Solving Vertical Transport and Chemistry in Air Pollution Models.

For the time integration of stiff transport-chemistry problems from air pollution modelling, standard ODE solvers are not feasible due to the large number of species and the 3D nature. The popular alternative, standard operator splitting, introduces artificial transients for short-lived species. This complicates the chemistry solution, easily causing large errors for such species. In the framework of an operational global air pollution model, we focus on the problem formed by chemistry and vertical transport, which is based on diffusion, cloud-related vertical winds, and wet deposition. Its specific nature leads to full Jacobian matrices, ruling out standard implicit integration. We compare Strang operator splitting with two alternatives: source splitting and an (unsplit) Rosenbrock method with approximate matrix factorization, all having equal computational cost. The comparison is performed with real data. All methods are applied with half-hour time steps, and give good accuracies. Rosenbrock is the most accurate, and source splitting is more accurate than Strang splitting. Splitting errors concentrate in short-lived species sensitive to solar radiation and species with strong emissions and depositions

Simulation of reaction-diffusion processes in three dimensions using CUDA

Numerical solution of reaction-diffusion equations in three dimensions is one of the most challenging applied mathematical problems. Since these simulations are very time consuming, any ideas and strategies aiming at the reduction of CPU time are important topics of research. A general and robust idea is the parallelization of source codes/programs. Recently, the technological development of graphics hardware created a possibility to use desktop video cards to solve numerically intensive problems. We present a powerful parallel computing framework to solve reaction-diffusion equations numerically using the Graphics Processing Units (GPUs) with CUDA. Four different reaction-diffusion problems, (i) diffusion of chemically inert compound, (ii) Turing pattern formation, (iii) phase separation in the wake of a moving diffusion front and (iv) air pollution dispersion were solved, and additionally both the Shared method and the Moving Tiles method were tested. Our results show that parallel implementation achieves typical acceleration values in the order of 5-40 times compared to CPU using a single-threaded implementation on a 2.8 GHz desktop computer.Comment: 8 figures, 5 table

An inverse Gaussian plume approach for estimating atmospheric pollutant emissions from multiple point sources

A method is developed for estimating the emission rates of contaminants into the atmosphere from multiple point sources using measurements of particulate material deposited at ground level. The approach is based on a Gaussian plume type solution for the advection-diffusion equation with ground-level deposition and given emission sources. This solution to the forward problem is incorporated into an inverse algorithm for estimating the emission rates by means of a linear least squares approach. The results are validated using measured deposition and meteorological data from a large lead-zinc smelting operation in Trail, British Columbia. The algorithm is demonstrated to be robust and capable of generating reasonably accurate estimates of total contaminant emissions over the relatively short distances of interest in this study

A new approximate matrix factorization for implicit time integration in air pollution modeling

Implicit time stepping typically requires solution of one or several linear systems with a matrix I−τJ per time step where J is the Jacobian matrix. If solution of these systems is expensive, replacing I−τJ with its approximate matrix factorization (AMF) (I−τR)(I−τV), R+V=J, often leads to a good compromise between stability and accuracy of the time integration on the one hand and its efficiency on the other hand. For example, in air pollution modeling, AMF has been successfully used in the framework of Rosenbrock schemes. The standard AMF gives an approximation to I−τJ with the error τ2RV, which can be significant in norm. In this paper we propose a new AMF. In assumption that −V is an M-matrix, the error of the new AMF can be shown to have an upper bound τ||R||, while still being asymptotically $O(\tau^2)$. This new AMF, called AMF+, is equal in costs to standard AMF and, as both analysis and numerical experiments reveal, provides a better accuracy. We also report on our experience with another, cheaper AMF and with AMF-preconditioned GMRES

A Reconfigurable Vector Instruction Processor for Accelerating a Convection Parametrization Model on FPGAs

High Performance Computing (HPC) platforms allow scientists to model computationally intensive algorithms. HPC clusters increasingly use General-Purpose Graphics Processing Units (GPGPUs) as accelerators; FPGAs provide an attractive alternative to GPGPUs for use as co-processors, but they are still far from being mainstream due to a number of challenges faced when using FPGA-based platforms. Our research aims to make FPGA-based high performance computing more accessible to the scientific community. In this work we present the results of investigating the acceleration of a particular atmospheric model, Flexpart, on FPGAs. We focus on accelerating the most computationally intensive kernel from this model. The key contribution of our work is the architectural exploration we undertook to arrive at a solution that best exploits the parallelism available in the legacy code, and is also convenient to program, so that eventually the compilation of high-level legacy code to our architecture can be fully automated. We present the three different types of architecture, comparing their resource utilization and performance, and propose that an architecture where there are a number of computational cores, each built along the lines of a vector instruction processor, works best in this particular scenario, and is a promising candidate for a generic FPGA-based platform for scientific computation. We also present the results of experiments done with various configuration parameters of the proposed architecture, to show its utility in adapting to a range of scientific applications.Comment: This is an extended pre-print version of work that was presented at the international symposium on Highly Efficient Accelerators and Reconfigurable Technologies (HEART2014), Sendai, Japan, June 911, 201

PARALLEL COMPUTATIONS WITH LARGE-SCALE AIR\ud POLLUTION MODELS

Large-scale mathematical models are very powerful tools in the efforts to provide more\ud information and more detailed information about the pollution levels, especially about pollution\ud levels which exceed certain critical values.. However, the model used must satisfy at\ud least two conditions: (i) it must be verified that the model results are reliable and (ii) it\ud should be possible to carry out different study by using the model. It is clear that comprehensive\ud studies about relationships between different input parameters and the model results\ud can only be carried out (a) if the numerical methods used in the model are sufficiently\ud fast and (b) if the code runs efficiently on the available high-speed computers.\ud Some results obtained recently by a new unified version of the Danish Eulerian Model will\ud be presented in this paper

Coupling traffic models on networks and urban dispersion models for simulating sustainable mobility strategies

AbstractThe aim of the present paper is to investigate the viability of macroscopic traffic models for modeling and testing different traffic scenarios, in order to define the impact on air quality of different strategies for the reduction of traffic emissions. To this aim, we complement a well assessed traffic model on networks (Garavello and Piccoli (2006) [1]) with a strategy for estimating data needed from the model and we couple it with the urban dispersion model Sirane (Soulhac (2000) [2])

Fast stable direct fitting and smoothness selection for Generalized Additive Models

Existing computationally efficient methods for penalized likelihood GAM fitting employ iterative smoothness selection on working linear models (or working mixed models). Such schemes fail to converge for a non-negligible proportion of models, with failure being particularly frequent in the presence of concurvity. If smoothness selection is performed by optimizing `whole model' criteria these problems disappear, but until now attempts to do this have employed finite difference based optimization schemes which are computationally inefficient, and can suffer from false convergence. This paper develops the first computationally efficient method for direct GAM smoothness selection. It is highly stable, but by careful structuring achieves a computational efficiency that leads, in simulations, to lower mean computation times than the schemes based on working-model smoothness selection. The method also offers a reliable way of fitting generalized additive mixed models