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

Webserver Version

A Transient Heat Treatment Problem
Forward Problem

Authors: G Rozza & AT Patera
in collaboration with DBP Huynh & NC Nguyen


Evaluation and Visualization Module

The user should first input the parameter μ = [μ1, μ2] such that μ in [0.01, 10] × [0.02, 0.2] and the timestep nk in [1, 150]. The user should also input a numerical parameter that relates to the desired accuracy of the RB output prediction Npr in [1, 28], Ndu in [1, 7]: the error in our prediction decreases as N increases. In addition, the user may need to input the control inputs, g(t) and h(t), as particular functions of time t.

The code then displays, for the desired parameter value μ = [μ1, μ2], (i) the variation of the field as a function of time, 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 [0.01, 10]:

μ2 in [0.02, 0.2]:

nk in [1, 150]:

Npr in [1, 28]:

Ndu in [1, 7]:

g(t) :

h(t) :

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