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arXiv · 2505.00286

A polytopal discrete de Rham scheme for the exterior calculus Einstein's equations

Todd A. Oliynyk·Jia Jia Qian
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Abstract

In this work, based on the $3+1$ decomposition in [24, 33], we present a fully exterior calculus breakdown of spacetime and Einstein's equations. Links to the orthonormal frame approach [38] are drawn to help understand the variables in this context. Two formulations are derived, discretised and tested using the exterior calculus discrete de Rham complex [13], and some discrete quantities are shown to be conserved in one of the cases.

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Todd A. Oliynyk, Jia Jia Qian. 2025-05-01. A polytopal discrete de Rham scheme for the exterior calculus Einstein's equations. https://doi.org/10.1103/6t8n-rlld

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