Resolve Gmsh issues

- Limit Gmsh to < 4.0
  Gmsh 4.0 doesn't partition correctly
  Addresses #697
- Export ghosts with Gmsh 4.x
  [Ghosts are broken](https://gitlab.onelab.info/gmsh/gmsh/issues/733),
  but export them anyway.
- Change refinement metric
- Limit refinements
  Gmsh refinement seems to stall out
- Don't partition tiny meshes
- Tolerate mangled Gmsh version string

  Assume Gmsh 3.0 if we can't parse the useless nonsense
  that Gmsh stuffs into stderr
- Ensure GmshMesh uses correct communicator

  More than one overlap will "downgrade" to a serial communicator
  because Gmsh doesn't give us more than one layer of ghosts

.appveyor.yml

@@ -64,8 +64,9 @@ install:
     - cmd: conda.exe config --add channels conda-forge
 
     # Configure the VM.
-    - cmd: if "%TARGET_ARCH%" == "x64" if "%CONDA_PY%" == "27" conda.exe install --quiet --name root --only-deps python=2.7 fipy
-    - cmd: if "%TARGET_ARCH%" == "x64" if "%CONDA_PY%" == "36" conda.exe install --quiet --name root --only-deps python=3.6 fipy
+    - cmd: if "%TARGET_ARCH%" == "x64" if "%CONDA_PY%" == "27" conda.exe install --quiet --name root python=2.7 fipy
+    - cmd: if "%TARGET_ARCH%" == "x64" if "%CONDA_PY%" == "36" conda.exe install --quiet --name root python=3.6 fipy "gmsh<4.0"
+    - cmd: conda.exe remove --quiet --force fipy
     # FIXME: fipy recipe on conda-forge doesn't have gmsh compatible with Python 2.7
     - ps: |
         $ErrorActionPreference = "Stop";

.circleci/config.yml

@@ -36,7 +36,7 @@ commands:
       - run:
           name: Create Conda Environment
           command: |
-            conda create -v --quiet --prefix << parameters.condaenv >> --show-channel-urls --channel conda-forge --only-deps << parameters.packages >>
+            conda create -v --quiet --prefix << parameters.condaenv >> --show-channel-urls --channel conda-forge << parameters.packages >> "gmsh<4.0"
             source activate ~/project/<< parameters.condaenv >>
             pip install future
             pip install scikit-fmm

.travis.yml

@@ -41,7 +41,7 @@ before_install:
   - hash -r
   - conda config --set always_yes yes --set changeps1 no
   - conda update -q conda
-  - conda create --quiet --name test-environment --show-channel-urls --channel conda-forge --only-deps python=$TRAVIS_PYTHON_VERSION fipy;
+  - conda create --quiet --name test-environment --show-channel-urls --channel conda-forge python=$TRAVIS_PYTHON_VERSION fipy "gmsh<4.0";
   - source activate test-environment
   # Useful for debugging any issues with conda
   - conda info -a

INSTALLATION.rst

@@ -256,6 +256,8 @@ Gmsh
 http://www.geuz.org/gmsh/
 
 :term:`Gmsh` is an application that allows the creation of irregular meshes.
+When running in parallel, :term:`FiPy` requires a version of :term:`Gmsh`
+>= 2.5 and < 4.0.
 
 SciPy
 =====

fipy/meshes/gmshMesh.py

@@ -92,7 +92,15 @@ def gmshVersion(communicator=parallelComm):
 
 def _gmshVersion(communicator=parallelComm):
     version = gmshVersion(communicator) or "0.0"
-    return StrictVersion(version)
+    try:
+        version = StrictVersion(version)
+    except ValueError:
+        # gmsh returns the version string in stderr,
+        # which means it's often unparsable due to irrelevant warnings
+        # assume it's OK and move on
+        version = StrictVersion("3.0")
+
+    return version
 
 def openMSHFile(name, dimensions=None, coordDimensions=None, communicator=parallelComm, order=1, mode='r', background=None):
     """Open a Gmsh `MSH` file
@@ -164,8 +172,8 @@ def openMSHFile(name, dimensions=None, coordDimensions=None, communicator=parall
             gmshFlags = ["-%d" % dimensions, "-nopopup"]
 
