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533 | class GmshMesher:
"""Handles meshing of the RVE using GMSH."""
def __init__(self, mesh_name: str = "FiberMatrixRVE"):
"""
Parameters
----------
mesh_name : str, optional
The name prefix for generated mesh files. Default is "FiberMatrixRVE".
"""
self.mesh_name = mesh_name
self._check_gmsh()
def _check_gmsh(self):
"""Checks if the gmsh library is imported.
Raises
------
ImportError
If gmsh is not available.
"""
if gmsh is None:
raise ImportError(
"GMSH python library is not installed. Please install it using 'pip install gmsh'."
)
def create_mesh(
self,
fibers: List[PeriodicPrimaryFiber],
boundaries: List[LinearBoundary],
mesh_size_factor: float = 1.0,
visualize_gui: bool = False,
check_periodicity: bool = False,
):
"""Creates the mesh using GMSH.
Parameters
----------
fibers : List[PeriodicPrimaryFiber]
List of fibers to include in the mesh.
boundaries : List[LinearBoundary]
List of boundaries defining the RVE.
mesh_size_factor : float, optional
Factor to control mesh refinement. Default is 1.0.
visualize_gui : bool, optional
If True, launches GMSH GUI to visualize the geometry/mesh. Default is False.
check_periodicity : bool, optional
If True, asserts that the generated mesh nodes on periodic boundaries match. Default is False.
Notes
-----
To ensure robust boolean operations (OpenCASCADE kernel), the geometry is temporarily
scaled up such that the RVE extent is order ~1.0. This avoids precision issues with
very small coordinates (e.g. 1e-6). The geometry is scaled back to original size
after boolean fragmenting and before mesh generation.
"""
gmsh.initialize()
gmsh.model.add(self.mesh_name)
# Use OpenCASCADE kernel for robust boolean operations
# 1. Create RVE Polygon
# The boundaries might not be in order. We need to chain them.
# Gather all points for scaling extent
all_b_points = []
for b in boundaries:
all_b_points.append(b.points[0])
all_b_points.append(b.points[1])
all_b_points = np.array(all_b_points)
# Boolean operations require the points to be sufficiently large in magnitude
rve_extent = np.linalg.norm(
np.max(all_b_points, axis=0) - np.min(all_b_points, axis=0)
)
scale_factor = 1.0 / rve_extent
# Sort boundaries to form a continuous loop
ordered_chain = [] # List of (LinearBoundary, start_point, end_point)
remaining_boundaries = list(boundaries)
# Pick the first one
if not remaining_boundaries:
raise ValueError("No boundaries provided.")
current_b = remaining_boundaries.pop(0)
# Orientation of the first one defines the loop direction
current_start = current_b.points[0] * scale_factor
current_end = current_b.points[1] * scale_factor
ordered_chain.append((current_b, current_start, current_end))
# Iteratively find the next connected boundary
while remaining_boundaries:
found_idx = -1
found_orientation = 0 # 0: p0->p1, 1: p1->p0
for i, b in enumerate(remaining_boundaries):
p0 = b.points[0] * scale_factor
