Iga implementation in PDE

[potto1]

• class UnitMeshNurbs
• class InterpolationIga
• Assembly
• Dirichlet & Neumann boundary conditions
• Visualization

[TTitscher]

We briefly discussed that, but I add it here for completeness.

Theoretically, as soon as the IGA elements implement the ElementInterface, everything should work. That includes:

• defining cells
• assemble them
• visualize them
• define constraints on nodes

[edit: Note, that there is no GetNode(...) in this interface. Maybe it should?]

I suggest adding a MeshIga that contains the members

• some container of ElementCollectionIga
• several NurbsGeometry instances, I guess one for each DofType. (No need to rename it to InterpolationIga)

and IGA methods like (I imagine)

• CreateUnitMesh(...)
• Refine(...)
• IncreaseOrder(...), ReduceOrder(...) or SetOrder(...)
• some kind of special Iga node selection

[Psirus]

I would leave the node selection out of the interface. As far as I understand it, FEM meshes have nodes, IGA meshes have control points. Just because "you can think of control points as nodes" is a helpful analogy for people who don't know much about IGA (like me), I think it will lead to frustration in the cases where you can't think of them as nodes any more. So imho, no GetNode at the interface, but at ElementFEM, and GetControlPoint at ElementIGA, and corresponding SelectNodeAtCoordinate/SelectControlPointAtCoordinate for MeshFEM/MeshIGA.

[TTitscher]

Apparently continued in #215.