{"product_id":"elliptic-marching-methods-and-domain-decomposition-5-symbolic-numeric-computation-9780849373787","title":"Elliptic Marching Methods and Domain","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eOne of the first things a student of partial differential equations learns is that it is impossible to solve elliptic equations by spatial marching. This new book describes how to do exactly that, providing a powerful tool for solving problems in fluid dynamics, heat transfer, electrostatics, and other fields characterized by discretized partial differential equations. \u003cbr\u003eElliptic Marching Methods and Domain Decomposition demonstrates how to handle numerical instabilities (i.e., limitations on the size of the problem) that appear when one tries to solve these discretized equations with marching methods. The book also shows how marching methods can be superior to multigrid and pre-conditioned conjugate gradient (PCG) methods, particularly when used in the context of multiprocessor parallel computers. Techniques for using domain decomposition together with marching methods are detailed, clearly illustrating the benefits of these techniques for applications in engineering, applied mathem\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"Together with an important historical perspective, this book uses the domain decomposition connection to develop and explore the nature of marching methods. Interesting analytical and anecdotal comparisons are made with direct methods and multigrid techniques, told by a scientist who has obviously has much experience with real practical problems.\"\u003cbr\u003e-Mathematical Reviews, 99a\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eBasic Marching Methods for 2D Elliptic Problems\u003cbr\u003eHigh-Order Equations\u003cbr\u003eExtending the Mesh Size: Domain Decomposition\u003cbr\u003eBanded Approximations to Influence Matrices\u003cbr\u003eMarching Methods in 3D\u003cbr\u003ePerformance of the 2D GEM Code\u003cbr\u003eVectorization and Parallelization\u003cbr\u003eSemidirect Methods for Nonlinear Equations of Fluid Dynamics\u003cbr\u003eComparison to Multigrid Methods\u003cbr\u003eAppendix A - Marching Schemes and Error Propagation for Various Discrete Laplacians\u003cbr\u003eAppendix B - Tridiagonal Algorithm for Periodic Boundary Conditions\u003cbr\u003eAppendix C - Gauss Elimination as a Direct Solver\u003cbr\u003eSubject Index\u003cbr\u003e\u003cbr\u003eTOC for NTI\/Flyer\u003c\/p\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":49406229807447,"sku":"9780849373787","price":194.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780849373787.jpg?v=1730495012","url":"https:\/\/bookcurl.com\/products\/elliptic-marching-methods-and-domain-decomposition-5-symbolic-numeric-computation-9780849373787","provider":"Book Curl","version":"1.0","type":"link"}