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Novel geometric parameterization scheme for the certified reduced basis analysis of a square unit cell. (English) Zbl 1501.65121

This research devised a new geometric parameterization scheme to rapidly yet accurately analyze a square unit cell model with respect to fiber radius changes. The proposed technique may result in a parameterized weak form that inherently admits affine parametric dependence, thereby supporting the a posteriori error analysis of a reduced basis (RB) solution. For rapid yet rigorous a posteriori error evaluation, the authors estimate a lower bound of a coercivity constant via the min-\(\theta\) method as well as the successive constraint method. Compared to the corresponding finite element analysis, the constructed reduced basis analysis may yield nearly the same solution at a computational speed about 29 times faster on average.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
49M41 PDE constrained optimization (numerical aspects)

Software:

DOLFIN; FEniCS
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Full Text: DOI

References:

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