20140429
In this presentation we will address different aspects concerning Reduced Basis (RB) methods for parametric partial differential equations (PDEs). This class of model reduction techniques enables rapid solution of parametric problems in the realtime or manyquery context and has gained quite some interest and wide development over the last decade After presenting the fundamentals for stationary elliptic problems (affine parametric assumption, offlineonline decomposition, greedy sampling, rigorous certification by efficient aposteriori error bounds), we will put an emphasis on basis generation, including also instationary problems (Greedy and PODGreedy procedures). Despite their samplingbased nature, these methods can be proven to be quasioptimal in a rigorous approximation theoretic sense. For complex problems, also adaptive extensions can be devised. Some sample applications include nonlinear transport problems, multiscale settings or parameter optimization scenarios.
Category: CE SeminarTechnische Universität Darmstadt
Graduate School CE
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D64293 Darmstadt

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