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In Section 3, we form orthonormal POD bases of a set of the snapshots by means of the POD method and establish the POD-based reduced-order TSCFE extrapolation iterative format including very few degrees of freedom but holding sufficiently high accuracy for the 2D heat equations.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com