Abstract
Reduced basis methods are particularly attractive to use in order to diminish the number of degrees of freedom associated with the approximation of a set of partial differential equations. The main idea is to construct ad hoc basis functions with a large information content. In this note, we propose to develop and analyze reduced basis methods for simulating hierarchical flow systems, which is of relevance for studying flows in a network of pipes, an example being a set of arteries or veins. We propose to decompose the geometry into generic parts (e.g., pipes and bifurcations), and to contruct a reduced basis for these generic parts by considering representative geometric snapshots. The global system is constructed by gluing the individual basis solutions together via Lagrange multipliers.
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Maday, Y., Rønquist, E.M. A Reduced-Basis Element Method. Journal of Scientific Computing 17, 447–459 (2002). https://doi.org/10.1023/A:1015197908587
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DOI: https://doi.org/10.1023/A:1015197908587