A Gridless Router Based on Hierarchical PB Corner Stitching Structure

A multi layer gridless area router is reported.Based on corner stitching,this router adopts tile expansion to explore path for each net.A heuristic method that penalizes nodes deviating from the destination is devised to accelerate the algorithm.Besides,an enhanced interval tree is used to manage the intermediate data structure.In order to improve the completion rate of routing,a new gridless rip up and rerouting algorithm is proposed.The experimental results indicate that the completion rate is improved after the rip up and reroute process and the speed of this algorithm is satisfactory.

GRIDLESS METHOD FOR UNSTEADY VISCOUS FLOWS

Gridless method is developed for unsteady viscous flows involving moving boundaries. The point distri- bution of gridless method is implemented in an isotropic or anisotropic way according to the features of viscous flows. In the area far away from the body, the traditional cloud of isotropic points is used, while in the adjacent area, the cloud of anisotropic points is distributed. In this way, the point spacing normal to the wall can be small enough for simulating the boundary layer, and meanwhile, the total number of points in the computational do- main can be controlled due to large spacing in other tangential direction through the anisotropic way. A fast mov- ing technique of clouds of points at each time-step is presented based on the attenuation law of disturbed motion for unsteady flows involving moving boundaries. In the mentioned cloud of points, a uniform weighted least- square curve fit method is utilized to discretize the spatial derivatives of the Navier-Stokes equations. The pro- posed gridless method, coupled with a dual time-stepping method and the Spalart-Allmaras turbulence model, is implemented for the Navier-Stokes equations. The computational results of unsteady viscous flows around a NLR7301 airfoil with an oscillating flap and a pitching NACA0012 airfoil are presented in a good agreement with the available experimental data.

A Gridless-Finite Volume Hybrid Algorithm for Euler Equations

A fast hybrid algorithm based on gridless method coupled with finite volume method （FVM） is developed for the solution to Euler equations. Compared with pure gridless method, the efficiency of the hybrid algorithm is improved to the level of finite volume method for most parts of the flow filed arc covered with grid cells. Moreover, the hybrid method is flexible to deal with the configurations as clouds of points are used to cover the region adjacent to the bodies. Mirror satellites and mirror grid cells arc introduced to the interface to accomplish data communication between the different parts of the flow field. The Euler Equations arc spatially discretized with finite volume method and gridless method in mesh and clouds of points respectively, and an explicit four-stage Runge-Kutta scheme is utilized to reach the steady-state solution. Internal flows in channels and external flows over airfoils arc investigated with hybrid method, and the solutions arc comparad to those using pure finite volume method and pure gridless method. Numerical examples show that the hybrid algorithm captures the shock waves accurately, and it is as efficient as fmite volume method.

Gridless Solution Method for Two-Dimensional Unsteady Flow

The main purpose of this paper is to develop a gridless method for unsteady flow simulation. A quadrantal point infilling strategy is developed to generate point and combine clouds of points automatically. A point-moving algorithm is introduced to ensure the clouds of points following the movements of bodyboundaries. A dual time method for solving the two-dimenslonal Euler equations in Arbitrary Lagrangian-Eulerian （ALE） formulation is presented. Dual time method allows the real-time step to be chosen on the basis of accuracy rather than stability. It also permits the acceleration techniques, which are commonly used to speed up steady flow calculations, to be used when marching the equations in pseudo time. The spatial derivatives, which are used to estimating the inviscid flux, are directly approximated by using local least-squares curve method. An explicit multistage Runge-Kutta algorithm is used to advance the flow equations in pseudo time. In order to accelerate the solution to convergence, local time stepping technique and residual averaging are employed. The results of NACA0012 airfoil in transonic steady flow are presented to verify the accuracy of the present spatial discretization method. Finally, two AGARD standard test cases in which NACA0012 airfoil and NACA64A010 airfoil oscillate in transonic flow are simulated. The computational results are compared with the experimental data to demonstrate the validity and practicality of the presented method.

Euler solution using adaptive Cartesian grid with a gridless boundary treatment

A quadtree-based adaptive Cartesian grid generator and flow solver were developed. The grid adaptation based on pressure or density gradient was performed and a gridless method based on the least-square fashion was used to treat the wall surface boundary condition, which is generally difficult to be handled for the common Cartesian grid. First, to validate the technique of grid adaptation, the benchmarks over a forward-facing step and double Mach reflection were computed. Second, the flows over the NACA 0012 airfoil and a two-element airfoil were calculated to validate the developed gridless method. The computational results indi- cate the developed method is reasonable for complex flows.

