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

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

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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

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Timothy J. Tautges Steven J. Owen Sandia National Laboratories University of Wisconsin-Madison Mini-symposium on Computational Geometry for Mechanics and Applications 5th 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.

Coupling of Smooth Faceted Surface Evaluations in the SIERRA FEA Code

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SLIDE 2

Outline

  • Introduction
  • CGM details
  • Integration into SIERRA for h-refinement
  • Examples
  • Summary & future work
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SLIDE 3

Introduction

  • Actual representation of the spatial

domain varies over the simulation process – Continuous representation: geometry (CAD) – Discretized representation: mesh – Other groupings (parallel decomposition, contact surfaces, shock interfaces, viz grouping)

  • Currently, relationship between

continuous & discretized representations is lost

  • However, many applications could

use these relationships!

System Design Geometric Modeling Meshing Decomposition Physical Modeling Solve Visualization Adaptive Problems Design Optimization

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SLIDE 4

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

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SLIDE 5

Why Is Integration Necessary? Example: H-Refinement With Linear Facets

  • SIERRA simulation of HE “cookoff”
  • Geometric discontinuity leads to

unphysical results!

Coarse grid (planar facets

  • n cylindrical boundary)

HE Concentric cylinders q” (other surfs adiabatic) Al Al

SIERRA h-adapted solution

Non-constant gas fraction at geometric discontinuity Non-constant angular refinement Courtesy of S. Bova, Sandia National Labs

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SLIDE 6

CGM - The Geometry Bus

  • CGM is a set of libraries that provide non-

manifold, solid model-based geometry modeling for analysis applications

Virtual Geometry, Topology Composite & Partition Geometry Merge Topology Facet (CUBIT) ACIS Pro E SolidWorks . . .

Healing IGES STEP Local Ops

CGM CUBIT GOMA MCNP_X SIERRA ...

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SLIDE 7

The Common Geometry Module (CGM)

ANSYS ABAQUS Net CDF Exodus II Auto Feat. Remove Auto Decomp Manual Decomp Advanced Hex Smoothing Tet Dicing Geode Hex Dicing H.T.P. OPT MS Plaster Tets MSC W W Swee p

  • Adv. Hex Smoothing

Int. Ass.. Automatic Algorithm Selection LP Map Submap Mult i Pave Hex Improv.

Skew Control

CUBIT

Virtual Geometry, Topology & Mesh Interface Composite & Partition Geometry Merge Topology

Facet (CUBIT) ACIS Pro E SolidWorks

. . .

Healing IGES STEP Local Ops

CGM

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SLIDE 8

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

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SLIDE 9

CGM Smooth Facets Implementation G1-Continuous Surface from Tri Facets

  • Quartic spline approximation

gives G1-continuous surface across triangular facets

  • Input: vertex coordinates, facet connectivity

(, normals at vertices)

  • Functions needed for meshing/evaluation:

closest point, normal, derivatives

– Derivatives approximated using differencing

  • 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 11th International Meshing Roundtable, 2002.

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Application-Based Interface to Facet Data NxM Interface – NO!!

Scanned data (rhibosome) Imported mesh Analysis data (deformed drop) Graphics facets Meshing Algorithms H-adaptivity Boundary Conditions …

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CGM-Based Interface to Facet Data Better…

Scanned data (rhibosome) Imported mesh Analysis data (deformed drop) Graphics facets CGM Meshing Algorithms H-adaptivity Boundary Conditions …

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Native (sub-CGM) Interface to Facet Data Best!

Scanned data (rhibosome) Imported mesh Analysis data (deformed drop) Graphics facets CGM Meshing Algorithms H-adaptivity Boundary Conditions …

  • Goals (both important):

– minimize data duplication – maximize code reuse

SIERRA Graphics Engine Mesh Database Facet Engine (CGM)

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CGM Implementation Facet Class Design

  • 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)

FacetEntity CGMPoint CGMFacetEdge CGMFacet PointData FacetEdgeData FacetData SierraPoint SierraFacetEdge SierraFacet

Fmwk_MeshObj(NODE) Fmwk_MeshObj(EDGE) Fmwk_MeshObj(FACE)

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SIERRA Faceted Surface Requirements

  • Fundamental requirement: smooth faceted surface must

pass through nodes (including displacements)

