Numerical Investigation of Sound Generation due to Laminar Flow Past Elliptic Cylinders

Numerical investigation of sound generation due to unsteady laminar flow past elliptic cylinders has been carried out using direct numerical simulation $(DNS)$ approach at a free-stream Mach number of $0.2$. Effects of aspect ratio $(0.6\le AR\le 1.0)$ and Reynolds number $(100\le Re \le 160)$ on the characteristics of radiated sound fields are analyzed. Two-dimensional compressible fluid flow equations are solved on a refined grid using high resolution dispersion relation preserving $(DRP)$ schemes. Using present $DNS$ data, equivalent noise sources as given by various acoustic analogies are evaluated. Amplitudes and frequencies associated with these noise sources are further related to characteristics of disturbance pressure fields. Disturbance pressure fields are intensified with increase in Reynolds number and aspect ratio. Thus, radiated sound power increases with increase in Reynolds number and aspect ratio. Among various cases studied here, minimum and maximum values of radiated sound power are found at $Re=120$ & $AR=0.6$ and $Re=160$ & $AR=1.0$, respectively. Directivity patterns show that the generated sound fields are dominated by the lift dipole for all cases. Next, proper orthogonal decomposition $(POD)$ technique has been implemented for decomposing disturbance pressure fields. The $POD$ modes associated with the lift and the drag dipoles have been identified. $POD$ analyses also clearly display that the radiated sound fields are dominated by the lift dipole only. Further, acoustic and hydrodynamic modes obtained using Doak's decomposition method have confirmed the patterns of radiated sound field intensities.     

Parallel Smoothed Aggregation Multilevel Schwarz Preconditioned Newton-Krylov Algorithms for Poisson-Boltzmann Problems

We study a multilevel Schwarz preconditioned Newton-Krylov algorithm to solve the Poisson-Boltzmann equation with applications in multi-particle colloidal simulation. The smoothed aggregation-type coarse mesh space is introduced in collaboration with the one-level Schwarz method as a composite preconditioner for accelerating the convergence of a Krylov subspace method for solving the Jacobian system at each Newton step. The important feature of the proposed solution algorithm is that the geometric mesh information needed for constructing the multilevel preconditioner is the same as the one-level Schwarz method on the fine mesh. Other components, such as the definition of the coarse mesh, all the mesh transfer operators, and the coarse mesh problem, are taken care of by the Trillinos/ML packages of the Sandia National Laboratories in the United States. After algorithmic parameter tuning, we show that the proposed smoothed aggregation multilevel Newton-Krylov-Schwarz (NKS) algorithm numerically outperforms than smoothed aggregation multigrid method and one-level version of the NKS algorithm with satisfactory parallel performances up to a few thousand cores. Besides, we investigate how the electrostatic forces between particles for the separation distance depend on the radius of spherical colloidal particles and valence ratios of cation and anion in a cubic system.     

基于Adaboost-SVR模型的我国碳排放强度分析与预测

首先对我国1960-2017年的碳排放趋势分5个阶段分析,发现虽然在不同时期存在波动,但长期来看,我国碳排放强度呈逐步下降趋势.然后对差分平稳后的序列数据建立Adaboost-SVR预测模型,采用RMSE、MAPE、MAE、MSE四个评价指标比较Adaboost-SVR模型与Adaboost-DT、SVR、BP神经网络对碳排放强度的预测精度.结果表明,组合模型明显优于其他3种模型,对于碳排放强度预测具有很高的可靠性.另外,通过使用Adaboost-SVR模型进行后续年份预测,发现我国未来碳排放强度总体将继续缓慢下降.最后,基于二氧化碳排放量的LMID分解结果,提出调整能源产业结构, 促进可再生能源利用等节能减排建议.     

极分解定理的注记

设H和K是Hilbert空间.首先,对给定的算子T∈B（H,K）,刻画了集合U_T={U∈B（H,K）：U是部分等距算子并且T=U（T^*T）^1/2}. 其次,对部分等距算子U∈B（H,K）,还给出集合T_U={T∈B（H,K）：N（T）=N（U）,R（T）=R（U）,T=U（T^*T）^1/2}的刻画. 最后,作为主要结果的应用得到了相关结论.     

A conservative parallel difference method for 2-dimension diffusion equation

In this paper, a conservative parallel difference scheme, which is based on domain decomposition method, for 2-dimension diffusion equation is proposed. In the construction of this scheme, we use the numerical solution on the previous time step to give a weighted approximation of the numerical flux. Then the sub-problems with Neumann boundary are computed by fully implicit scheme. What is more, only local message communication is needed in the program. We use the method of discrete functional analysis to give the proof of the unconditional stability and second-order convergence accuracy. Some numerical tests are given to verify the theory results.     

