基于多格网算法的卫星图像恢复

将求解二次椭圆偏微分方程问题的多格网算法应用到卫星影像的恢复中。其基本思想是在将由总变分求极小生成的偏微分方程离散成为差分方程的过程中,采用不同大小的格网。在取得较好恢复结果的同时,提高了传统图像恢复算法的运算效率,降低了恢复运算所需要的时间。

Three-dimensional forward modeling of DC resistivity using the aggregation-based algebraic multigrid method

To speed up three-dimensional （3D） DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method （AGMG）. We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner （AGMG-CG） to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling （3DDCXH）. In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.

Multi-scale seismic full waveform inversion in the frequency-domain with a multi-grid method

Although full waveform inversion in the frequency domain can overcome the local minima problem in the time direction, such problem still exists in the space direction because of the media subsurface complexity. Based on the optimal steep descent methods, we present an algorithm which combines the preconditioned bi-conjugated gradient stable method and the multi-grid method to compute the wave propagation and the gradient space. The multiple scale prosperity of the waveform inversion and the multi-grid method can overcome the inverse problems local minima defect and accelerate convergence. The local inhomogeneous three-hole model simulated results and the Marmousi model certify the algorithm effectiveness.

浅谈统计相关模型在地理建模中的应用

地理学的研究内容复杂,其要素相互联系,过程多为不可控制,不同于物理学和化学。定量的解释地理问题是地理学的发展趋势,运用统计相关模型来进行地理建模已经成为非常普遍的研究手段。该文通过概述植物响应气候变化、空气污染物与气象因子之间的关系、人口数据统计分析3个方面的应用,大致介绍了统计相关模型在地理建模方面的发展,同时由于统计模型优于数据分析而弱于逻辑推理,仍需不断改进完善。

Multiresolution analysis over triangle meshes: method and data structure

A robust and efficient algorithm is presented to build multiresolution models (MRMs) of arbitrary meshes without requirement of subdivision connectivity. To overcome the sampling difficulty of arbitrary meshes, edge contraction and vertex expansion are used as downsampling and upsampling methods. Our MRMs of a mesh are composed of a base mesh and a series of edge split operations, which are organized as a directed graph. Each split operation encodes two parts of information. One is the modification to the mesh, and the other is the dependency relation among splits. Such organization ensures the efficiency and robustness of our MRM algorithm. Examples demonstrate the functionality of our method.

3-D direct current resistivity forward modeling by adaptive multigrid finite element method

Based on the fact that 3-D model discretization by artificial could not always be successfully implemented especially for large-scaled problems when high accuracy and efficiency were required, a new adaptive multigrid finite element method was proposed. In this algorithm, a-posteriori error estimator was employed to generate adaptively refined mesh on a given initial mesh. On these iterative meshes, V-cycle based multigrid method was adopted to fast solve each linear equation with each initial iterative term interpolated from last mesh. With this error estimator, the unknowns were nearly optimally distributed on the final mesh which guaranteed the accuracy. The numerical results show that the multigrid solver is faster and more stable compared with ICCG solver. Meanwhile, the numerical results obtained from the final model discretization approximate the analytical solutions with maximal relative errors less than 1%, which remarkably validates this algorithm.

