Linear gradient structures and discrete gradient methods for conservative/dissipative differential-algebraic equations
Sign Up to like & getrecommendations! Published in 2019 at "BIT Numerical Mathematics"
DOI: 10.1007/s10543-019-00759-2
Abstract: In this paper, the use of discrete gradients is considered for differential-algebraic equations (DAEs) with a conservation/dissipation law. As one of the most popular numerical methods for conservative/dissipative ordinary differential equations, the framework of the… read more here.
Keywords: differential algebraic; methods conservative; conservative dissipative; linear gradient ... See more keywords
Relative-perfectness of discrete gradient vector fields and multi-parameter persistent homology
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DOI: 10.1007/s10878-021-00729-x
Abstract: The combination of persistent homology and discrete Morse theory has proven very effective in visualizing and analyzing big and heterogeneous data. Indeed, topology provides computable and coarse summaries of data independently from specific coordinate systems… read more here.
Keywords: gradient vector; perfectness; discrete gradient; homology ... See more keywords
Allowing cycles in discrete Morse theory
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DOI: 10.1016/j.topol.2017.05.008
Abstract: Discrete gradient vector fields are combinatorial structures that can be used for accelerating the homology computation of CW complexes, such as simplicial or cubical complexes, by reducing their number of cells. Consequently, they provide a… read more here.
Keywords: vector; gradient vector; allowing cycles; vector field ... See more keywords