基于EMD-GA-BP与EMD-PSO-LSSVM的中国碳市场价格预测

由于碳交易市场价格的波动性大及相互影响关系的复杂性,本文试图构建碳价格长期和短期的最优预测模型。考虑到碳交易价格波动的趋势性和周期性特点,基于经验模态分解算法(EMD)、遗传算法(GA)—神经网络(BP)模型、粒子群算法(PSO)—最小二乘支持向量机(LSSVM)模型及由它们构建的组合预测模型,对中国碳市场交易价格进行短期预测和长期预测。实证分析中将影响碳交易价格的不同宏观经济因素和碳价格时间序列因素做为输入变量,分别代入组合模型进行预测。研究结果表明,在短期预测中,EMD-GA-BP模型预测效果优于GA-BP模型和PSO-LSSVM模型;而在长期预测中,组合模型EMD-PSO-LSSVM模型预测效果优于只考虑碳价格波动趋势性或周期性预测效果。     

Enclosings of decompositions of complete multigraphs in 2‐factorizations

Let k, m, n, λ, and μ be positive integers. A decomposition of into edge‐disjoint subgraphs is said to be enclosed by a decomposition of into edge‐disjoint subgraphs if and, after a suitable labeling of the vertices in both graphs, is a subgraph of and is a subgraph of for all . In this paper, we continue the study of enclosings of given decompositions by decompositions that consist of spanning subgraphs. A decomposition of a graph is a 2‐factorization if each subgraph is 2‐regular and spanning, and is Hamiltonian if each subgraph is a Hamiltonian cycle. We give necessary and sufficient conditions for the existence of a 2‐factorization of that encloses a given decomposition of whenever and . We also give necessary and sufficient conditions for the existence of a Hamiltonian decomposition of that encloses a given decomposition of whenever and either or and , or , , and .     

A weighted singular value decomposition for the discrete inverse problems

In this paper, we introduce and analyze a new singular value decomposition (SVD) called weighted SVD (WSVD) using a new inner product instead of the Euclidean one. We use the WSVD to approximate the singular values and the singular functions of the Fredholm integral operators. In this case, the new inner product arises from the numerical integration used to discretize the operator. Then, the truncated WSVD (TWSVD) is used to regularize the Nyström discretization of the first‐kind Fredholm integral equations. Also, we consider the weighted LSQR (WLSQR) to approximate the solution obtained by the TWSVD method for large problems. Numerical experiments on a few problems are used to illustrate that the TWSVD can perform better than the TSVD.     

Domain decomposition preconditioners for multiscale problems in linear elasticity

We analyze two‐level overlapping Schwarz domain decomposition methods for vector‐valued piecewise linear finite element discretizations of the PDE system of linear elasticity. The focus of our study lies in the application to compressible, particle‐reinforced composites in 3D with large jumps in their material coefficients. We present coefficient‐explicit bounds for the condition number of the two‐level additive Schwarz preconditioned linear system. Thereby, we do not require that the coefficients are resolved by the coarse mesh. The bounds show a dependence of the condition number on the energy of the coarse basis functions, the coarse mesh, and the overlap parameters, as well as the coefficient variation. Similar estimates have been developed for scalar elliptic PDEs by Graham et al. 1 The coarse spaces to which they apply here are assumed to contain the rigid body modes and can be considered as generalizations of the space of piecewise linear vector‐valued functions on a coarse triangulation. The developed estimates provide a concept for the construction of coarse spaces, which can lead to preconditioners that are robust with respect to high contrasts in Young's modulus and the Poisson ratio of the underlying composite. To confirm the sharpness of the theoretical findings, we present numerical results in 3D using vector‐valued linear, multiscale finite element and energy‐minimizing coarse spaces. The theory is not restricted to the isotropic (Lamé) case, extends to the full‐tensor case, and allows applications to multiphase materials with anisotropic constituents in two and three spatial dimensions. However, the bounds will depend on the ratio of largest to smallest eigenvalue of the elasticity tensor.     

A new model for sparse and low-rank matrix decomposition

The robust principal component analysis (RPCA) model is a popular method for solving problems with the nuclear norm and $\ell_1$ norm. However, it is time-consuming since in general one has to use the singular value decomposition in each iteration. In this paper, we introduce a novel model to reformulate the existed model by making use of low-rank matrix factorization to surrogate the nuclear norm for the sparse and low-rank decomposition problem. In such case we apply the Penalty Function Method (PFM) and Augmented Lagrangian Multipliers Method (ALMM) to solve this new non-convex optimization problem. Theoretically, corresponding to our methods, the convergence analysis is given respectively. Compared with classical RPCA, some practical numerical examples are simulated to show that our methods are much better than RPCA.