China Ocean ReAnalysis(CORA)version 1.0 products and validation for 2009-18

China Ocean ReAnalysis(CORA) version 1.0 products for the period 2009-18 have been developed and validated.The model configuration and assimilation algorithm have both been updated compared to those of the 51-year(1958-2008) products.The assimilated observations include temperature and salinity field data,satellite remote sensing sea surface temperature,and merged sea surface height(SSH) anomaly data.The validation includes the following three aspects:(1) Temperature,salinity,and SSH anomaly root-mean-square errors(RMSEs) are computed as a primary evaluation of the reanalysis quality.The 0-2000 m domain-averaged RMSEs of temperature and salinity are 0.61℃ and 0.08 psu,respectively.The SSH anomaly RMSE is less than 0.2 m in most regions.(2) The 35°N temperature section is used to evaluate the ability to reproduce the thermocline,mixing layer,and Yellow Sea cold water mass.In summer,the thermocline is reinforced,with the gradient changing from 3℃ in May to 10℃ in August.The mixing-layer depth reproduced by CORA is consistent with that computed from the observed climatology.The Yellow Sea cold water mass forms at a depth of 50 m.(3) The reanalysis current is examined against the tracks of some drifting buoys.The results show that the reanalysis current can capture the mesoscale eddies near the Kuroshio,which are similar to those described by the drifting buoys.Overall,the 2009-18 CORA reanalysis products are capable of reproducing major oceanic phenomena and processes in the coastal waters of China and adjacent seas.

3D Engineering Model Retrieval Based on Enhanced Shape Distributions

To reuse and share the valuable knowledge embedded in repositories of engineering models for accelerating the design process, improving product quality, and reducing costs, it is crucial to devise search engines capable of matching 3D models efficiently and effectively. In this paper, an enhanced shape distributions-based technique of using geometrical and topological information to search 3D engineering models represented by polygonal meshes was presented. A simplification method of polygonal meshes was used to simplify engineering model as the pretreatment for generation of sample points. The method of sampling points was improved and a pair of functions that was more sensitive to shape was employed to construct a 2D shape distribution. Experiments were conducted to evaluate the proposed algorithm utilizing the Engineering Shape Benchmark (ESB) database. The experiential results suggest that the search effectiveness is significantly improved by enforcing the simplification and enhanced shape distributions to engineering model retrieval.

Equality Testing for Soil Grid Unit Resolutions to Polygon Unit Scales with DNDC Modeling of Regional SOC Pools

Matching soil grid unit resolutions with polygon unit map scales is important to minimize the uncertainty of regional soil organic carbon(SOC) pool simulation due to their strong influences on the modeling.A series of soil grid units at varying cell sizes was derived from soil polygon units at six map scales,namely,1:50 000(C5),1:200 000(D2),1:500 000(P5),1:1 000 000(N1),1:4 000 000(N4) and 1:14 000 000(N14),in the Taihu Region of China.Both soil unit formats were used for regional SOC pool simulation with a De Nitrification-DeC omposition(DNDC) process-based model,which spans the time period from 1982 to 2000 at the six map scales.Four indices,namely,soil type number(STN),area(AREA),average SOC density(ASOCD) and total SOC stocks(SOCS) of surface paddy soils that were simulated by the DNDC,were distinguished from all these soil polygon and grid units.Subjecting to the four index values(IV) from the parent polygon units,the variations in an index value(VIV,%) from the grid units were used to assess its dataset accuracy and redundancy,which reflects the uncertainty in the simulation of SOC pools.Optimal soil grid unit resolutions were generated and suggested for the DNDC simulation of regional SOC pools,matching their respective soil polygon unit map scales.With these optimal raster resolutions,the soil grid units datasets can have the same accuracy as their parent polygon units datasets without any redundancy,when VIV < 1% was assumed to be a criterion for all four indices.A quadratic curve regression model,namely,y = – 0.80 × 10^(–6)x^2 + 0.0228 x + 0.0211(R^2 = 0.9994,P < 0.05),and a power function model R? = 10.394?^(0.2153)(R^2 = 0.9759,P < 0.05) were revealed,which describe the relationship between the optimal soil grid unit resolution(y,km) and soil polygon unit map scale(1:10 000x),the ratio(R?,%) of the optimal soil grid size to average polygon patch size(?,km^2) and the ?,with the highest R^2 among different mathematical regressions,respectively.This knowledge may facilitate the grid partitioning of regions during the investigation and simulation of SOC pool dynamics at a certain map scale,and be referenced to other landscape polygon patches' mesh partition.

