Serendipity discrete complexes with enhanced regularity
Daniele Di Pietro, Marien Hanot, Marwa Salah
TL;DR
This paper introduces a novel abstract construction to develop serendipity variants of discrete de Rham complexes with improved regularity, enabling new mathematical tools for computational applications.
Contribution
It presents a new general framework for creating serendipity complexes from existing ones, specifically applied to rot-rot and Stokes complexes in the discrete de Rham context.
Findings
New abstract construction for complexes with isomorphic cohomology
Development of serendipity versions of rot-rot and Stokes complexes
Enhanced regularity in discrete de Rham complexes
Abstract
In this work we address the problem of finding serendipity versions of approximate de Rham complexes with enhanced regularity. The starting point is a new abstract construction of general scope which, given three complexes linked by extension and reduction maps, generates a fourth complex with cohomology isomorphic to the former three. This construction is used to devise new serendipity versions of rot-rot and Stokes complexes derived in the Discrete de Rham spirit.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Medical Imaging Techniques and Applications · Computational Drug Discovery Methods