A grey model approach to indoor air quality management in rooms based on real-time sensing of particles and volatile organic compounds

The study presents an attempt to develop a model for the management of indoor air quality based on real-time sensing of particulate matter (nano and micro particles) and volatile organic compounds. The development of the model used a grey box approach where the initial data on pollutant variation was collected during the experimental phase, and further applied to the pollutant mass balance model. The pollution sources have been analyzed in a controlled environment to obtain patterns of temporal variation, which have been approximated by mathematical functions. Approximations allowed the employment of pollutant mass balance model for determining the variation of pollutant source and further to modeling variation of pollutant concentration with changing air change rate. The proposed management approach can be applied to control indoor air quality in homes, assuring optimal utilization of the air handling unit in order to achieve the acceptable indoor air quality in the lowest time span and optimal energy use.     

A dynamic evaluation framework for ambient air pollution monitoring

Accurate real-time prediction of urban air quality is one of the most important problems in control and improve ambient air condition globally. Therefore, the modeling and applications of air pollutant forecasting and evaluation has attracted the attention of researchers in recent years. Based on the method of fuzzy mathematical synthetic evaluation, this paper built a dynamic evaluation model for the purpose of mastering the future air quality immediately. A newly proposed computational intelligence optimization algorithm is improved to optimize the least square support vector machine, which can generate rolling forecasts of six air pollutants concentration. The information of future air quality status is built by the fuzzy synthetic assessment model based on entropy weighing method. The results and analysis of air quality monitoring show that accurate and reliable forecast of urban air pollutants concentration are possible and the air quality conditions can be evaluated objectively. Through the simulation design, it proves that the proposed dynamic evaluation model can provide a practical tool for ambient air ambient quality evaluation.     

An iterative langevin solution for turbulent dispersion in the atmosphere

In this work we present an alternative hybrid method to solve the Langevin equation and we apply it to simulate air pollution dispersion in inhomogeneous turbulence conditions. The method solves the Langevin equation, in semi-analytical manner, by the method of successive approximations or Picard's Iterative Method. Solutions for Gaussian and non-Gaussian turbulence conditions, considering Gaussian, bi-Gaussian and Gram–Charlier probability density functions are obtained. The models are applied to study the pollutant dispersion in all atmospheric stability and in low-wind speed condition. The proposed approach is evaluated through the comparison with experimental data and results from other different dispersion models. A statistical analysis reveals that the model simulates very well the experimental data and presents results comparable or even better than ones obtained by the other models.     

Stancu type generalization of the q-Phillips operators

In this work we apply the discontinuous Galekin (dG) spectral element method on meshes made of simplicial elements for the approximation of the elastodynamics equation. Our approach combines the high accuracy of spectral methods, the geometrical flexibility of simplicial elements and the computational efficiency of dG methods. We analyze the dissipation, dispersion and stability properties of the resulting scheme, with a focus on the choice of different sets of basis functions. Finally, we apply the method on benchmark as well as realistic test cases.     

Computational Methods for Pricing American Put Options

This work develops computational methods for pricing American put options under a Markov-switching diffusion market model. Two methods are suggested in this paper. The first method is a stochastic approximation approach. It can handle option pricing in a finite horizon, which is particularly useful in practice and provides a systematic approach. It does not require calibration of the system parameters nor estimation of the states of the switching process. Asymptotic results of the recursive algorithms are developed. The second method is based on a selling rule for the liquidation of a stock for perpetual options. Numerical results using stochastic approximation and Monte Carlo simulation are reported. Comparisons of different methods are made. This research was supported in part by the National Science Foundation and in part by the Wayne State University Research Enhancement Program.     

