TY - BOOK ID - 8210630 TI - Reduced Basis Methods for Partial Differential Equations : An Introduction AU - Quarteroni, Alfio. AU - Manzoni, Andrea. AU - Negri, Federico. PY - 2016 SN - 3319154303 3319154311 PB - Cham : Springer International Publishing : Imprint: Springer, DB - UniCat KW - Differential equations, Partial KW - Calculus KW - Mathematics KW - Physical Sciences & Mathematics KW - Partial differential equations KW - Differential equations, partial. KW - Engineering mathematics. KW - Hydraulic engineering. KW - Partial Differential Equations. KW - Mathematical Modeling and Industrial Mathematics. KW - Mathematical and Computational Engineering. KW - Engineering Fluid Dynamics. KW - Engineering, Hydraulic KW - Engineering KW - Fluid mechanics KW - Hydraulics KW - Shore protection KW - Engineering analysis KW - Mathematical analysis KW - Partial differential equations. KW - Mathematical models. KW - Applied mathematics. KW - Fluid mechanics. KW - Hydromechanics KW - Continuum mechanics KW - Models, Mathematical KW - Simulation methods KW - Differential equations, Partial. UR - https://www.unicat.be/uniCat?func=search&query=sysid:8210630 AB - This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis. The whole mathematical presentation is made more stimulating by the use of representative examples of applicative interest in the context of both linear and nonlinear PDEs. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The book will be ideal for upper undergraduate students and, more generally, people interested in scientific computing. ER -