EAN: 9783319154305

REDUCED BASIS METHODS FOR PARTIAL DIFFERENTIAL ...

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. All these pseudocodes
are in fact implemented in a MATLAB package that is freely available at https:  github.com
redbkit

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