Application of multigrid NLS-4DVar in radar radial velocity data assimilation with WRF-ARW

The nonlinear least-squares four-dimensional variational assimilation(NLS-4DVar)method intro-duced here combines the merits of the ensemble Kalman lter and 4DVar assimilation methods.The multigrid NLS-4DVar method can be implemented without adjoint models and also corrects small-to large-scale errors with greater accuracy.In this paper,the multigrid NLS-4DVar method is used in radar radial velocity data assimilations.Observing system simulation experiments were conducted to determine the capability and efficiency of multigrid NLS-4DVar for assimilating radar radial velocity with WRF-ARW(the Advanced Research Weather Research and Forecasting model).The results show signi cant improvement in 24-h cumulative precipitation prediction due to improved initial conditions after assimilating the radar radial velocity.Additionally,the multigrid NLS-4DVar method reduces computational cost.

Strategies for h-Adaptive Refinement for a Finite Element Treatment of Harmonic Oscillator Schrodinger Eigenproblem

A Schrodinger eigenvalue problem is solved for the 219 quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two competing methods of adaptively discretizing the real-space grid on which computations are performed without modifying the standard polynomial basis-set traditionally used in finite element interpolations; namely, （i） an application of the Kelly error estimator, and （ii） a refinement based on the local potential level. When the performance of these methods are compared to standard uniform global refinement, we find that they significantly improve the total time spent in the eigensolver.

Research on a Multi-grid Model for Passenger Evacuation in Ships

In order to enhance the authenticity and accuracy of passenger evacuation simulation in ships, a new multi-grid model was proposed on the basis of a traditional cellular automata model. In the new model finer lattices were used, interaction of force among pedestrians or between pedestrians and constructions was considered, and static floor fields in a multi-level exit environment were simplified into cabin and exit static floor fields. Compared with the traditional cellular automata model, the multi-grid model enhanced the continuity of the passengers'track and the precision of the boundary qualifications. The functions of the dislocation distribution of passengers as well as partial overlap of tracks due to congestion were realized. Furthermore, taking the typical cabin environment as an example, the two models were used to analyze passenger evacuation under the same conditions. It was found that the laws of passenger evacuation simulated by the two models are similar, while the simulation's authenticity and accuracy are enhanced by the multi-grid model.

An Algorithm of the Adaptive Grid and Fuzzy Interacting Multiple Model

This paper studies the algorithm of the adaptive grid and fuzzy interacting multiple model （AGFIMM） for maneuvering target tracking, while focusing on the problems of the fixed structure multiple model （FSMM） algorithm＇s cost-efficiency ratio being not high and the Markov transition probability of the interacting multiple model （IMM） algorithm being difficult to determine exactly. This algorithm realizes the adaptive model set by adaptive grid adjustment, and obtains each model matching degree in the model set by fuzzy logic inference. The simulation results show that the AGFIMM algorithm can effectively improve the accuracy and cost-efficiency ratio of the multiple model algorithm, and as a result is suitable for enineering apolications.

Numerical simulation on conjugate heat transfer of turbine cascade

Numerical simulation on conjugate heat transfer of an internal cooled turbine vane was carried out. Numerical techniques employed included the third-order accuracy TVD scheme, multi-block structured grids and the technique of arbitrary curved mesh. Comparison between results of commercial CFD codes with several turbulence models and those of this code shows that it is incorrect of commercial CFD codes to predict the thermal boundary layer with traditional turbulence models, and that turbulence models considering transition lead to more accurate heat transfer in thermal boundary layer with some reliability and deficiency yet. The results of this code are close to those of CFX with transition model.

Mixed Communication Method on the Grid-based for Wireless Sensor Networks

When senors transmit their data to the sink via multi-hop communication, the sensors closer to the sink are burdened with heavy relay traffic and tend to die early. On the contrary, if all sensors transmit datas to the sink via single-hop communication, the sensors further from the sink will die much more quickly than those closer to the sink. In this paper, we first develop an analytical model to derive the optimal cluster radius. Then we propose a mixed communication method on grid-based where the sensors can transmit data to the sink in either single-hop or multi-hop. Finally, we conduct extensive experiments and show that our method outperforms LEACH and HEED in terms of network lifetime by balancing energy consumption.

