Filling Arbitrary Holes in Finite Element Models

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Filling Arbitrary Holes in Finite Element Models

• 17th International Meshing Roundtable
• 2008
• Schilling, Bidmon, Sommer, and Ertl

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Motivation

• Computer-Aided Engineering (CAE)
• Preprocessing for Finite Element analysis
• e.g. computational fluid dynamics simulation for
  acoustics
• thousands of holes

Source Schilling et al.
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Related Work

• Volumetric Approaches
• Split region around a hole into inner and outer
  parts
• Boundary layer defines missing surface
• Davis et al. Signed distance function is
  extended through the volume until it spans all
  holes
• Resulting quality not sufficient for CAE
• Podolak et al. Spatial decomposition for
  complex holes
• Hard to treat many independent meshes
• Geometry-Based Techniques (more promising)
• Wang et al. Moving least squares (MLS) to
  reconstruct locally smooth surface
• MLS Evaluate vertices neighborhood using
  weighted least squares
• Unsuitable for CAE general hole shapes
• Tekumalla et al. Advancing front method to
  close holes incrementally
• Liepa et al. Dynamic programming to create
  minimal surfaces
• Holes need not be planar
• basis of this new work

Source Schilling et al.
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Types of Holes
Source Schilling et al.
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Hole Patching Requirements

• Preserve existing geometric features.
• Provide acceptable results even when neighborhood
  information is absent.
• Interactive influence on shape of patching mesh.

Source Schilling et al.
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Setting up Semantic Holes across Multiple Meshes

• Balance user effort and computation speed for
  complex semantic holes.
• vs, vt are selected by user (could be from
  different meshes)
• Use a bounding volume hierarchy to calculate
  distances and find connecting node pairs.
• Connection criteria (see Figure 3)
• Minimize r. 2) Minimize dj 3)
  Minimize

Source Schilling et al.
vj1
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Setting up Semantic Holes across Multiple Meshes
(continued)
Source Schilling et al.
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Patching Holes Advancing Front

• Adapted from Tekumalla et al.
• Edge (by default) is part of advancing front.

bisector of edge
uses MLS
makeConvex
addVertices
Source Schilling et al.
DP approach from Liepa et al. is adapted to
fill small, simple holes with minimal surfaces.
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Patching Holes Potential Advancing Front
Problems

• Enclosed feature lines can be removed by
  makeConvex.
• MLS in addVertices can extend patching mesh too
  far (see Figure 6.)

11 Tekumalla et al. 12 Wang et al.
Source Schilling et al.
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Patching Holes Fixing Advancing Front Problems

• In makeConvex, test avoid cutting feature lines
  (Fig. 7a).
• Instead of MLS, place new node in plane of
  adjacent element. User-defined bending angle is
  enforced later.

Source Schilling et al.
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Patching Holes User-Defined Bending
Source Schilling et al.
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Patching Holes Collinearity Issue

• Collinear neighboring nodes can prevent a node
  from moving, hindering optimization.
• Moving might increase distance to neighbors.

Source Schilling et al.
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Patching Holes Fronts Missing Each Other

• Fronts not oriented towards each other can miss
  each other as they grow.

consider as a neighbor
Source Schilling et al.
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Patching Holes Bending Enforced by User

• Sometimes only C0 continuity is desired.
• Initial maximum bend is allowed.

Source Schilling et al.
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Patching HolesEdge Lengths of New Triangles

• Two user-controllled edge length options

leaves gap between meshes
(a)
(b)
Source Schilling et al.
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Results

• Hole detection, hole meshing and volume mesh
  generation can be done now in hours rather than
  days.
• Hole classification filters help reduce number of
  holes.
• Car model 463 parts and 3359 initial holes,
  reduced to 248 holes. 201 holes closed
  automatically.

Source Schilling et al.
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Results
Source Schilling et al.
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Results
Source Schilling et al.