HYBRID CARTESIAN GRID/GRIDLESS METHOD FOR CALCULATING VISCOUS FLOWS OVER MULTI-ELEMENT AIRFOILS

A hybrid Cartesian grid/gridless method is developed for calculating viscous flows over multi-element airfoils.The method adopts an unstructured Cartesian grid to cover most areas of the computational domain and leaves only small region adjacent to the aerodynamic bodies to be filled with the cloud of points used in the gridless methods,which results in a better combination of the computational efficiency of the Cartesian grid and the flexibility of the gridless method in handling complex geometries.The clouds of points in the local gridless region are implemented in an anisotropic way according to the features of the thin boundary layer of the viscous flows over the airfoils,and the clouds of points at the vicinity of the interface between the grid and the gridless regions are also controlled by using an adaptive refinement technique during the generation of the unstructured Cartesian grid.An implementation of the resulting hybrid method is presented for solving two-dimensional compressible Navier-Stokes(NS)equations.The simulations of the viscous flows over a RAE2822airfoil or a two-element airfoil are successfully carried out,and the obtained results agree well with the available experimental data.

A Preconditioned Gridless Method for Solving Euler Equations at Low Mach Numbers

A preconditioned gridless method is developed for solving the Euler equations at low Mach numbers.The preconditioned system in a conservation form is obtained by multiplying apreconditioning matrix of the type of Weiss and Smith to the time derivative of the Euler equations,which are discretized using agridless technique wherein the physical domain is distributed by clouds of points.The implementation of the preconditioned gridless method is mainly based on the frame of the traditional gridless method without preconditioning,which may fail to converge for low Mach number simulations.Therefore,the modifications corresponding to the affected terms of preconditioning are mainly addressed.The numerical results show that the preconditioned gridless method still functions for compressible transonic flow simulations and additionally,for nearly incompressible flow simulations at low Mach numbers as well.The paper ends with the nearly incompressible flow over a multi-element airfoil,which demonstrates the ability of the method presented for treating flows over complicated geometries.

Application of Gridless Method to Simulation of Compressible Multi-Material Flows

The least-square gridless method was extended to simulate the compressible multi-material flows. The algorithm was accomplished to solve the Arbitrary Lagrange-Euler( ALE) formulation. The local least-square curve fits was adopted to approximate the spatial derivatives of a point on the base of the points in its circular support domain,and the basis function was linear. The HLLC( Harten-Lax-van Leer-Contact) scheme was used to calculate the inviscid flux. On the material interfaces,the gridless points were endued with a dual definition corresponding to different materials. The moving velocity of the interface points was updated by solving the Riemann problem. The interface boundary condition was built by using the Ghost Fluid Method( GFM).Computations were performed for several one and two dimensional typical examples. The numerical results show that the interface and the shock wave are well captured,which proves the effectiveness of gridless method in dealing with multi-material flow problems.

Gridless Variational Bayesian Inference of Line Spectral from Quantized Samples

Efficient estimation of line spectral from quantized samples is of significant importance in information theory and signal processing,e.g.,channel estimation in energy efficient massive MIMO systems and direction of arrival estimation.The goal of this paper is to recover the line spectral as well as its corresponding parameters including the model order,frequencies and amplitudes from heavily quantized samples.To this end,we propose an efficient gridless Bayesian algorithm named VALSE-EP,which is a combination of the high resolution and low complexity gridless variational line spectral estimation(VALSE)and expectation propagation(EP).The basic idea of VALSE-EP is to iteratively approximate the challenging quantized model of line spectral estimation as a sequence of simple pseudo unquantized models,where VALSE is applied.Moreover,to obtain a benchmark of the performance of the proposed algorithm,the Cram′er Rao bound(CRB)is derived.Finally,numerical experiments on both synthetic and real data are performed,demonstrating the near CRB performance of the proposed VALSE-EP for line spectral estimation from quantized samples.

Numerical Simulation for the External Combustion of Base-Bleed Projectile Using Gridless Method

The gridless method coupled with finite rate chemistry model is employed to simulate the external combustion flow fields of M864 base bleed projectile. The fluid dynamics process is described by Euler Equation in 2-D axisymmetric coordinate. The numerical method is based on least-square gridless method,and the inviscid flux is calculated by multi-component HLLC( Harten-Lax-van Leer-Contact) scheme,and a H2-CO reaction mechanism involving 9 species and 11 reactions is used. The computations are performed for the full projectile configuration of Ma = 1. 5,2,and 3. The hot air injection cases and inert cases are simulated for comparison. The numerical results show that due to the combustion in the weak region,the recirculation zone enlarges and moves downstream,the base pressure increases and the total drag force coefficient decreases. At Ma = 3. 0,the rear stagnation point shifts downstream approximate 0. 26 caliber,and the base pressure increases about 53. 4%,and the total drag force coefficient decreases to 0. 182 which agrees well with the trajectory model prediction. Due to neglecting the effects of viscosity and turbulence,there exists a certain difference at Ma = 1. 5,2. 0.

