From 297377e60ffee1a65499b25b3819eda29c3f1f43 Mon Sep 17 00:00:00 2001
From: Thomas Gibson <gibsonthomas1120@hotmail.com>
Date: Thu, 3 Jun 2021 14:58:22 -0500
Subject: [PATCH] Update doc refs in timestepping utility functions
---
grudge/dt_utils.py | 17 +++++++++--------
1 file changed, 9 insertions(+), 8 deletions(-)
diff --git a/grudge/dt_utils.py b/grudge/dt_utils.py
index 7efa47a2..cf5e3f08 100644
--- a/grudge/dt_utils.py
+++ b/grudge/dt_utils.py
@@ -46,15 +46,15 @@ from pytools import memoize_on_first_arg, memoize_in
@memoize_on_first_arg
def dt_non_geometric_factor(
dcoll: DiscretizationCollection, scaling=None, dd=None) -> float:
- r"""Computes the non-geometric scale factor:
+ r"""Computes the non-geometric scale factor following [Hesthaven_2008]_,
+ section 6.4:
.. math::
- C\operatorname{min}_i\left( \Delta r_i \right),
+ c_{ng} = \operatorname{min}\left( \Delta r_i \right),
where :math:`\Delta r_i` denotes the distance between two distinct
- nodes on the reference element, and :math:`C > 0` is a scaling
- constant.
+ nodes on the reference element.
:arg scaling: a :class:`float` denoting the scaling factor. By default,
the constant is set to 2/3.
@@ -98,15 +98,16 @@ def dt_non_geometric_factor(
@memoize_on_first_arg
def dt_geometric_factor(dcoll: DiscretizationCollection, dd=None) -> float:
- r"""Computes a geometric scaling factor, defined as the minimum radius of
- an inscribed circle/sphere in a mesh cell.
+ r"""Computes a geometric scaling factor for each cell following [Hesthaven_2008]_,
+ section 6.4, defined as the inradius (radius of an inscribed circle/sphere).
Specifically, the inradius for each element is computed using the following
- formula for simplicial cells (triangles/tetrahedra):
+ formula from [Shewchuk_2002]_, Table 1, for simplicial cells
+ (triangles/tetrahedra):
.. math::
- r_{in} = \frac{d V}{\sum_{i=1}^{N_{faces}} F_i},
+ r_D = \frac{d V}{\sum_{i=1}^{N_{faces}} F_i},
where :math:`d` is the topological dimension, :math:`V` is the cell volume,
and :math:`F_i` are the areas of each face of the cell.
--
GitLab