A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Systematic implementation of higher order Whitney forms in methods based on discrete exterior calculus (2022)

Lohi, J. (2022). Systematic implementation of higher order Whitney forms in methods based on discrete exterior calculus. Numerical Algorithms, 91(3), 1261-1285. https://doi.org/10.1007/s11075-022-01301-2

JYU-tekijät tai -toimittajat

Julkaisun tiedot

Julkaisun kaikki tekijät tai toimittajat: Lohi, Jonni

Lehti tai sarja: Numerical Algorithms

ISSN: 1017-1398

eISSN: 1572-9265

Julkaisuvuosi: 2022

Ilmestymispäivä: 18.04.2022

Volyymi: 91

Lehden numero: 3

Artikkelin sivunumerot: 1261-1285

Kustantaja: Springer

Julkaisumaa: Yhdysvallat (USA)

Julkaisun kieli: englanti

DOI: https://doi.org/10.1007/s11075-022-01301-2

Julkaisun avoin saatavuus: Avoimesti saatavilla

Julkaisukanavan avoin saatavuus: Osittain avoin julkaisukanava

Julkaisu on rinnakkaistallennettu (JYX): https://jyx.jyu.fi/handle/123456789/80716

Tiivistelmä

We present a systematic way to implement higher order Whitney forms in numerical methods based on discrete exterior calculus. Given a simplicial mesh, we first refine the mesh into smaller simplices which can be used to define higher order Whitney forms. Cochains on this refined mesh can then be interpolated using higher order Whitney forms. Hence, when the refined mesh is used with methods based on discrete exterior calculus, the solution can be expressed as a higher order Whitney form. We present algorithms for the three required steps: refining the mesh, solving the coefficients of the interpolant, and evaluating the interpolant at a given point. With our algorithms, the order of the Whitney forms one wishes to use can be given as a parameter so that the same code covers all orders, which is a significant improvement on previous implementations. Our algorithms are applicable with all methods in which the degrees of freedom are integrals over mesh simplices — that is, when the solution is a cochain on a simplicial mesh. They can also be used when one simply wishes to approximate differential forms in finite-dimensional spaces. Numerical examples validate the generality of our algorithms.

YSO-asiasanat: osittaisdifferentiaaliyhtälöt; numeeriset menetelmät; interpolointi; differentiaalilaskenta; diskreetti matematiikka

Vapaat asiasanat: higher order Whitney forms; cochains; differential forms; interpolation; discrete exterior calculus; simplicial mesh

Liittyvät organisaatiot

OKM-raportointi: Kyllä

Raportointivuosi: 2022

JUFO-taso: 2