Gradient Smoothing Methods with Programming

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【簡介】 This unique compendium presents the Gradient Smoothing Methods (GSMs), as a general solver for linear and nonlinear PDEs (Partial Differential Equations) with a focus on fluids and flowing solids. The volume introduces the basic concepts and theories of the gradient smoothing technique used in the GSMs. Formulations for both Eulerian-GSM and Lagrangian-GSM are presented. The key ingredients of GSMs and its effectiveness in solving challenging fluid/solid flow problems with complex geometries are then discussed. Applications of GSM are highlighted, including compressible and incompressible flows, hydrodynamics with flexible free surface, and flowing solids with material strength and large deformation in geotechnical engineering, in particular, landslide simulations. In-house MATLAB codes are provided for both Eulerian and Lagrangian GSMs, along with detailed descriptions. More efficient FORTRAN source codes for solving complex engineering problems are also available on Github. 【目錄】 About the Authors Introduction Theory for Gradient Smoothing Methods Eulerian GSM for Solving Poisson Equation Eulerian GSM for Compressible Flows Eulerian GSM for Incompressible Flows Theory and Formulation for Lagrangian GSM L-GSM for Incompressible Hydrodynamics L-GSM for Granular Flows in Geotechnical Engineering Programming with GSMs and Source Codes Index

SMOOTHING AND REGRESSION

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A comprehensive introduction to a wide variety of univariate and multivariate smoothing techniques for regression Smoothing and Regression: Approaches, Computation, and Application bridges the many gaps that exist among competing univariate and multivariate smoothing techniques. It introduces, describes, and in some cases compares a large number of the latest and most advanced techniques for regression modeling. Unlike many other volumes on this topic, which are highly technical and specialized, this book discusses all methods in light of both computational efficiency and their applicability for real data analysis. Using examples of applications from the biosciences, environmental sciences, engineering, and economics, as well as medical research and marketing, this volume addresses the theory, computation, and application of each approach. A number of the techniques discussed, such as smoothing under shape restrictions or of dependent data, are presented for the first time in book form. Special features of this book include: * Comprehensive coverage of smoothing and regression with software hints and applications from a wide variety of disciplines * A unified, easy-to-follow format * Contributions from more than 25 leading researchers from around the world * More than 150 illustrations also covering new graphical techniques important for exploratory data analysis and visualization of high-dimensional problems * Extensive end-of-chapter references For professionals and aspiring professionals in statistics, applied mathematics, computer science, and econometrics, as well as for researchers in the applied and social sciences, Smoothing and Regression is a unique and important new resource destined to become one the most frequently consulted references in the field.