A full multigrid method for nonlinear eigenvalue problems

We introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of the nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and nonlinear eigenvalue problems on the coarsest finite element space. The linearized boundary value problems are solved by some multigrid iterations.Besides the multigrid iteration, all other efficient iteration methods for solving boundary value problems can serve as the linear problem solver. We prove that the computational work of this new scheme is truly optimal,the same as solving the linear corresponding boundary value problem. In this case, this type of iteration scheme certainly improves the overfull efficiency of solving nonlinear eigenvalue problems. Some numerical experiments are presented to validate the efficiency of the new method.

Shape optimization of the caudal fin of the three-dimensional self-propelled swimming fish

Shape optimization of the caudal fin of the three-dimensional self-propelled swimming fish,to increase the swimming efficiency and the swimming speed and control the motion direction more easily,is investigated by combining optimization algorithms,unsteady computational fluid dynamics and dynamic control in this study.The 3D computational fluid dynamics package contains the immersed boundary method,volume of fluid method,the adaptive multi-grid finite volume method and the control strategy of fish swimming.Through shape optimizations of various swimming speeds,the results show that the optimal caudal fins of different swimming modes are not exactly the same shape.However,the optimal fish of high swimming speed,whose caudal fin shape is similar to the crescent,also have higher efficiency and better maneuverability than the other optimal bionic fish at low and moderate swimming speeds.Finally,the mechanisms of vorticity creation of different optimal bionic fish are studied by using boundary vorticity-flux theory,and three-dimensional wake structures of self-propelled swimming of these fish are comparatively analyzed.The study of vortex dynamics reveals the nature of efficient swimming of the 3D bionic fish with the lunate caudal fin.

Asymptotic expansions of finite element solutions to Robin problems in H^3 and their application in extrapolation cascadic multigrid method

For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the asymptotic error expansions of bilinear finite element have the accuracy of O(h3)for u∈H3.Based on the obtained asymptotic error expansions for linear finite elements,extrapolation cascadic multigrid method(EXCMG)can be used to solve Robin problems effectively.Furthermore,by virtue of Richardson not only the accuracy of the approximation is improved,but also a posteriori error estimation is obtained.Finally,some numerical experiments that confirm the theoretical analysis are presented.

Extrapolation cascadic multigrid method on piecewise uniform grid

The triangular linear finite elements on piecewise uniform grid for an elliptic problem in convex polygonal domain are discussed. Global superconvergence in discrete Hi-norm and global extrapolation in discrete L2-norm are proved. Based on these global estimates the conjugate gradient method （CG） is effective, which is applied to extrapolation cascadic multigrid method （EXCMG）. The numerical experiments show that EXCMG is of the global higher accuracy for both function and gradient.

Numerical simulations and vorticity dynamics of self-propelled swimming of 3D bionic fish

Numerical simulations and the control of self-propelled swimming of three-dimensional bionic fish in a viscous flow and the mechanism of fish swimming are carried out in this study,with a 3D computational fluid dynamics package,which includes the immersed boundary method and the volume of fluid method,the adaptive multi-grid finite volume method,and the control strategy of fish swimming.Firstly,the mechanism of 3D fish swimming was studied and the vorticity dynamics root was traced to the moving body surface by using the boundary vorticity-flux theory.With the change of swimming speed,the contributions of the fish body and caudal fin to thrust are analyzed quantitatively.The relationship between vortex structures of fish swimming and the forces exerted on the fish body are also given in this paper.Finally,the 3D wake structure of self-propelled swimming of 3D bionic fish is presented.The in-depth analysis of the 3D vortex structure in the role of 3D biomimetic fish swimming is also performed.