A numerical computation of a non-dimensional form of stream water quality model with hydrodynamic advection–dispersion–reaction equations

Mathematical models of water quality assessment problems often arise in environmental science. The modelling often involves numerical methods to solve the equations. In this research, two mathematical models are used to simulate pollution due to sewage effluent in the nonuniform flow of water in a stream with varied current velocity. The first is a hydrodynamic model that provides the velocity field and elevation of the water flow. The second is a dispersion model, where the commonly used governing factor is the one-dimensional advection–dispersion–reaction equation that gives the pollutant concentration fields. In the simulation processes, we used the Crank–Nicolson method system of a hydrodynamic model and the backward time central space scheme for the dispersion model. Finally, we present a numerical simulation that confirms the results of the techniques.     

浅水中污染物扩散的自适应有限元分析法

介绍浅水中污染物扩散分析中的有限元法.分析包括两个部分:1)流场速度、水面高度的计算;2)根据扩散模型计算污染物浓度场.联合使用了自适应网格技术以期提高解的精度,同时减少计算时间和计算机内存的消耗.通过几个有已知解的实例验证了有限元公式和计算机程序.最后,使用这种联合方法分析泰国Chao Phraya河附近海湾中的污染物扩散.     

基于区间数的空气质量模糊综合评价模型

针对空气质量评价的不确定性,引入区间数概念进行2016年辽宁省各城市的空气质量综合评价和分析.参照国家大气质量标准,选用SO2、NO2、CO、PM2.5、PM10五种大气主要污染物作为评价因子,利用区间数计算污染因子的隶属度进行分析.考虑到城市差异,采用区间梯形隶属度函数,同时考虑区间数排序函数及可信度对区间数排序进行修正,避免了单因素得分区间数的发散,并综合确定评价等级.实例分析验证了该评价方法的可行性,依据收集的数据和此方法的结论得出空气质量的好坏与污染源分布、污染物扩散条件以及季节等因素有关.     

Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling

In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a single optimal solution, the set of optimal compromises, the so-called Pareto set, has to be approximated. When the problem under consideration is described by a partial differential equation (PDE), as is the case for fluid flow, the computational cost rapidly increases and makes its direct treatment infeasible. Reduced order modeling is a very popular method to reduce the computational cost, in particular in a multi query context such as uncertainty quantification, parameter estimation or optimization. In this article, we show how to combine reduced order modeling and multiobjective optimal control techniques in order to efficiently solve multiobjective optimal control problems constrained by PDEs. We consider a global, derivative free optimization method as well as a local, gradient-based approach for which the optimality system is derived in two different ways. The methods are compared with regard to the solution quality as well as the computational effort and they are illustrated using the example of the flow around a cylinder and a backward-facing-step channel flow.

     

Adaptive weak approximation of stochastic differential equations

Adaptive time‐stepping methods based on the Monte Carlo Euler method for weak approximation of Itô stochastic differential equations are developed. The main result is new expansions of the computational error, with computable leading‐order term in a posteriori form, based on stochastic flows and discrete dual backward problems. The expansions lead to efficient and accurate computation of error estimates. Adaptive algorithms for either stochastic time steps or deterministic time steps are described. Numerical examples illustrate when stochastic and deterministic adaptive time steps are superior to constant time steps and when adaptive stochastic steps are superior to adaptive deterministic steps. Stochastic time steps use Brownian bridges and require more work for a given number of time steps. Deterministic time steps may yield more time steps but require less work; for example, in the limit of vanishing error tolerance, the ratio of the computational error and its computable estimate tends to 1 with negligible additional work to determine the adaptive deterministic time steps. © 2001 John Wiley & Sons, Inc.     

Relaxation strategies for nested Krylov methods

This paper studies computational aspects of Krylov methods for solving linear systems where the matrix–vector products dominate the cost of the solution process because they have to be computed via an expensive approximation procedure. In recent years, so-called relaxation strategies for tuning the precision of the matrix–vector multiplications in Krylov methods have proved to be effective for a range of problems. In this paper, we will argue that the gain obtained from such strategies is often limited. Another important strategy for reducing the work in the matrix–vector products is preconditioning the Krylov method by another iterative Krylov method. Flexible Krylov methods are Krylov methods designed for this situation. We combine these two approaches for reducing the work in the matrix–vector products. Specifically, we present strategies for choosing the precision of the matrix–vector products in several flexible Krylov methods as well as for choosing the accuracy of the variable preconditioner such that the overall method is as efficient as possible. We will illustrate this computational scheme with a Schur-complement system that arises in the modeling of global ocean circulation.     

