Worcester Polytechnic Institute Electronic Theses and Dissertations Collection

Title page for ETD etd-033009-151933

Document Typedissertation
Author NameGhadyani, Hamid R
Email Address hamid at hamid.cc
TitleTetrahedral Meshes in Biomedical Applications: Generation, Boundary Recovery and Quality Enhancements
DepartmentMechanical Engineering
  • John M. Sullivan , Jr., Advisor
  • Mark Richman, Graduate Committee Rep
  • Allen Hoffman, Co-Advisor
  • Brian Savilonis, Co-Advisor
  • Subhadra Srinivasan, Co-Advisor
  • Keywords
  • tetrahedral element
  • fem
  • tetrahedron
  • mesh smoothing
  • finite element
  • delaunay
  • constrained
  • mesh generation
  • Date of Presentation/Defense2009-03-23
    Availability unrestricted


    Mesh generation is a fundamental precursor to finite element implementations for solution of partial differential equations in engineering and science. This dissertation advances the field in three distinct but coupled areas. A robust and fast three dimensional mesh generator for arbitrarily shaped geometries was developed. It deploys nodes throughout the domain based upon user-specified mesh density requirements. The system is integer and pixel based which eliminates round off errors, substantial memory requirements and cpu intensive calculations. Linked, but fully detachable, to the mesh generation system is a physical boundary recovery routine. Frequently, the original boundary topology is required for specific boundary condition applications or multiple material constraints. Historically, this boundary preservation was not available. An algorithm was developed, refined and optimized that recovers the original boundaries, internal and external, with fidelity. Finally, a node repositioning algorithm was developed that maximizes the minimum solid angle of tetrahedral meshes. The highly coveted 2D Delaunay property that maximizes the minimum interior angle of a triangle mesh does not extend to its 3D counterpart, to maximize the minimum solid angle of a tetrahedron mesh. As a consequence, 3D Delaunay created meshes have unacceptable sliver tetrahedral elements albeit composed of 4 high quality triangle sides. These compromised elements are virtually unavoidable and can foil an otherwise intact mesh. The numerical optimization routine developed takes any preexisting tetrahedral mesh and repositions the nodes without changing the mesh topology so that the minimum solid angle of the tetrahedrons is maximized. The overall quality enhancement of the volume mesh might be small, depending upon the initial mesh. However, highly distorted elements that create ill-conditioned global matrices and foil a finite element solver are enhanced significantly.

  • ghadyani_hamid.pdf

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