From bb309331092d96590dbde2e3b3df7a549f3f9b39 Mon Sep 17 00:00:00 2001 From: Jan Petykiewicz Date: Sat, 4 Jan 2020 18:19:49 -0800 Subject: [PATCH] more explanation about grid figures --- meanas/fdmath/__init__.py | 15 ++++++++++++--- 1 file changed, 12 insertions(+), 3 deletions(-) diff --git a/meanas/fdmath/__init__.py b/meanas/fdmath/__init__.py index 2c29c6b..16030e4 100644 --- a/meanas/fdmath/__init__.py +++ b/meanas/fdmath/__init__.py @@ -435,9 +435,15 @@ The result looks something like this: have been omitted to make the insides of the cubes easier to visualize. -This figure shows where all the components are located; however, it is also useful to show -what volumes those components are responsible for representing. Consider the Ex component: -two of its nearest neighbors are E fore-vectors, labeled `[E]` in the figure. +The above figure shows where all the components are located; however, it is also useful to show +what volumes those components correspond to. Consider the Ex component at `m = +1/2`: it is +shifted in the x-direction by a half-cell from the E fore-vector at `m = 0` (labeled `[E]` +in the figure). It corresponds to a volume between `m = 0` and `m = +1` (the other +dimensions are not shifted, i.e. they are still bounded by `n, p = +-1/2`). (See figure +below). Since `m` is an index and not an x-coordinate, the Ex component is not necessarily +at the center of the volume it represents, and the x-length of its volume is the derived +quantity `dx'[0] = (dx[0] + dx[1]) / 2` rather than the base `dx`. +(See also `Scalar derivatives and cell shifts`). [figure: Ex volumes] p= @@ -482,6 +488,9 @@ two of its nearest neighbors are E fore-vectors, labeled `[E]` in the figure. uniform cell sizes result in off-center volumes like the center cell here. +The next figure shows the volumes corresponding to the Hy components, which +are shifted in two dimensions (x and z) compared to the base grid. + [figure: Hy volumes] p= z y mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm __ +1/2 s