Greedy sampling of distributed parameters in the reduced-basis method by numerical optimization

In the present paper the authors study second-order elliptic parametric partial differential equations (μPDEs), where the parameters are scalars or distributed functions. By utilizing a modified greedy algorithm a reduced-basis approximation is derived. This new strategy combines the classical greedy algorithm with techniques from PDE constrained optimization. Numerical examples for the Graetz problem illustrate the efficiency of the strategy to handle not only scalar, but also distributed parameter functions.

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