Numerical solution of linear Volterra integral equations of the second kind with sharp gradients

Collocation methods are a well-developed approach for the numerical solution of smooth and weakly singular Volterra integral equations. In this paper, we extend these methods through the use of partitioned quadrature based on the qualocation framework, to allow the efficient numerical solution of linear, scalar Volterra integral equations of the second kind with smooth kernels containing sharp gradients. In this case, the standard collocation methods may lose computational efficiency despite the smoothness of the kernel. We illustrate how the qualocation framework can allow one to focus computational effort where necessary through improved quadrature approximations, while keeping the solution approximation fixed. The computational performance improvement introduced by our new method is examined through several test examples. The final example we consider is the original problem that motivated this work: the problem of calculating the probability density associated with a continuous-time random walk in three dimensions that may be killed at a fixed lattice site. To demonstrate how separating the solution approximation from quadrature approximation may improve computational performance, we also compare our new method to several existing Gregory, Sinc, and global spectral methods, where quadrature approximation and solution approximation are coupled.     

Numerical simulation of pollutant dispersion in street canyons: Geometric and thermal effects

Numerical investigations on pollutant dispersion in street canyons with emission sources located near the ground level are performed in the present work. Pollutant dispersion problems in urban areas are usually studied considering the street canyon model, which consists of long streets laterally confined by buildings. Significant changes can be observed in wind flow patterns and pollutant concentration fields when thermal and geometric effects are considered. Thus, the objective of this study is to investigate numerically the wind flow and pollutant dispersion for the following cases: (a) a two-dimensional street canyon model considering three different aspect ratios and four different wall heating configurations; (b) a flow domain with two immersed buildings arranged in two distinct configurations; (c) a three-dimensional urban area model composed of a building set and street intersections. Expected flow structures were obtained inside the canyon when different aspect ratios and wall heating configurations were considered. Flow phenomena such as separation/reattachment were observed when two-buildings models were analyzed. Finally, three-dimensional flow structures, with some characteristic that are not observed in two-dimensional models, affecting the pollutant removal, were simulated in the last case, highlighting the relevance of model dimensionality. The wind flow and pollutant dispersion are investigated using a numerical model based on the finite element formulation utilized by some of the authors of this work, which is extended here to deal with problems of heat and mass transport in the urban micro-scale. Turbulence is reproduced using Large Eddy Simulation (LES) and thermal effects on the momentum equations are considered as a buoyancy force, according to Boussinesq approximation.     

Adaptive Bayesian Nonstationary Modeling for Large Spatial Datasets Using Covariance Approximations

Gaussian process models have been widely used in spatial statistics but face tremendous modeling and computational challenges for very large nonstationary spatial datasets. To address these challenges, we develop a Bayesian modeling approach using a nonstationary covariance function constructed based on adaptively selected partitions. The partitioned nonstationary class allows one to knit together local covariance parameters into a valid global nonstationary covariance for prediction, where the local covariance parameters are allowed to be estimated within each partition to reduce computational cost. To further facilitate the computations in local covariance estimation and global prediction, we use the full-scale covariance approximation (FSA) approach for the Bayesian inference of our model. One of our contributions is to model the partitions stochastically by embedding a modified treed partitioning process into the hierarchical models that leads to automated partitioning and substantial computational benefits. We illustrate the utility of our method with simulation studies and the global Total Ozone Matrix Spectrometer (TOMS) data. Supplementary materials for this article are available online.     