p1 = b.points[1] * scale_factor
# Check connectivity to current_end
if np.linalg.norm(p0 - current_end) < 1e-4:
found_idx = i
found_orientation = 0
break
elif np.linalg.norm(p1 - current_end) < 1e-4:
found_idx = i
found_orientation = 1
break
if found_idx == -1:
raise RuntimeError(
f"Could not find connected boundary in loop during meshing. Current tip: {current_end}"
)
b = remaining_boundaries.pop(found_idx)
if found_orientation == 0:
ordered_chain.append(
(b, b.points[0] * scale_factor, b.points[1] * scale_factor)
)
current_end = b.points[1] * scale_factor
else:
ordered_chain.append(
(b, b.points[1] * scale_factor, b.points[0] * scale_factor)
)
current_end = b.points[0] * scale_factor
# Create GMSH Lines
occ_line_tags = []
first_pt_tag = gmsh.model.occ.addPoint(
ordered_chain[0][1][0], ordered_chain[0][1][1], 0
)
prev_pt_tag = first_pt_tag
for i in range(len(ordered_chain)):
item = ordered_chain[i]
# If last segment, connect to first point
if i == len(ordered_chain) - 1:
next_pt_tag = first_pt_tag
else:
p_end = item[2]
next_pt_tag = gmsh.model.occ.addPoint(p_end[0], p_end[1], 0)
l_tag = gmsh.model.occ.addLine(prev_pt_tag, next_pt_tag)
occ_line_tags.append(l_tag)
prev_pt_tag = next_pt_tag
rve_wire = gmsh.model.occ.addWire(occ_line_tags)
rve_face = gmsh.model.occ.addPlaneSurface([rve_wire])
# 2. Add Fibers (Disks)
fiber_disks = []
def add_fiber_disk(f):
return gmsh.model.occ.addDisk(
f.center[0] * scale_factor,
f.center[1] * scale_factor,
0,
f.radius * scale_factor,
f.radius * scale_factor,
)
for f in fibers:
fiber_disks.append(add_fiber_disk(f))
for g in f.ghost_fibers:
fiber_disks.append(add_fiber_disk(g))
gmsh.model.occ.synchronize()
if visualize_gui:
gmsh.fltk.run()
# 3. Clip fibers to RVE using Intersect
# We want the part of fibers INSIDE the RVE.
# Object=Fibers, Tool=RVE
rve_dimtag = (2, rve_face)
fiber_dimtags = [(2, t) for t in fiber_disks]
# Intersect(Fibers, RVE). removeObject=True (consume fibers), removeTool=False (keep RVE).
clipped_fibers_dimtags, _ = gmsh.model.occ.intersect(
fiber_dimtags, [rve_dimtag], removeObject=True, removeTool=False
)
gmsh.model.occ.synchronize()
if visualize_gui:
gmsh.fltk.run()
# 4. Fragment
# Embed the clipped fibers into the RVE face.
out_dimtags, out_dimtags_map = gmsh.model.occ.fragment(
[rve_dimtag], clipped_fibers_dimtags
)
if not out_dimtags_map:
raise RuntimeError(
f"GMSH Fragment operation returned empty map. "
f"rve_dimtag={rve_dimtag}, # clipped_fibers={len(clipped_fibers_dimtags)}"
)
# Now that boolean operations are done, we can scale the geometry back to its original size.
gmsh.model.occ.dilate(
out_dimtags,
0,
0,
0,
1.0 / scale_factor,
1.0 / scale_factor,
1.0 / scale_factor,
)
gmsh.model.occ.synchronize()
if visualize_gui:
gmsh.fltk.run()
# 5. Identify Matrix vs Fibers
# use out_dimtags_map from fragment operation to trace lineage.
# Collect all tags that come from the fiber inputs
fiber_surface_tags = set()