Gridless Net Routing of Integrate Circuit with Particle Swarm Optimization Algorithm

Particle swarm optimization algorithm is presented for the layout of ＂Integrate Circuit （IC）＂ design. Particle swarm optimization based on swarm intelligence is a new evolutionary computational tool and is successfully applied in function optimization, neural network design, classification, pattern recognition, signal processing and robot technology and so on. A modified algorithm is presented and applied to the layout of IC design. For a given layout plane, first of all, this algorithm generates the corresponding grid group by barriers and nets＇ ports with the thought ofgridless net routing, establishes initialization fuzzy matrix, then utilizes the global optimization character to find out the best layout route only if it exits. The results of model simulation indicate that PSO algorithm is feasible and efficient in IC layout design.

L型互质阵的虚拟共轭插值二维DOA估计方法

针对现有互质阵DOA估计方法无法充分利用非连续阵元信息和信号时域信息,而导致的DOA估计精度低、虚拟阵列的阵列孔径小和自由度少的问题,本文提出了一种L型互质阵的虚拟共轭插值二维DOA估计方法。该方法首先以L型互质阵的阵列接收数据为基础,通过求解其互相关函数,来构造虚拟共轭增广阵列的接收数据矩阵;然后通过阵列插值补零和选取协方差矩阵非零列,得到含有部分缺失项的虚拟均匀线阵接收数据矩阵,并依据原子范数的思想,构造无网格凸优化问题,对虚拟均匀线阵协方差矩阵的缺失项进行填充,再使用求根多重信号分类方法得到入射信号与x轴和z轴正方向夹角的估计值;最终基于虚拟信源功率的唯一性,通过构建相关代价函数实现各轴夹角估计值的匹配,进而根据各轴夹角与方位角和俯仰角的关系,得到相匹配的方位角和俯仰角估计值。本文方法提高了DOA估计精度,扩展了阵列孔径,提高了自由度,且通过求根多重信号分类方法,降低了计算复杂度。仿真实验结果表明,本文方法能够实现二维DOA估计与角度匹配,且相比于对比方法,本文方法能够估计更多的信号源,拥有更加优越的DOA估计性能。

面向1比特稀疏阵列的无网格测向方法

随着天线阵列规模的不断增大以及天线阵元数目的不断增加,模数转换器成本攀升。1比特量化技术能够有效减小数据规模,降低计算量,而基于1比特量化器的阵列定位是亟待解决的问题。本文提出了1比特量化器下的测向方法,该方法适用于均匀线性阵列及稀疏线性阵列,具有较强的适应性。首先根据1比特量化下协方差矩阵的多种特征建立协方差矩阵重构优化问题,再对该问题进行求解,最后通过范德蒙德分解定理得到角度的估计值。由于该方法不需要网格划分,因此实现了无网格估计,具有较高的估计精度。

A Yield-Driven Gridless Router

A new gridless router to improve the yield of IC layout is presented. The improvement of yield is achieved by reducing the critical areas where the circuit failures are likely to happen. This gridless area router benefits from a novel cost function to compute critical areas during routing process, and heuristically lays the patterns on the chip area where it is less possible to induce critical area. The router also takes other objectives into consideration, such as routing completion rate and nets length. It takes advantage of gridless routing to gain more flexibility and a higher completion rate. The experimental results show that critical areas are effectively decreased by 21% on average while maintaining the routing completion rate over 99%.

Preconditioned gridless methods for solving three-dimensional Euler equations at low Mach numbers

In this paper,preconditioned gridless methods are developed for solving the threedimensional(3D)Euler equations at low Mach numbers.The preconditioned system is obtained by multiplying a preconditioning matrix of the type of Weiss and Smith to the time derivative of the 3D Euler equations,which are discretized under the clouds of points distributed in the computational domain by using a gridless technique.The implementations of the preconditioned gridless methods are mainly based on the frame of the traditional gridless method without preconditioning,which may fail to have convergence for flow simulations at low Mach numbers,therefore the modifications corresponding to the affected terms of preconditioning are mainly addressed in the paper.An explicit four-stage Runge–Kutta scheme is first applied for time integration,and the lower-upper symmetric Gauss-Seidel(LU-SGS)algorithm is then introduced to form the implicit counterpart to have the further speed up of the convergence.Both the resulting explicit and implicit preconditioned gridless methods are validated by simulating flows over two academic bodies like sphere or hemispherical headform,and transonic and nearly incompressible flows over one aerodynamic ONERA M6 wing.The gridless clouds of both regular and irregular points are used in the simulations,which demonstrates the ability of the method presented for coping with flows over complicated aerodynamic geometries.Numerical results of surface pressure distributions agree well with available experimental data or simulated solutions in the literature.The numerical results also show that the preconditioned gridless methods presented still functions for compressible transonic flow simulations and additionally,for nearly incompressible flow simulations at low Mach numbers as well.The convergence of the implicit preconditioned gridless method,as expected,is much faster than its explicit counterpart.

