Reduced basis method for the rapid and reliable solution of partial differential equationsReport as inadecuate




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1 LJLL - Laboratoire Jacques-Louis Lions

Abstract : Numerical approximation of the solution of partial differential equations plays an important role in many areas such as engineering, mechanics,physics,chemistry, biology

. for computer-aided design-analysis, computer-aided decision-making or simply better understanding. The fidelity of the simulations with respect to reality is achieved through the combined efforts to derive: i better models, ii faster numerical algorithm, iii more accurate discretization methods and iv improved large scale computing resources. In many situations, including optimization and control, the same model, depending on a parameter that is changing, has to be simulated over and over,multiplying by a large factor up to 100 or 1000 the solution procedure cost of one simulation. The reduced basis method allows to define a surrogate solution procedure, that,thanks to the complementary design of fidelity certificates on outputs, allows to speed up the computations by two to three orders of magnitude while maintaining a sufficient accuracy. We present here the basics of this approach for linear and non linear elliptic and parabolic PDE-s.





Author: Yvon Maday -

Source: https://hal.archives-ouvertes.fr/



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