[aspect-devel] Advice for optimizing particle advection for 2D Spherical Shell Models

[Timo Heister]

>> After, burrowing through the Deal.II documentation, I have found implemented
>> functionality for transforming vectors from unit to real but not the other
>> way around. Is there a black box solution that already exists within Deal.II
>> which converts vectors from real to unit?
>
> Sorry, I do not know one, but there still might be one.

Check out the transform_unit_to_real_cell, etc. functions inside the
mapping: https://urldefense.proofpoint.com/v2/url?u=https-3A__www.dealii.org_8.5.0_doxygen_deal.II_classMapping.html-23ae5df63553eb8ed170c3b90524853dd48&d=DwIBaQ&c=Ngd-ta5yRYsqeUsEDgxhcqsYYY1Xs5ogLxWPA_2Wlc4&r=c08Btfq4m9QEScXN3ZQwLZzzWQE7S8CYq1IYuzKV_Zk&m=IZUo2SgLQlkV3Ss2KUMK7zRlp7SDmcPwREjqwYm17sI&s=8ZTnjxyGgaBWdjHqSf3VUQLljCeVbb6zvPsU2vtz5mE&e= 

>> We also looked through the implementation of
>> transform_from_real_to_unit_cell() which uses a newton iteration to
>> transform a point in physical space to a point in the unit space. Will a
>> similar technique be necessary to transform a vector from real to unit?
>
> I would guess so.

It of course depends on the mapping you use, but the direction
unit->real is typically much cheaper as it is an evaluation of a
polynomial inside the mapping. With a MappingManifold, both directions
should be equally cheap (we are basically just mapping from spherical
to cartesian coordinates or the other way around). Maybe it makes
sense to use MappingManifold if you have many particles?

Best,
Timo

-- 
Timo Heister
http://www.math.clemson.edu/~heister/