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Numerical Modelling of Random Processes and Fields
Computer-aided modelling is one of the most effective means of getting to the root of a natural phenomenon and of predicting the consequences of human impact on the environment. General methods of numerical modelling of random processes have been effectively developed and the area of applications has rapidly expanded in recent years. This book deals with the development and investigation of numerical methods for simulation of random processes and fields. The book opens with a description of scalar and vector-valued Gaussian models, followed by non-Gaussian models. Furthermore, issues of convergence of approximate models of random fields are studied. The last part of this book is devoted to applications of stochastic modelling, in which new application areas such as simulation of meteorological processes and fields, sea surface undulation, and stochastic structure of clouds, are presented.
Spectral Models of Random Fields in Monte Carlo Methods
Spectral models were developed in the 1970s and have appeared to be very promising for various applications. Nowadays, spectral models are extensively used for stochastic simulation in atmosphere and ocean optics, turbulence theory, analysis of pollution transport for porous media, astrophysics, and other fields of science. The spectral models presented in this monograph represent a new class of numerical methods aimed at simulation of random processes and fields. The book is divided into four chapters, which deal with scalar spectral models and some of their applications, vector-valued spectral models, convergence of spectral models, and problems of optimisation and convergence for functional Monte Carlo methods. Furthermore, the monograph includes four appendices, in which auxiliary information is presented and additional problems are discussed. The book will be of value and interest to experts in Monte Carlo methods, as well as to those interested in the theory and applications of stochastic simulation.
Large-Scale Scientific Computing
This book constitutes the thoroughly refereed post-proceedings of the Third International Conference on Large-Scale Scientific Computing, LSSC 2001, held in Sozopol, Bulgaria, in June 2001. The 7 invited full papers and 45 selected revised papers were carefully reviewed for inclusion in the book. The papers are organized in topical sections on robust preconditioning algorithms, Monte-Carlo methods, advanced programming environments for scientific computing, large-scale computations in air pollution modeling, large-scale computations in mechanical engineering, and numerical methods for incompressible flow.
Light Scattering Reviews 4
This fourth volume of Light Scattering Reviews is composed of three parts. The ?rstpartisconcernedwiththeoreticalandexperimentalstudiesofsinglelightsc- tering by small nonspherical particles. Light scattering by small particles such as, for instance, droplets in the terrestrial clouds is a well understood area of physical optics. On the other hand, exact theoretical calculations of light scattering p- terns for most of nonspherical and irregularly shaped particles can be performed only for the restricted values of the size parameter, which is proportional to the ratio of the characteristic size of the particle to the wavelength?. For the large nonspherical particles, approximations are used ...
Algorithms for Approximation
Approximation methods are vital in many challenging applications of computational science and engineering. This is a collection of papers from world experts in a broad variety of relevant applications, including pattern recognition, machine learning, multiscale modelling of fluid flow, metrology, geometric modelling, tomography, signal and image processing. It documents recent theoretical developments which have lead to new trends in approximation, it gives important computational aspects and multidisciplinary applications, thus making it a perfect fit for graduate students and researchers in science and engineering who wish to understand and develop numerical algorithms for the solution of their specific problems. An important feature of the book is that it brings together modern methods from statistics, mathematical modelling and numerical simulation for the solution of relevant problems, with a wide range of inherent scales. Contributions of industrial mathematicians, including representatives from Microsoft and Schlumberger, foster the transfer of the latest approximation methods to real-world applications.
Numerical Solution of Stochastic Differential Equations
The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP
Computational Methods in Transport: Verification and Validation
The focus of this book deals with a cross cutting issue affecting all transport disciplines, whether it be photon, neutron, charged particle or neutrino transport. That is, verification and validation. In this book, we learn what the astrophysicist, atmospheric scientist, mathematician or nuclear engineer do to assess the accuracy of their code. What convergence studies, what error analysis, what problems do each field use to ascertain the accuracy of their transport simulations.
Applied Mathematics and Computational Mechanics for Smart Applications
This book presents best selected research papers presented at the Thirteenth International Conference on Applied Mathematics and Mechanics in the Aerospace Industry (AMMAI 2020), held from September 6 to September 13, 2020, at the Alushta Health and Educational Center (The Republic of Crimea). The book is dedicated to solving actual problems of applied mechanics using modern computer technology including smart paradigms. Physical and mathematical models, numerical methods, computational algorithms, and software complexes are discussed, which allow to carry out high-precision mathematical modeling in fluid, gas, and plasma mechanics, in general mechanics, deformable solid mechanics, in strength, destruction and safety of structures, etc. Technologies and software systems that provide effective solutions to the problems at various multi-scale levels are considered. Special attention is paid to the training of highly qualified specialists for the aviation and space industry. The book is recommended for specialists in the field of applied mathematics and mechanics, mathematical modeling, information technologies, and developers of modern applied software systems.
