Geometric Modeling and Mesh Generation for hpAdaptive FEM

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Geometric Modeling and Mesh Generation for
hp-Adaptive FEM

• Leszek Demkowicz, Dong Xue

Institute of Computational Engineering and
Science The University of Texas at Austin
Team D. Pardo, Y.Zhang, J.Kurtz
Collaboration T. Tautges(Sandia National Lab),
A. Zdunek(Swedish Aeronautical Institute)
Web http//www.ticam.utexas.edu/cynthia/paper/p
roject.html
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Outline

• Geometric Modeling Package and Mesh Generation
• Motivation
• Geometry and Topology
• Transfinite Interpolation and Implicit
  Parameterization
• Two Approaches
• Interface with Cubit
• Interface with Geometric Reconstruction Technique
• Future work

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What is GMP ?

• Construct exact and compatible
  parameterizations for 2D and 3D manifolds.

• Bottom up hierarchical manner
• points gt curves gt triangles(rectangles) gt
  prisms(hexahedrons)
• A 2D object a union of of linear
  (curvilinear)triangles (rectangles)
• A 3D object a union of of linear(curvilinear)
  hexahedrons.
• Construct parameterizations for each entities

• Provide derivatives of the mappings wrt
  reference coordinates for points in reference
  frame

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Why GMP?

• Success of hp Adaptive FE simulations
• Precise geometrical representation
• appropriate mesh generation method
• Foundation for generating the initial mesh and
  update during mesh refinements
• Fully automatic preparation of topology
  information.

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Topological entities and parameterizations in GMP

• Topological Entities
• Surfaces
• Points
• Curves
• Triangles
• Rectangles
• Prisms
• Hexahedrons

Particular type Complete connectivity

• Parameterization
• Explicit
• Implicit

Structure is open
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Standard transfinite interpolation -
Parameterization technique 1
Purpose construct parameterizations using given
parameterizations of lower-dimensioned entities.
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Implicit parameterizations - Parameterization
technique 1
Purpose construct geometric model conforming to
high order surfaces.
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GMP interface Approach 1

• Interface with coarse meshes generated from
  volumetric imaging data.
• e.g, MRI, CT
• Developed at CCV, ICES

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Head Model(1)

• 3D geometric model
• Reconstructed as a mesh of linear
  hexahedra
• Provide connectivity information for curvilinear
  hexahedra

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Head Model(2)

• Simulate EM waves
• Enclose the head within a truncating sphere
• Mesh the sphere and the head

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Head Model(3)

• Transform the connectivity information into
  GMP entities.
• Construct the parameterizations for hexahedra
• Total numbers of each GMP entity

• Points 25744
• Curves 8448
• Rectangles 4424
• Hexahedrons 704

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GMP interface Approach 2

• Interface with CUBIT developed at
• Sandia National Labs
• Exodus II
• Run GMP Interface to construct actual
  parameterizations.
• E.g. Induction Logging Instrument

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Tools with tilted loop antennas- Geometric model
construction

• Two tilted loop antennas wrapped around the axial
  tool body
• Tool is embedded in a 3D volume
• Construct the overall geometric model in CUBIT

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Tools with tilted loop antennas - Mesh
generation process

• Generate the mesh in CUBIT
• Set interval size
• Set mesh schemes
• Generate the mesh for the model
• Inspect mesh for quality

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Tools with tilted loop antennas Geometric
Model in GMP

• Interface obtains the topology information
• GMP constructs parameterizations for linear
  (curvilinear) hexahedra
• Total numbers of each GMP entity
• Surfaces 1021
• Points 5109
• Curves 14560
• Rectangles 13860
• Hexahedrons 4400

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Future work

• C1 continuous geometry reconstruction using
  A-patch .
• Accessing the binary Genesis files using netCDF
• http//www.ticam.utexas.edu/cynthia/paper/project
  .html