# Inputs to fragment: [rve_dimtag] + clipped_fibers_dimtags
# Index 0 is RVE. Indices 1..N are Fibers.
for i in range(len(clipped_fibers_dimtags)):
# Map index is 1 + i
generated_dimtags = out_dimtags_map[1 + i]
for dt in generated_dimtags:
fiber_surface_tags.add(dt[1])
# Collect all tags that come from the RVE input
rve_related_tags = set()
for dt in out_dimtags_map[0]:
rve_related_tags.add(dt[1])
# Matrix surfaces are those in RVE lineage that are NOT in Fiber lineage
final_matrix_tags = list(rve_related_tags - fiber_surface_tags)
final_fiber_tags = list(fiber_surface_tags)
gmsh.model.occ.synchronize()
# 6. Apply Periodic Conditions
# Re-fetch lines as they might have been split
lines = gmsh.model.getEntities(1)
boundary_line_map = {b: [] for b in boundaries}
# Calculate a relative tolerance for boundary matching based on RVE extent
boundary_dist_tolerance = rve_extent * 1e-8
for l in lines:
tag = l[1]
com = gmsh.model.occ.getCenterOfMass(1, tag)
for b_idx, b in enumerate(boundaries):
# Distance to segment
dist = b.get_distance_to_fiber(np.array(com[:2]))
if dist < boundary_dist_tolerance:
boundary_line_map[b].append(tag)
for b in boundaries:
if b.type == BoundaryType.PERIODIC and b.pair is not None:
if hasattr(b, "index") and b.index < b.pair.index:
secondary_tags = boundary_line_map[b]
primary_tags = boundary_line_map[b.pair]
# Simple translation vector from Primary to Secondary
# P + T = S => T = S - P
# Let's take midpoint of boundary
mid_s = (b.points[0] + b.points[1]) / 2.0
mid_p = (b.pair.points[0] + b.pair.points[1]) / 2.0
trans = mid_s - mid_p
translation = [
1,
0,
0,
trans[0],
0,
1,
0,
trans[1],
0,
0,
1,
0,
0,
0,
0,
1,
]
if secondary_tags and primary_tags:
matched_secondary, matched_primary = (
self._get_periodic_boundary_mapping(
secondary_tags, primary_tags, translation
)
)
if matched_secondary:
if len(matched_secondary) != len(secondary_tags) or len(
matched_primary
) != len(primary_tags):
print(
f"Warning: Partial periodic match for boundary {b.index} vs {b.pair.index}. Matched {len(matched_secondary)} segments."
)
print(
f" Total Secondary: {len(secondary_tags)}, Total Primary: {len(primary_tags)}"
)
gmsh.model.mesh.setPeriodic(
1, matched_secondary, matched_primary, translation
)
else:
print(
f"Warning: No matching periodic segments found for boundary {b.index} vs {b.pair.index}."
)
# 7. Physical Groups and Generation
p_matrix = gmsh.model.addPhysicalGroup(2, final_matrix_tags)
gmsh.model.setPhysicalName(2, p_matrix, "Matrix")
p_fibers = gmsh.model.addPhysicalGroup(2, final_fiber_tags)
gmsh.model.setPhysicalName(2, p_fibers, "Fibers")
if mesh_size_factor:
gmsh.model.mesh.setSize(gmsh.model.getEntities(0), mesh_size_factor)
gmsh.model.mesh.generate(2)
if visualize_gui:
gmsh.fltk.run()
gmsh.write(self.mesh_name + ".msh")
gmsh.write(self.mesh_name + ".vtk")
if check_periodicity:
self._check_periodicity(
boundaries, boundary_line_map, boundary_dist_tolerance
)
gmsh.finalize()
def _is_inside_fiber(self, point_3d, fiber):
"""Checks if a point lies strictly inside a fiber (excluding boundary).
Parameters
----------
point_3d : Sequence[float]
The 3D point to check (z is ignored).
fiber : Fiber
The fiber to check against.
Returns
-------
bool
True if the point is inside the fiber radius (with a small buffer).
"""
dist = np.linalg.norm(np.array(point_3d[:2]) - fiber.center)
return dist < fiber.radius * (1.0 - 1e-6)
def _check_periodicity(self, boundaries, boundary_line_map, tolerance):
"""Verifies that nodes on periodic boundaries match up.
Parameters
----------
boundaries : List[LinearBoundary]
List of boundaries to check.
boundary_line_map : dict
Mapping from boundaries to curve tags.
tolerance : float
Distance tolerance for node matching.
