Rapid Reliable Solution
of the Parametrized Partial Differential Equations
of Continuum Mechanics and Transport

Webserver Version

The Heterogeneous Thermal Block Problem
Authors: G Rozza and AT Patera


Evaluation and Visualization Module

The user should first input the parameter μ = [μ1, μ2, μ3, μ4, μ5, μ6, μ7, μ8, μ9] such that μ in [0.1, 10] × [0.1, 10] × [0.1, 10] × [0.1, 10] × [0.1, 10] × [0.1, 10] × [0.1, 10] × [0.1, 10] × [0.1, 10]. The user should also input a numerical parameter that relates to the desired accuracy of the RB output prediction Npr in [1, 53], Ndu in [1, 54]: the error in our prediction decreases as N increases.

The code then displays, for the desired parameter value μ = [μ1, μ2, μ3, μ4, μ5, μ6, μ7, μ8, μ9], (i) the contour of the field and (ii) the value of the output/quantity of interest. In each case, we also provide a certificate of fidelity that rigorously bounds the error in our RB prediction relative to the highly accurate (and hence very expensive) "truth'' Finite Element solution.

μ1 in [0.1, 10]:

μ2 in [0.1, 10]:

μ3 in [0.1, 10]:

μ4 in [0.1, 10]:

μ5 in [0.1, 10]:

μ6 in [0.1, 10]:

μ7 in [0.1, 10]:

μ8 in [0.1, 10]:

μ9 in [0.1, 10]:

Npr in [1, 53]:

Ndu in [1, 54]:

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