  • 2 cases:

– Static mesh:

  • Smooth surface can use
  • riginal points/facets

– Dynamic mesh:

  • Smooth surface must use

updated node positions, including 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

k=1 k=2 k=3 t=1 t=2 t=3

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Refinement Templates

  • Sierra surface elements may be decomposed into tris, and may have

h-refined neighbors:

  • CGM uses triangular facets

Ł Sierra surface elements will have multiple facets

  • Refinement templates can be used to avoid storing facet connectivity on

every CGM facet: – 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

h=2 h=0 h=1

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4 Triangle Refinement Templates

htype = 0

f0

htype = 1

f0 f1 e0

  • rd

htype = 2

e0 e1 f0 f1 f2

  • rd

htype = 3

e0 e1 f0 f1 f2

  • rd=0

e2 f3

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SLIDE 17

e2 f3 f0 e0 f2 e1 f1 f0 f3 f4 f2 f1 e3 e0 e1 e2 f0 e0 e4 f3 e1 f4 f5 e3 f2 e2 f1

htype = 5 htype = 4 htype = 3

  • rd=0
  • rd
  • rd

f0 f0 f1 f2 e0 e1 f0 e0 e2 f2 e1 f3

htype = 0 htype = 2 htype = 1

  • rd
  • rd
  • rd

f1 f1 e0 n0 n1 n2 n3 n4 n5 n6 n7

6 Quadrilateral Refinement Templates

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SLIDE 18

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

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Example 1 Uniform H-Refinement on Cylinder

8 elements 64 elements 512 elements 4096 elements

  • Initial coarse hex

mesh representing cylinder

  • 2nd pass of uniform

h-refinement

  • 3rd pass of uniform

h-refinement

  • Uniform h-refinement

with new nodes on boundary snapped to the smooth-faceted surfaces

  • New node locations computed exactly on the cylinder (within tolerance)
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SLIDE 20
  • Initial coarse hex

mesh representing concentric spheres

  • Uniform h-refinement

with new nodes on boundary and at block interfaces snapped to the CGM geometry

56 elements 448 elements 3584 elements 28,672 elements

  • New node locations computed exactly on the spheres (within tolerance)
  • 2nd pass of uniform

h-refinement

  • 3rd pass of uniform

h-refinement

Example 2 Uniform H-Refinement on Sphere

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SLIDE 21
  • 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 3 SIERRA “Crease” Test

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SLIDE 22

Exterior facets Facets at block interfaces A B Multiple facets meeting at edge AB Normals defining continuous surfaces across edge AB

  • Definition of facet-based surfaces
  • n internal and external material

boundaries

Example 4 SIERRA “Warped” Test

  • Test also shows definition of

smooth surfaces across adjoining blocks – Angle-based – Normals aligned consistent with mesh

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SLIDE 23

Refine Hexes can become inverted

Open Issue: Quality Degeneration From Boundary-Only h-refinement

  • Uniform refinement of concentric spheres,

snapping new nodes to the boundary:

  • Interior refinement should account for boundary

snapping

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SLIDE 24

Why Use CGM?

  • Common interface to geometry in various formats:

– Solid model – Facet-based (FE mesh, scanned/CT data, etc.) – Virtual (CUBIT-specific representation)

  • Reliability/Support

– CUBIT links it directly, unmodified – If it’s broken in CGM, it’s broken in CUBIT too

  • Leverages future CUBIT geometry work

– SolidWorks*, Pro/E** ports – Automatic detail suppression (using virtual geometry) – Facet-based geometry modeling & model acquisition

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SLIDE 25

Summary & Future Work

  • CGM has been integrated into SIERRA multi-physics code

– Models smooth-faceted surfaces for static & deforming* meshes – Facet data evaluates SIERRA node positions/element connectivity directly

  • No data copies

– Facet-based modeling code in CGM used without modification

  • Interface classes used for facet objects
  • Support being developed for solid model distribution on

parallel computers

Timothy J. Tautges, Hong-Jun Kim, “On the Partitioning and Initialization of Solid Geometry Models on Parallel Computers”, submitted to 8th International conference on numerical grid generation in computational field simulations, Honolulu, HI, June 2-6, 2002.

  • Research paths:

– Investigate hierarchical data models – Dynamic meshes with lazy update of surface data