"""
for b in boundaries:
if b.type == BoundaryType.PERIODIC and b.pair is not None:
# Ensure we only check once per pair
if hasattr(b, "index") and b.index < b.pair.index:
secondary_tags = boundary_line_map[b]
primary_tags = boundary_line_map[b.pair]
if not secondary_tags or not primary_tags:
continue
# Calculate translation
mid_s = (b.points[0] + b.points[1]) / 2.0
mid_p = (b.pair.points[0] + b.pair.points[1]) / 2.0
trans = mid_s - mid_p
# Get nodes
secondary_node_tags = []
secondary_coords = []
for t in secondary_tags:
node_tags, coords, _ = gmsh.model.mesh.getNodes(
1, t, includeBoundary=True
)
secondary_node_tags.extend(node_tags)
for i in range(0, len(coords), 3):
secondary_coords.append(coords[i : i + 3])
primary_node_tags = []
primary_coords = []
for t in primary_tags:
node_tags, coords, _ = gmsh.model.mesh.getNodes(
1, t, includeBoundary=True
)
primary_node_tags.extend(node_tags)
for i in range(0, len(coords), 3):
# Apply translation to primary nodes
p = np.array(coords[i : i + 3])
p[0] += trans[0]
p[1] += trans[1]
primary_coords.append(p)
primary_node_tags = np.array(primary_node_tags)
secondary_node_tags = np.array(secondary_node_tags)
if not secondary_coords or not primary_coords:
continue
# Robust comparison using KDTree
secondary_coords = np.array(secondary_coords)
primary_coords = np.array(primary_coords)
tree = KDTree(secondary_coords)
# Query distances to nearest neighbors
dists, closest_indices = tree.query(primary_coords, k=1)
unmatched_indices = np.where(dists > tolerance)[0]
if len(unmatched_indices) > 0:
max_msg = (
f"Max discrepancy: {np.max(dists[unmatched_indices]):.2e}"
)
unmatched_primary_tags = primary_node_tags[unmatched_indices]
unmatched_closest_indices = closest_indices[unmatched_indices]
unmatched_secondary_tags = secondary_node_tags[
unmatched_closest_indices
]
# Show up to 10 unmatched nodes for diagnostic purposes
num_show = 10
unmatched_details = []
for i in range(min(num_show, len(unmatched_indices))):
idx = unmatched_indices[i]
p_tag = unmatched_primary_tags[i]
s_tag = unmatched_secondary_tags[i]
dist = dists[idx]
unmatched_details.append(
f" Primary Tag {p_tag} -> Closest Secondary Tag {s_tag} (dist: {dist:.2e})"
)
unmatched_str = "\n".join(unmatched_details)
if len(unmatched_indices) > num_show:
unmatched_str += (
f"\n ... and {len(unmatched_indices) - num_show} more."
)
raise RuntimeError(
f"Periodic mesh verification failed for boundary {b.index} vs {b.pair.index}.\n"
f"Total # of Primary Nodes: {len(primary_coords)}\n"
f"Total # of Unmatched Nodes (dist > {tolerance}): {len(unmatched_indices)}\n"
f"{max_msg}\n"
f"Unmatched Node Details:\n{unmatched_str}"
)
else:
avg_dist = np.mean(dists) if len(dists) > 0 else 0
print(
f"Periodic check passed (KDTree) for boundary {b.index} <-> {b.pair.index} (avg dist: {avg_dist:.2e})"
)
def _get_periodic_boundary_mapping(
self,
secondary_tags: List[int],
primary_tags: List[int],
translation: List[float],
) -> Tuple[List[int], List[int]]:
"""Finds a 1-to-1 mapping between secondary and primary curve segments based on CoM.
Parameters
----------
secondary_tags : List[int]
List of curve tags on the secondary boundary.
primary_tags : List[int]
List of curve tags on the primary boundary.
translation : List[float]
The 16-element transformation matrix (GMSH format).
Returns
-------
Tuple[List[int], List[int]]
A tuple of (matched_secondary_tags, matched_primary_tags).
"""
matched_secondary = []
matched_primary = []
remaining_primaries = list(primary_tags)
trans_vec = np.array(translation[3:12:4]) # Extract [tx, ty, tz]
# In GMSH: Secondary = Primary + Translation, so Primary = Secondary - Translation
for s_tag in secondary_tags:
s_com = np.array(gmsh.model.occ.getCenterOfMass(1, s_tag))
expected_p_com = s_com - trans_vec
best_idx = -1
min_dist = 1e-6 # Tolerance
for i, p_tag in enumerate(remaining_primaries):
p_com = np.array(gmsh.model.occ.getCenterOfMass(1, p_tag))
dist = np.linalg.norm(p_com - expected_p_com)
if dist < min_dist:
min_dist = dist
best_idx = i
if best_idx != -1:
matched_secondary.append(s_tag)
matched_primary.append(remaining_primaries[best_idx])
remaining_primaries.pop(best_idx)
return matched_secondary, matched_primary
|