SimiLie

Github repo here.

SimiLie is a performance-portable (CPU & GPU) C++20 library aiming to extent the capabilities of Kokkos and DDC to offer a complete toolkit able to perform tensor calculus, differential calculus and solving PDE. A key paradigm is the exclusive support of structured meshes to avoid sparse linear algebra and produce mostly-embarrassing parallel code. It should be able to address any multiphysical problem on fixed grid from eventually-relativistic classical field theory (in particular: solid & fluid mechanics, electromagnetism and gravitation).

Important

Absolute WIP, there is no guarantee for proper working. Only OPENMP and CUDA backends have been tested.

Development plan

1. Short term: simulate electromagnetism on manifold.
2. Mid term (months): simulate geometrodynamics.
3. Long term: generalize to all kinds of classical gauge theories.
4. Extra-long term (years): quantization.

References

• Desbrun, M., Kanso, E., Tong, Y. (2008). Discrete Differential Forms for Computational Modeling. In: Bobenko, A.I., Sullivan, J.M., Schröder, P., Ziegler, G.M. (eds) Discrete Differential Geometry. Oberwolfach Seminars, vol 38. Birkhäuser Basel.
• Finite element exterior calculus. Douglas N. Arnold. CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM 2018.
• Gravitation. By C.W. Misner, K.S. Thorne and J.A. Wheeler. ISBN 0-7167-0334-3, ISBN 0-7167-0344-0 (pbk). San Francisco: W.H. Freeman and Company, 1973
• Celada, M., González, D., & Montesinos, M. (2016). BF gravity. Classical and Quantum Gravity, 33(21), 213001.
• Group Theory, Birdtracks, Lie’s, and Exceptional Groups, Predrag Cvitanović, Princeton University Press July 2008.