of the two-grid approach for the later PB-FHR core design.

TWO-GRID METHOD FOR CHARACTERISTICS FINITE-ELEMENT SOLUTION OF 2D NONLINEAR CONVECTION-DOMINATED DIFFUSION PROBLEM

For two-dimension nonlinear convection diffusion equation, a two-grid method of characteristics finite-element solution was constructed. In this method the nonlinear iterations is only to execute on the coarse grid and the fine-grid solution can be obtained in a single linear step. For the nonlinear convection-dominated diffusion equation, this method can not only stabilize the numerical oscillation but also accelerate the convergence and improve the computational efficiency. The error analysis demonstrates if the mesh sizes between coarse-grid and fine-grid satisfy the certain relationship, the two-grid solution and the characteristics finite-element solution have the same order of accuracy. The numerical is more efficient than that of characteristics example confirms that the two-grid method finite-element method.

Two-grid partition of unity method for second order elliptic problems

A two-grid partition of unity method for second order elliptic problems is proposed and analyzed. The standard two-grid method is a local and parallel method usually leading to a discontinuous solution in the entire computational domain. Partition of unity method is employed to glue all the local solutions together to get the global continuous one, which is optimal in HI-norm. Furthermore, it is shown that the L^2 error can be improved by using the coarse grid correction. Numerical experiments are reported to support the theoretical results.

Analysis of a two-grid method for semiconductor device problem

The mathematical model of a semiconductor device is governed by a system of quasi-linear partial differential equations.The electric potential equation is approximated by a mixed finite element method,and the concentration equations are approximated by a standard Galerkin method.We estimate the error of the numerical solutions in the sense of the Lqnorm.To linearize the full discrete scheme of the problem,we present an efficient two-grid method based on the idea of Newton iteration.The main procedures are to solve the small scaled nonlinear equations on the coarse grid and then deal with the linear equations on the fine grid.Error estimation for the two-grid solutions is analyzed in detail.It is shown that this method still achieves asymptotically optimal approximations as long as a mesh size satisfies H=O(h^1/2).Numerical experiments are given to illustrate the efficiency of the two-grid method.

Two-grid method for characteristic mixed finite-element solutions of nonlinear convection-diffusion equations

A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlinear systems by two steps. The error analysis shows that the two-grid scheme combined with the characteristic mixed finite-element method can decrease numerical oscillation caused by dominated convections and solve nonlinear advection-dominated diffusion problems efficiently.

A Two-Grid Technique for the Penalty Method of the Steady Navier-Stokes Equations

A two grid technique for solving the steady incompressible Navier Stokes equations in a penalty method was presented and the convergence of numerical solutions was analyzed. If a coarse size H and a fine size h satisfy H=O(h 13-s )(s=0(n=2);s=12(n=3), where n is a space dimension), this method has the same convergence accuracy as the usual finite element method. But the two grid method can save a lot of computation time for its brief calculation. Moreover, a numerical test was couducted in order to verify the correctness of above theoretical analysis.

准噶尔盆地深层油气勘探地震采集关键技术及效果

准噶尔盆地目前4 500 m以深的深层油气探明率较低,近年来深层油气勘探目标成为该地区勘探发现的战略接替区。为了查清地下深层结构,重新构建和部署了准噶尔盆地二维地震格架线,利用以往采集资料和重新采集的新资料拼接形成了数十条线组成的二维格架网。基于“两宽一高”技术体系,采用一系列采集关键技术,如“高激发密度、高接收密度、高覆盖密度和长排列”的“三高一长”采集技术,解决了准噶尔盆地深层油气勘探地震采集面临的深层目标地震信号“能量低、干扰强、成像差和不成像”等难题。新采集并经后期处理后的资料成像效果显著提高,为建立盆地石炭系-二叠系统一的地层格架、明确石炭系隆凹格局、查清富烃凹陷下组合地层及烃源岩展布特征提供了良好的资料基础,为下一步深层油气勘探工作提供了有效指导。

基于光伏动态电流参考值的两级式光伏并网系统低电压穿越控制策略

随着光伏接入容量的不断提升,电网电压跌落时光伏脱网会影响系统稳定运行,因此光伏系统应具备低电压穿越(LVRT)能力。然而,目前常用的两级式光伏并网系统LVRT控制策略存在光伏动态响应慢及控制效果受限于光伏P–U特性曲线的数学模型精度等问题,且未考虑局部阴影条件下的适用性。基于此,提出一种基于光伏动态电流参考值的LVRT控制策略。首先,在建立两级式光伏并网系统及光伏电池P–U特性数学模型的基础上,分别对目前常用的基于定直流母线电压和基于光伏P–U特性曲线的LVRT控制的原理及不足进行了分析。其次,针对前级boost电路的控制构造了具有自适应收敛特性的光伏输出电流动态参考值以对光伏工作点进行直接调整。该策略无需对光伏P–U特性曲线数学模型进行求解,避免求解误差的同时加快了光伏动态响应速度。此外,在最大功率跟踪(MPPT)算法中引入故障解耦模块,在电网低电压故障期间对MPPT输出电压参考值进行锁定,避免MPPT无效运算带来的电压参考值偏移,使系统在故障结束时能以最快速度恢复至最大功率点。最后,通过仿真将所提策略与目前常用的基于定直流母线电压和基于光伏P–U特性曲线的LVRT控制策略在多种环境条件下进行对比。仿真结果表明:与定直流母线电压控制策略相比,所提策略下光伏动态响应快;与现有基于光伏P–U特性曲线的控制策略相比,所提策略不受P–U特性误差的影响,在辐照度变化尤其局部阴影条件下均能很好地实现低电压穿越。

