Coupling of Smooth Faceted Surface Evaluations in the SIERRA FEA - PowerPoint PPT Presentation

Coupling of Smooth Faceted Surface Evaluations in the SIERRA FEA Code Timothy J. Tautges Steven J. Owen Sandia National Laboratories University of Wisconsin-Madison Mini-symposium on Computational Geometry for Mechanics and Applications 5 th World Congress on Computational Mechanics July 9, 2002 Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94AL85000.

Outline • Introduction • CGM details • Integration into SIERRA for h-refinement • Examples • Summary & future work

Introduction • Actual representation of the spatial domain varies over the simulation System Design process – Continuous representation: Geometric Modeling geometry (CAD) – Discretized representation: mesh Meshing Design Optimization Adaptive Problems – Other groupings (parallel decomposition, contact surfaces, Decomposition shock interfaces, viz grouping) • Currently, relationship between Physical Modeling continuous & discretized representations is lost Solve • However, many applications could use these relationships! Visualization

Introduction • Solid geometry is widely used in simulation – Larger simulations making it possible to resolve small geometric features – Linking directly to design enables design-based simulation, iterations – Applications: adaptive refinement, flow over curved geometry, monte carlo transport, … • Geometry functionality found in CUBIT Mesh Generation Toolkit encapsulated in CGM libraries • CGM being integrated into FE codes (GOMA, SIERRA) and MCNP_X monte carlo xport code

Why Is Integration Necessary? Example: H-Refinement With Linear Facets Concentric cylinders • SIERRA simulation of HE “cookoff” Al HE Al SIERRA h-adapted solution q” (other surfs adiabatic) Coarse grid (planar facets on cylindrical boundary) Non-constant angular refinement Non-constant gas fraction at geometric discontinuity • Geometric discontinuity leads to unphysical results! Courtesy of S. Bova, Sandia National Labs

CGM - The Geometry Bus • CGM is a set of libraries that provide non- manifold, solid model-based geometry modeling for analysis applications CUBIT GOMA SIERRA MCNP_X ... CGM Virtual Geometry, Topology Composite & Partition Merge Topology Geometry Healing Facet (CUBIT) . . . ACIS IGES Pro E SolidWorks STEP Local Ops

The Common Geometry Module (CGM) CUBIT Hex Improv. Adv. Hex Smoothing W Advanced Hex Smoothing W Mult Automatic Swee i Tet Dicing Geode p Algorithm Hex Auto Selection Dicing H.T.P. OPT MS Auto Decomp Submap Manual Feat. Map Int. Plaster Tets MSC Decomp Remove Pave ANSYS LP Skew Control Ass.. Exodus II Net CDF ABAQUS CGM Virtual Geometry, Topology & Mesh Interface Composite & Partition Merge Topology Geometry Facet Healing . . . Pro E SolidWorks IGES ACIS (CUBIT) STEP Local Ops

Facet-Based Smooth Surfaces Requirements • Wealth of previous work on smooth surface modeling on discrete facets – Hoppe et. al, Floater, Walton and Meek, etc. • Requirements: – Build C1-continuous surfaces from patches of triangular facets – Use these surfaces as replacement or auxiliary surface representation for mesh generation and adaptation – Treat facet data from many sources, including graphics facets, mesh elements, and point cloud triangulations – Maximize code and data re-use in facet-based surface approximation

CGM Smooth Facets Implementation G1-Continuous Surface from Tri Facets • Quartic spline approximation gives G1-continuous surface across triangular facets • D. J. Walton, D. S. Meek, “A triangular G1 patch from boundary curves”, CAD 28:2, pp. 113-123, 1996. • S. J. Owen, D. R. White, T. J. Tautges, “Facet-based surfaces for 3d mesh generation”, submitted to 11 th International Meshing Roundtable, 2002. • Input: vertex coordinates, facet connectivity (, normals at vertices) • Functions needed for meshing/evaluation: closest point, normal, derivatives – Derivatives approximated using differencing

Application-Based Interface to Facet Data NxM Interface – NO!! Meshing Boundary H-adaptivity … Algorithms Conditions Imported mesh Analysis data (deformed drop) Graphics Scanned data facets (rhibosome)

CGM-Based Interface to Facet Data Better… Meshing Boundary H-adaptivity … Algorithms Conditions CGM Imported mesh Analysis data (deformed drop) Graphics Scanned data facets (rhibosome)

