fasshauer meshfree approximation methods with matlab

Meshless methods are becoming popular, principally due to their abilities to deal with complex geometrical problems with inhomogeneous or variable properties, the use of general-purpose algorithms, and the lack of a mesh requirement. Localized mesh adaptation has been shown to help alleviate global meshing requirements and improve accuracy ( Pepper and Wang 2009). Extracting realistic estimates of 3D wind from sparse meteorological data requires the use of numerical modeling-typically employing procedures based on extensive numerical meshing involving finite-difference, finite-volume, and finite-element methods (FDM, FVM, and FEM, respectively). Unfortunately, the lack of adequate meteorological data makes this particularly difficult. Used as class notes for graduate courses at Northwestern University, Illinois Institute of Technology, and Vanderbilt University, this book will appeal to both mathematics and engineering graduate students.An accurate depiction of 3D wind fields, especially in complex terrain, is crucial when conducting atmospheric studies. A good balance is supplied between the necessary theory and implementation in terms of many MATLAB programs, with examples and applications to illustrate key points. Meshfree approximation methods, such as radial basis function and moving least squares method, are discussed from a scattered data approximation and partial differential equations point of view. Whereas other works focus almost entirely on theoretical aspects or applications in the engineering field, this book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods.The emphasis here is on a hands-on approach that includes MATLAB routines for all basic operations.

Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present.

Fasshauer meshfree approximation methods with matlab