Meshfree Approximation Methods with MATLAB (Paperback)

Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present. 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, such as radial basis function and moving least squares method, are discussed from a scattered data approximation and partial differential equations point of view. 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. 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.

無網格逼近方法是一個相對新的研究領域，目前只有少數幾本書籍涵蓋此主題。其他作品主要集中在理論方面或在工程領域的應用，而本書提供了理解無網格逼近方法所需的重要理論結果。本書強調實踐方法，並提供了所有基本操作的MATLAB程式。從散點數據逼近和偏微分方程的角度討論了無網格逼近方法，如基於半徑的函數和移動最小二乘法。在MATLAB程序、示例和應用方面，提供了理論和實現之間的良好平衡。本書被用作西北大學、伊利諾伊理工學院和范德堡大學研究生課程的課堂筆記，適合數學和工程研究生閱讀。