diff --git a/experiments/LOG_DENSITY_ASSESSMENT_2026-09-19.md b/experiments/LOG_DENSITY_ASSESSMENT_2026-09-19.md index 3b46d91..0ca9ad4 100644 --- a/experiments/LOG_DENSITY_ASSESSMENT_2026-09-19.md +++ b/experiments/LOG_DENSITY_ASSESSMENT_2026-09-19.md @@ -311,6 +311,19 @@ convergence result, speedup, or virial improvement is claimed. ## Primary-source context +The analogy to 1D stellar codes is supported by MESA's current +[`star_utils.f90`](https://github.com/MESAHub/mesa/blob/main/star/private/star_utils.f90): +`get_rho_and_lnd_from_xh` reconstructs a zone's density with `exp(lnd)`, while +`store_rho_in_xh` stores `log(rho)`. Its documented +[`T(tau)` atmosphere treatment](https://docs.mesastar.org/en/latest/atm/t-tau.html) +sets surface pressure and temperature at a selected optical depth. An ordinary +atmosphere match with positive gas pressure therefore avoids requiring +`log(0)` at an exact vacuum interface; this is the relevant inference for our +boundary choice, not a claim about every MESA mode. These zonewise logarithmic +variables support investigating independent log density, but do not establish +positivity between nodes of our high-order FEM reconstruction or resolve its +exact zero-density free surface. + Vijaywargiya and Fu, *Two Finite Element Approaches for the Porous Medium Equation That Are Positivity Preserving and Energy Stable* (2024), formulate a pointwise exponential log-density method and explicitly discuss the infinite