Bug/mortar discretization (#88)

* new mortar segmentation tests which are failing

* test_problems_mortar_3d.jl: first test (Tet4) pass

* solvers.jl: diagonal of A is now properly filled, if that option is used. Another option is to remove zero rows from matrix system, which is on by default

* problems_mortar.jl: added new function diagnose_interface to calculate quantities from interface hopefully revealing bugs in calculation

* problems_mortar_3d.jl: added docstring for check_orientation! and removed flooding debug messages not helping to debug anything

* solvers.jl: Another way to solve Ax = b

* Refactored code to make implementation of Tri6 assemble! easier

* Patch test with linear Tet4 elements and quadratic Tet10 elements pass

When using quadratic elements, in polygon clipping algorithm element is divided to linear sub-elements as proposed in [Puso2008]. Interpolation of Lagrange multiplier space is done using quadratic shape functions.

References
----------

[Puso2008] Puso, Michael A., T. A. Laursen, and Jerome Solberg. "A segment-to-segment mortar contact method for quadratic elements and large deformations." Computer Methods in Applied Mechanics and Engineering 197.6 (2008): 555-566.

* increased coverage by adding diagnose_interface

* test using dual basis, failing for unknown reason

* Fixed dual basis construction for Mortar/Tet4

The coefficient matrix Ae for one particular slave element e is the result performing numerical integration on *all* integration cells associated with this element [Popp2013]. Ae cannot be calculated "cell-wise" like it was done before. Now patch test will pass also using `interface.properties.dual_basis = true` option. Partially integrated slave elements are supported as well.

References
----------

[Popp2013] Popp, Alexander, et al. "Improved robustness and consistency of 3D contact algorithms based on a dual mortar approach." Computer Methods in Applied Mechanics and Engineering 264 (2013): 67-80.

* Minor modifications to preprocess.jl

- removed two functions which are unimplemented (but maybe planned in future)
- added function create_node_set_from_element_set!, which can be used, like name suggests, to create a node set from nodes belonging to some set of elements.

* solvers.jl: now prints a list of overconstrained nodes which can be easily copy-pasted to problem.assembly.removed_dofs list to solver overconstrained situation manually

* Increase code coverage

Added a new test which tests dual basis 3d mortar + adjust option when using Tet4 in elasticity problem.

* Tet10 + Dual basis still failing, others are working

* mortar 3d low level tests

* linear surface element projection tests pass

* Introduced basis transform constant alpha

Tet10 + dual basis patch test still failing, but single element low level routine tests gives expected results with alpha=0.2

* added new integration rule FPG12 for triangular elements

* added drop_tolerance option to remove very small values from constraint matrices

* Introduced a basis transform matrix T

Constructing bi-orthogonal basis for quadratic surfaces is ill-conditioned. By doing a basis transform N' = N*T for slave side displacement vector it's possible to construct a bi-orthogonal basis in a same way than with linear elements. Setting alpha=0.2 ensures that quadratic basis functions are strictly positive in practical cases.

* fix 3d clipping test routine, accepts only 3d vertices

* dropped number of integration poitns from 12 to 7 in quadratic mortar surfaces intrestingly gives more accurate results, maybe something numerical error in FPG12 integration rule..?

* added two displacement patch tests + output writing for all cases

* %s/Int64/Int/g

* Changed test data location

* Fine tuning of logging levels

src/solvers.jl

@@ -109,11 +109,13 @@ end
 function check_for_overconstrained_dofs(solver::Solver)
     overdetermined = false
     constrained_dofs = Set{Int}()
+    all_overconstrained_dofs = Set{Int}()
     boundary_problems = get_boundary_problems(solver)
     for problem in boundary_problems
         new_constraints = Set(problem.assembly.C2.I)
         new_constraints = setdiff(new_constraints, problem.assembly.removed_dofs)
         overconstrained_dofs = intersect(constrained_dofs, new_constraints)
+        all_overconstrained_dofs = union(all_overconstrained_dofs, overconstrained_dofs)
         if length(overconstrained_dofs) != 0
             warn("problem is overconstrained, finding overconstrained dofs... ")
             overdetermined = true
@@ -133,6 +135,8 @@ function check_for_overconstrained_dofs(solver::Solver)
         constrained_dofs = union(constrained_dofs, new_constraints)
     end
     if overdetermined
+        warn("List of all overconstrained dofs:")
+        warn(sort(collect(all_overconstrained_dofs)))
         error("problem is overconstrained, not continuing to solution.")
     end
     return true
@@ -276,6 +280,7 @@ function solve!(solver::Solver, K, C1, C2, D, f, g, u, la, ::Type{Val{3}})
 
     u[:] = x[1:solver.ndofs]
     la[:] = x[solver.ndofs+1:end]
+
     return true
 end