Translations

The following implementations of the AbstractTranslationTrait are available, enabling the specification of translations in a tree and reducing computational and storage requirements.

The translations can be computed with the translations function. The result is a tuple containing two vectors:

• The first vector contains NamedTuples with fields receivingnode, translatingnode, and translationID. The translationID is the id of the translation in the translation directions.
• The second vector contains the translation directions.

This can for example look like

m = meshsphere(1.0, 0.1)
tree = TwoNTree(vertices(m), 0.1)

# define iterator, which specifies which translations occur (we use the default isnear() function)
tfiterator = H2Trees.TranslatingNodesIterator(; isnear=H2Trees.isnear())
# we are going to aggregate all nodes, even though that might not be needed and we use the AggregateMode
plans = H2Trees.galerkinplans(tree, H2Trees.AggregateAllNodesFunctor(), tfiterator, H2Trees.AggregateMode())

# the translations can be found in the testdisaggregationplan in AggregateMode
for translationtrait in [H2Trees.AllTranslations(), H2Trees.DirectionInvariance(),  H2Trees.DirectionInvariancePerLevel()]
    translationinfo, translations = H2Trees.translations(tree, plans.testdisaggregationplan, translationtrait)
    println("For translationtrait $(typeof(translationtrait)) we have $(length(translations)) unique translations.")
end

For translationtrait AllTranslations we have 17344 unique translations.
For translationtrait DirectionInvariance we have 768 unique translations.
For translationtrait DirectionInvariancePerLevel we have 768 unique translations.

and in the Petrov-Galerkin case

mx = meshsphere(1.0, 0.1)
my = meshsphere(2.0, 0.1)

tree = TwoNTree(vertices(mx), vertices(my), 0.1)
testtree = H2Trees.testtree(tree)
trialtree = H2Trees.trialtree(tree)

# define iterator, which specifies which translations occur (we use the default isnear() function)
tfiterator = H2Trees.TranslatingNodesIterator(; isnear=H2Trees.isnear())

# we are going to aggregate all nodes, even though that might not be needed and we use the AggregateMode
plans = H2Trees.petrovplans(tree, H2Trees.AggregateAllNodesFunctor(), tfiterator, H2Trees.AggregateMode())

# the translations can be found in the testdisaggregationplan in AggregateMode
for translationtrait in [H2Trees.AllTranslations(), H2Trees.DirectionInvariance(),  H2Trees.DirectionInvariancePerLevel()]
    translationinfo, translations = H2Trees.translations(tree, plans.testdisaggregationplan, translationtrait)
    println("For translationtrait $(typeof(translationtrait)) we have $(length(translations)) unique translations.")
end

For translationtrait AllTranslations we have 8614 unique translations.
For translationtrait DirectionInvariance we have 711 unique translations.
For translationtrait DirectionInvariancePerLevel we have 711 unique translations.