Improved C1 shape functions for simplex meshes

Barnes, Daniel C.

doi:10.1016/j.jcp.2020.109852

Improved C¹ shape functions for simplex meshes

Journal Article · Tue Sep 29 00:00:00 EDT 2020 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2020.109852· OSTI ID:1670766

Barnes, Daniel C. ^[1]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Using continuously-differentiable (C¹) interpolation methods previously developed for computer visualization and other applications, a new class of shape functions is constructed and applied to electrostatic (ES) Particle-In-Cell (PIC) simulations on simplex (triangle or tetrahedral) meshes. The resulting shape functions are non-negative and partition unity,and lead to a reduction of shot noise and aliasing associated with particle interpolation to and from the mesh. For an energy-conserving implementation as chosen, C¹ interpolation of the potential leads to a continuous (C⁰) electric field, with associated improved fidelity of particle motion.

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000; NA0003525

OSTI ID:: 1670766

Alternate ID(s):: OSTI ID: 1810901

Report Number(s):: SAND2020--10391J; 690982

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 424; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Whitney Forms of Higher Degree Rapetti, Francesca; Bossavit, Alain SIAM Journal on Numerical Analysis, Vol. 47, Issue 3 https://doi.org/10.1137/070705489	journal	January 2009

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Improved C1 shape functions for simplex meshes

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Improved C¹ shape functions for simplex meshes