页岩气藏两相流固耦合无网格数值模拟

针对页岩气藏受两相复杂流动与流固耦合作用影响导致产能预测难度大的问题,将渗流场分为主改造区、次改造区和未改造区,结合多流态统一输运模型及等效连续非均匀介质物理模型,建立多尺度气-水两相流动流固耦合数学模型,并利用无网格广义有限差分法对数学模型进行编程求解。研究结果表明:无网格广义有限差分法能适应不同计算域情况,避免传统差分网格与非结构网格耦合所导致的运算不稳定;压降前缘在未改造区的传播仅为20 m左右,固体位移主要发生在次改造区与未改造区的交界区域;忽略应力场的影响,气井投产初期产气量被显著高估,到生产后期这种影响逐渐下降;低初始含水饱和度的页岩气藏更有益于开发,储层优选时应重点考虑含水饱和度。研究成果对流固耦合数值模拟及非常规油气藏产能预测具有指导意义。

低信噪比下非冗余阵列的无网格DOA估计

波达方向(direction of arrival,DOA)是阵列信号处理模型中的非线性参数,当信噪比较低时,其估计值会偏离真实值。为了降低无网格DOA估计方法中该问题的阈值,介绍了一种基于无网格的基于协方差的稀疏迭代估计(sparse iterative covariance-based estimation,SPICE)方法。引入了最大似然求根多重信号分类(maximum likelihood root multiple signal classification,ML-Root-MUSIC)来计算DOA,使用最大似然准则来选择根,可以降低阈值并获得更好的分辨率特性。在原始无网格SPICE的优化问题中加入了负熵项,使得无网格SPICE的均方根误差曲线更接近于Cramer-Rao下界。最后,蒙特卡罗仿真实验验证了所提方法在低信噪比非冗余阵列情况下的优越性。

基于ANM的非均匀圆阵二维DOA估计

传统的基于原子范数最小化(Atomic Norm Minimization,ANM)的波达方向(Direction of Arrival,DOA)估计算法无法直接应用于不满足范德蒙德结构的非均匀圆阵,针对这一问题提出了一种基于虚拟阵列变换的改进方法。以某非均匀圆阵作原始阵列为例,首先通过虚拟阵列变换处理原始阵列接收的数据,使其转换为虚拟的均匀L阵接收数据,将非均匀圆阵上的DOA估计问题转化为两个均匀线阵上的DOA估计问题,再利用基于ANM的DOA估计算法与L型阵的二维角度关系还原出方位角和俯仰角。通过仿真与实测实验验证了所提算法应用于非均匀圆阵的可行性,并分析其DOA估计结果,证明其拥有较高的估计精度。

使用重加权原子范数最小化的稀疏可重构直线阵列设计

为克服网格失配问题并提升阵列性能,提出了使用重加权原子范数最小化的稀疏可重构直线阵列设计方法,将稀疏可重构直线阵列设计问题表示为多测量矢量稀疏优化模型,并通过重加权原子范数最小化算法解算出阵元位置和阵元激励。区别于经典压缩感知方法,该方法借助原子范数理论建立了阵元数量、阵元位置和阵元激励联合优化的无网格稀疏优化模型,从而可以克服网格失配问题,并提升阵列波束图的匹配精度。仿真实验表明,与压缩感知类方法相比,重加权原子范数最小化算法可以设计出波束匹配精度高一个数量级的稀疏可重构直线阵列。

稀疏恢复空时自适应处理技术研究综述

相较于传统空时自适应处理(STAP)技术,稀疏恢复(SR)STAP技术在小样本条件下杂波抑制性能显著提升,因此适用于现实非均匀杂波环境.本文首先阐述了SR STAP基本原理,分析了机载雷达杂波空时稀疏特性;然后总结了SR STAP发展历史与现状,并在此基础上针对其相关科学问题进行了探讨,包括:空时谱估计还是杂波抑制、单观测样本还是多观测样本、白化还是置零、重构算法参数依赖还是不依赖、非平稳杂波下是否适用及干扰条件下是否可行;最后给出了当前SR STAP技术走向实用化过程中所面临的关键问题,即网格失配和空域误差影响,并分别讨论了无网格压缩感知和字典自校正的解决途径.