Numerically Stable Methods for the Computation of Exit Rates in Markov Chains

We consider the exit rate from a finite class of transient states of a continuous-time Markov chain and develop numerically stable methods for the computation with bounded from above approximation error of the steady-state exit rate and the time-dependent exit rate. Finally, we develop an also numerically stable method for the computation with bounded from above approximation error of reachable bounds for the time-dependent exit rate which are independent of the initial probability distribution. Applications for the latter include the cyclic analysis of fault-tolerant systems and the analysis of fault-tolerant systems with unobservable up state. The methods compare well from a computational cost point of view with existing alternatives, some with inferior quality regarding error control.     

A nonstandard multigrid method with flexible multiple semicoarsening for the numerical solution of the pressure equation in a Navier-Stokes solver

Numerical methods for the incompressible Reynolds-averaged Navier-Stokes equations discretized by finite difference techniques on collocated cell-centered structured grids are considered in this paper. A widespread solution method to solve the pressure-velocity coupling problem is to use a segregated approach, in which the computational work is deeply controlled by the solution of the pressure problem. This pressure equation is an elliptic partial differential equation with possibly discontinuous or anisotropic coeffficients. The resulting singular linear system needs efficient solution strategies especially for 3-dimensional applications. A robust method (close to MG-S [22,34]) combining multiple cell-centered semicoarsening strategies, matrix-independent transfer operators, Galerkin coarse grid approximation is therefore designed. This strategy is both evaluated as a solver or as a preconditioner for Krylov subspace methods on various 2- or 3-dimensional fluid flow problems. The robustness of this method is shown. This revised version was published online in June 2006 with corrections to the Cover Date.     

Multi-parameter extrapolation methods for boundary integral equations

Multi-parameter extrapolation was first introduced by Zhou et al. for solving partial differential equations with finite element methods in 1994. The method is based on a domain decomposition and independent discretization of the subdomains resulting in a multi-parameter error expansion. This permits a generalized extrapolation technique. The algorithm is naturally parallel since the main computational work is spent in solving independent linear systems. Here the method is extended to the case of boundary integral equations on polygonal domains, where singularities require graded meshes. A complete analysis is given, based on weighted norm techniques. Several numerical experiments demonstrate the mathematical features and practical usefulness of the method. This revised version was published online in June 2006 with corrections to the Cover Date.     

Hierarchical Low Rank Approximation of Likelihoods for Large Spatial Datasets

Datasets in the fields of climate and environment are often very large and irregularly spaced. To model such datasets, the widely used Gaussian process models in spatial statistics face tremendous challenges due to the prohibitive computational burden. Various approximation methods have been introduced to reduce the computational cost. However, most of them rely on unrealistic assumptions for the underlying process and retaining statistical efficiency remains an issue. We develop a new approximation scheme for maximum likelihood estimation. We show how the composite likelihood method can be adapted to provide different types of hierarchical low rank approximations that are both computationally and statistically efficient. The improvement of the proposed method is explored theoretically; the performance is investigated by numerical and simulation studies; and the practicality is illustrated through applying our methods to two million measurements of soil moisture in the area of the Mississippi River basin, which facilitates a better understanding of the climate variability. Supplementary material for this article is available online.     

Multi-scale B-spline method for 2-D elastic problems

In this paper, quadratic B-spline functions are used for solution of 2-D elastic problems. Because B-spline functions are directly used as basis function, there is no need to use meshes and nodes in function approximation. In order to improve the computational efficiency, different scales are used for sub-domains of entire problem domain in function approximation. The modified variational form and Lagrange multipliers method are used for coupling of different scale in function approximation. Compared with meshless methods and other wavelet based methods, this multi-scale B-spline-based method is simple and easy to work with for numerical analysis. Furthermore, the computational efficiency of the multi-scale method is much higher than that of single scale approach. The numerical examples of 2-D elastic problems indicate that the present method is effective and stable for solving complicated problems.