多孔介质中单相流地应力耦合问题的二重网格混合有限元法

本文提出了多孔介质中单相流耦合地应力问题的二重网格混合有限元法.本文首先给出了多孔介质中的单相流的控制方程及地应力问题的控制方程,推导了多孔介质中的微可压缩流体的单相流耦合地应力问题的非线性控制方程.然后,为数值求解该方程本文提出了二重网格混合有限元法,将问题转化为在粗网格上求解小规模非线性问题、在细网格上求解大规模线性问题,以提高计算效率.最后,数值算例验证了方法的有效性.

不对称故障下低电压穿越的多目标解耦控制策略

在传统不对称故障低电压穿越控制中,由于控制自由度有限,并网逆变器控制存在无法同时实现输出电流负序分量和直流侧电压二倍频波动抑制的问题。对此,文中提出一种不对称故障下两级式光伏并网系统低电压穿越的多目标解耦控制策略。该策略将逆变器的控制目标设置为输出电流负序分量抑制,给出了综合考虑逆变器输出电流限幅和无功输出需求的逆变器电流内环控制参考值计算方法;通过双向Buck-Boost变换器将超级电容接入直流母线电容两端维持其电压稳定,并将直流侧电压二倍频波动转移至超级电容输入侧进行抑制。仿真结果表明,相比传统控制方法,所提控制策略有效降低了逆变器三相间的不平衡度,改善了输出电流畸变,减小了直流侧电压二倍频波动。

基于双层网络频率控制的分布式风电并网研究

为研究含通信控制层的双层电网中分布式风电入网位置的选择,电网层采用二阶类Kuramoto模型进行建模,通信控制层收集发电机及其邻居节点信息形成控制信号并调整发电机的频率。根据负荷到原电网发电机节点的平均距离定义了3种并网方式,研究比较了含功率波动的分布式风电并网时最佳的入网位置。研究表明,加入双层网络频率控制可有效提高电网的同步性能和抗扰能力;分布式风电选择离原电网发电机节点平均距离小的负荷并网可提高电网稳定性。

武汉广电全媒体中心主体结构设计

武汉广电全媒体中心建筑体型复杂,具有大悬挑、大跨度转换等不规则项。针对项目特点,简要介绍了项目的结构体系,对正常使用状态下的大悬挑转换、单层双向索网幕墙等结构重难点的设计进行了阐述。同时,针对各层薄弱复杂连接楼盖,在地震作用下进行分塔模型与整体模型的分析对比。结果表明:通过利用顶部异形空间桁架和楼层大跨度连廊形成东西塔弹性对撑的自平衡效应,有效削减单层双向索网幕墙索力对主体结构的附加作用效应,同时为幕墙提供具有足够刚度的约束边界;对于双向同向下凹的大跨屋盖,利用造型的几何悬垂效应,采用单层双向悬垂受力钢网格结构,实现建筑和结构有机结合;地震作用下,采用取消薄弱连接楼盖的分塔模型和整体模型对竖向构件进行包络设计,提高竖向抗侧力构件的安全度。

基于广义积分器二自由度PID控制的LCL逆变器

传统有源阻尼控制可抑制LCL逆变器谐振,但需要增加额外的电压或电流传感器。为此,提出了一种无需额外传感器的基于广义积分器的LCL并网逆变器单电流反馈二自由度PID控制(GI-2DoF-PID),GI-2DoF-PID比例积分环节实现并网电流无静差跟踪,而基于广义积分器的微分环节则增强LCL逆变器的阻尼特性。推导了控制系统的传递函数,分析了其稳定裕度与动态特性,提出跟踪和抗扰动优化的参数设计原则并选取了合适的控制参数。最后,构建了基于PLECS系统仿真模型,仿真结果表明:基于GI-2DoF-PID控制的LCL并网逆变器可以有效抑制谐振;电网电压严重畸变时,其满载并网电流畸变率仅为3%,远低于国家标准的要求;当系统从半载跳变到满载时,系统超调量低,响应速度快。

面向多场景辅助服务的大规模电动汽车聚合可调度容量建模

大规模电动汽车聚合可调度容量是含电动汽车的虚拟电厂参与多层级多场景电力平衡辅助服务的重要技术指标之一。然而,现有电动汽车聚合可调度容量模型难以适应大规模电动汽车与省级电力调度中心互动场景。为此,文中从面向电力系统调峰、调频和调压多级多场景调控新视角,提出了数据驱动和机器学习相结合的双层聚类电动汽车聚合可调度容量建模方法。该方法通过构建电动汽车-充电桩广义储能单元的个体可调度容量模型,结合基于密度空间的聚类算法和改进的自组织映射深度聚类算法,有效地融合了电动汽车电量的时间分布和充电桩的空间分布特性,构建了面向调峰、调频和调压多场景调控的聚合可调度容量模型。采用了某省实际充电记录数据对提出的方法进行了验证,获得了“早间型”“中午型”“晚间型”等多种充电画像类型,实现了时空分布各异的电动汽车广义储能系统的自主聚合和省市级规模电动汽车参与电网不同辅助服务潜能的评估,并为聚合可调度容量的预测奠定了数据基础。