             if communicator.Nproc > 1:
-                if version < StrictVersion("2.5"):
-                    warnstr = "Cannot partition with Gmsh version < 2.5. " \
+                if not (StrictVersion("2.5") < version <= StrictVersion("4.0")):
+                    warnstr = "Cannot partition with Gmsh version < 2.5 or >= 4.0. " \
                                + "Reverting to serial."
                     warnings.warn(warnstr, RuntimeWarning, stacklevel=2)
                     communicator = serialComm
@@ -176,6 +184,11 @@ def openMSHFile(name, dimensions=None, coordDimensions=None, communicator=parall
                         raise ValueError("'dimensions' must be specified to generate a mesh from a geometry script")
                 else: # gmsh version is adequate for partitioning
                     gmshFlags += ["-part", "%d" % communicator.Nproc]
+                    if version >= StrictVersion("4.0"):
+                        # Gmsh 4.x needs to be told to generate ghost cells
+                        # Unfortunately, the ghosts are broken
+                        # https://gitlab.onelab.info/gmsh/gmsh/issues/733
+                        gmshFlags += ["-part_ghosts"]
 
             gmshFlags += ["-format", "msh2"]
 
@@ -1514,23 +1527,24 @@ class Gmsh2D(Mesh2D):
 
     >>> from fipy import CellVariable, numerix
 
-    >>> std = []
+    >>> error = []
     >>> bkg = None
     >>> from builtins import range
     >>> for refine in range(4):
     ...     square = Gmsh2D(geo, background=bkg) # doctest: +GMSH
     ...     x, y = square.cellCenters # doctest: +GMSH
     ...     bkg = CellVariable(mesh=square, value=abs(x / 4) + 0.01) # doctest: +GMSH
-    ...     std.append((numerix.sqrt(2 * square.cellVolumes) / bkg).std()) # doctest: +GMSH
+    ...     error.append(((2 * numerix.sqrt(square.cellVolumes) / bkg - 1)**2).cellVolumeAverage) # doctest: +GMSH
 
-    Check that the mesh is monotonically approaching the desired density
+    Check that the mesh is (semi)monotonically approaching the desired density
+    (the first step may increase, depending on the number of partitions)
 
-    >>> print(numerix.greater(std[:-1], std[1:]).all()) # doctest: +GMSH
+    >>> print(numerix.greater(error[:-1], error[1:]).all()) # doctest: +GMSH
     True
 
     and that the final density is close enough to the desired density
 
-    >>> print(std[-1] < 0.2) # doctest: +GMSH
+    >>> print(error[-1] < 0.02) # doctest: +GMSH
     True
 
     The initial mesh doesn't have to be from Gmsh
@@ -1578,6 +1592,10 @@ def __init__(self,
                                    mode='r',
                                    background=background)
 
+        # openMSHFile may have "downgraded" the communicator
+        # if, e.g., too many overlaps were requested
+        communicator = self.mshFile.communicator
+
         (verts,
          faces,
          cells,
@@ -1947,6 +1965,10 @@ def __init__(self, arg, communicator=parallelComm, order=1, background=None):
                                     mode='r',
                                     background=background)
 
+        # openMSHFile may have "downgraded" the communicator
+        # if, e.g., too many overlaps were requested
+        communicator = self.mshFile.communicator
+
         (verts,
          faces,
          cells,
@@ -2225,7 +2247,7 @@ def _test(self):
         >>> yogmsh.cellCenters.value.size == yogrid.cellCenters.value.size # doctest: +GMSH
         True
 
-        >>> mesh = GmshGrid2D(nx=2, ny=2) # doctest: +GMSH
+        >>> mesh = GmshGrid2D(nx=2, ny=2, communicator=serialComm) # doctest: +GMSH
 
         >>> mesh.numberOfCells == 4 # doctest: +GMSH
         True
@@ -2310,7 +2332,8 @@ def _test(self):
         >>> numerix.allclose(yogmsh._faceAreas, yogrid._faceAreas) # doctest: +GMSH
         True
 
-        >>> mesh = GmshGrid3D(nx=2, ny=2, nz=2) # doctest: +GMSH
+        >>> mesh = GmshGrid3D(nx=2, ny=2, nz=2,
+        ...                   communicator=serialComm) # doctest: +GMSH
 
         >>> ccs = [[ 0.5,  0.5,  0.5,  0.5,  1.5,  1.5,  1.5,  1.5],
         ...    [ 0.5,  0.5,  1.5,  1.5,  0.5,  0.5,  1.5,  1.5],