{"product_id":"9789814578479","title":"Dirichlet??????Dirichlet Domain Decomposition Methods for Elliptic Problems: h and hp Finite Element Discretizations","description":"Domain decomposition (DD) methods provide powerful tools for constructing parallel numerical solution algorithms for large scale systems of algebraic equations arising from the discretization of partial differential equations. These methods are well-established and belong to a fast developing area. In this volume, the reader will find a brief historical overview, the basic results of the general theory of domain and space decomposition methods as well as the description and analysis of practical DD algorithms for parallel computing. It is typical to find in this volume that most of the presented DD solvers belong to the family of fast algorithms, where each component is efficient with respect to the arithmetical work. Readers will discover new analysis results for both the well-known basic DD solvers and some DD methods recently devised by the authors, e.g., for elliptic problems with varying chaotically piecewise constant orthotropism without restrictions on the finite aspect ratios.  The hp finite element discretizations, in particular, by spectral elements of elliptic equations are given significant attention in current research and applications. This volume is the first to feature all components of Dirichlet–Dirichlet-type DD solvers for hp discretizations devised as numerical procedures which result in DD solvers that are almost optimal with respect to the computational work. The most important DD solvers are presented in the matrix\/vector form algorithms that are convenient for practical use.\u003cstrong\u003eContents:\u003c\/strong\u003e  \u003cul\u003e \u003cli\u003eIntroduction\u003c\/li\u003e \u003cli\u003eFundamentals of the Schwarz Methods\u003c\/li\u003e \u003cli\u003eOverlapping Domain Decomposition Methods\u003c\/li\u003e \u003cli\u003eNonoverlapping DD Methods for \u003ci\u003eh\u003c\/i\u003e FE Discretizations in 2d\u003c\/li\u003e \u003cli\u003eBPS-type DD Preconditioners for 3d Elliptic Problems\u003c\/li\u003e \u003cli\u003eDD Algorithms for Discretizations with Chaotically Piecewise Variable Orthotropism\u003c\/li\u003e \u003cli\u003eNonoverlapping DD Methods for \u003ci\u003ehp\u003c\/i\u003e Discretizations of 2d Elliptic Equations\u003c\/li\u003e \u003cli\u003eFast Dirichlet Solvers for 2d Reference Elements\u003c\/li\u003e \u003cli\u003eNonoverlapping Dirichlet–Dirichlet Methods for \u003ci\u003ehp\u003c\/i\u003e Discretizations of 3d Elliptic Equations\u003c\/li\u003e \u003c\/ul\u003e \u003cbr\u003e\u003cstrong\u003eReadership:\u003c\/strong\u003e Graduate students and researchers in academia, laboratories and research institutions, and industry.\u003cb\u003eKey Features:\u003c\/b\u003e  \u003cul\u003e \u003cli\u003eOptimal in computational work and robust domain decomposition (DD) solvers for h- and hp-finite element equations\u003c\/li\u003e \u003cli\u003eUnique treatment of DD algorithms for hp spectral discretizations\u003c\/li\u003e \u003cli\u003eIncludes analysis and algorithmic descriptions of DD methods\u003c\/li\u003e \u003cli\u003eWritten by famous experts in finite element methods and numerical analysis\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"World Scientific Publishing Company, Incorporated","offers":[{"title":"Default Title","offer_id":47144683372784,"sku":"9789814578479","price":102.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9789814578479_p0.jpg?v=1763691122","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9789814578479","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}