Native (sub-CGM) Interface to Facet Data Best! Meshing Boundary H-adaptivity … Algorithms Conditions CGM Graphics Engine SIERRA Mesh Database Facet Engine (CGM) Imported mesh Analysis data (deformed drop) Graphics facets • Goals (both important): Scanned data – minimize data duplication (rhibosome) – maximize code reuse

CGM Implementation Facet Class Design FacetEntity CGMPoint CGMFacetEdge CGMFacet PointData FacetEdgeData FacetData SierraPoint SierraFacetEdge SierraFacet Fmwk_MeshObj(NODE) Fmwk_MeshObj(EDGE) Fmwk_MeshObj(FACE) • CGM: abstract classes defining functions for topology traversal, point location, generic smooth surface functionality • CGM Facet Data: local storage of facet data, functions • SIERRA Interface: functions implemented using SIERRA mesh data classes (Fmwk_MeshObj)

SIERRA Faceted Surface Requirements • Fundamental requirement: smooth faceted surface must pass through nodes (including displacements) • 2 cases: k=3 k=1 k=2 – Static mesh: • Smooth surface can use original points/facets – Dynamic mesh: • Smooth surface must use updated node positions, including t=1 t=2 t=3 new nodes from h-refinement • Faceted surface must be dynamic in point locations AND facets • SIERRA h-adapted quads & tris, CGM tri facets Ł Ł Ł Ł template-based face to facet(s) mapping

Refinement Templates • Sierra surface elements may be decomposed into tris, and may have h-refined neighbors: • CGM uses triangular facets Sierra surface elements will have multiple facets Ł • Refinement templates can be used to avoid storing facet connectivity on every CGM facet: h=2 h=1 h=0 – Saves space (static tables & 2 or 3 int variables per Fmwk_MeshObj) – Indexing using ints, so it’s fast – Sierra functions/data still used for inter-element & unambiguous intra-element connectivity

4 Triangle Refinement Templates htype = 0 htype = 1 e0 f0 f0 f1 ord htype = 2 htype = 3 f2 f2 e2 e1 e0 e1 f3 e0 f0 f1 f0 f1 ord ord=0

6 Quadrilateral Refinement Templates htype = 1 htype = 2 htype = 0 n1 n2 f2 f2 f1 e0 e2 e1 e0 e0 n5 f3 e1 f1 f0 f0 f0 f1 n4 n3 ord ord ord n0 htype = 3 htype = 4 htype = 5 f2 n6 f3 f2 f2 f3 f3 e4 e3 e2 e2 f4 f5 e1 n7 e1 f4 e0 e0 e3 e0 e1 e2 f1 f0 f0 f1 f0 f1 ord ord ord=0

Pseudo code facet_edge->facets(facet_list) – If (my SIERRA owner == FACE) // interior facet edge • Get owning facets from static fedge-facet tables – Else // on SIERRA edge • Get SIERRA faces owning sierra edge • For each SIERRA face: – Get local rotation wrt refinement template for this face – Get facets from static fedge-facet tables

Example 1 Uniform H-Refinement on Cylinder • Initial coarse hex • Uniform h-refinement mesh representing 8 elements 64 elements with new nodes on cylinder boundary snapped to the smooth-faceted surfaces 512 elements 4096 elements • 3 rd pass of uniform • 2 nd pass of uniform h-refinement h-refinement • New node locations computed exactly on the cylinder (within tolerance)

Example 2 Uniform H-Refinement on Sphere • Uniform h-refinement • Initial coarse hex 56 elements 448 elements mesh representing with new nodes on boundary and at block concentric spheres interfaces snapped to the CGM geometry • 2 nd pass of uniform 3584 elements 28,672 elements • 3 rd pass of uniform h-refinement h-refinement • New node locations computed exactly on the spheres (within tolerance)

Example 3 SIERRA “Crease” Test • Demonstrates smooth surfaces defined from Sierra elements including discontinuities. • Crease becomes a feature where the feature angle criteria (f=135) is met, then two normals at facet vertices along the crease are defined. • Changing the feature angle also changes the length of the crease. For this test, 16 locations and normals (4X4 grid) are evaluated for every quad face.

Example 4 SIERRA “Warped” Test • Definition of facet-based surfaces on internal and external material boundaries Facets at block interfaces Exterior facets • Test also shows definition of smooth surfaces across adjoining blocks B – Angle-based A – Normals aligned consistent with mesh Normals defining Multiple facets meeting continuous surfaces at edge AB across edge AB

Open Issue: Quality Degeneration From Boundary-Only h-refinement • Uniform refinement of concentric spheres, snapping new nodes to the boundary: Refine Hexes can become inverted • Interior refinement should account for boundary snapping