Domain should know its physical dimension #203

Problem description

A Domain only knows its logical dimension, dim. It has no ldim or pdim, although its mappings may have a physical dimension larger than the logical one. As a consequence:

• The physical coordinates of a mapped surface are wrong. They are built from dim in BasicDomain.coordinates:

  from sympde.api import Mapping, Square
  
  domain = Mapping('F', ldim=2, pdim=3)(Square('Omega'))
  print(domain.coordinates)  # [x, y] (expected: [x, y, z])

• Code that needs the physical dimension computes it from the mappings, in several places: Domain.todict in Keep the physical dimension of mappings in Domain.export / Domain.from_file #201, _physical_dimension() in sympde/utilities/plotting.py in Update Multipatch API #188, and the check requested in Domain.join accepts patches with different physical dimensions #140.

• Nothing ensures that all patches of a domain have the same physical dimension (Domain.join accepts patches with different physical dimensions #140).

Suggested solution

• Add the properties Domain.ldim and Domain.pdim. pdim is the common physical dimension of the mappings, or ldim for an unmapped domain; it relies on all patches having the same physical dimension, which is checked when the domain is created (Domain.join accepts patches with different physical dimensions #140).
• Build the physical coordinates from pdim.
• Use domain.pdim wherever the physical dimension is currently computed from the mappings.
• Replace dim with ldim everywhere, without keeping dim as an alias: the dim property and the dim constructor argument of the domain classes (BasicDomain, Domain, InteriorDomain, NCube, ...), and their uses in SymPDE. The dim argument of Mapping, a shorthand for ldim = pdim = dim, is kept.

Note

Replacing dim with ldim is a breaking change for the projects that depend on SymPDE:

• PSYDAC: about 65 uses of .dim on domains.
• IGA-Python: 10 calls with dim= and 2 uses of .dim in the examples of chapter 1.
• GeLaTo: 31 calls Domain('Omega', dim=DIM) in its tests.

Building the physical coordinates from pdim also changes the symbolic expressions on mapped domains with pdim > ldim.