Computational Science in LACSI

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Computational Science in LACSI

• PDE discretization on unstructured meshes
• Current focus polyhedral mimetic finite
  difference methods for the Laplacian operator in
  parabolic (diffusion) equations
• Customer Shavano Project (appropriate for many
  others)
• PI Prof. Yuri Kuznetsov, UH Dept of Mathematics
• A successful collaboration with X-3 (Scott
  Runnels) and T-7 (Misha Shashkov, Konstantin
  Lipnikov)
• Tools for code-based sensitivity, VV
• Computing derivatives with automatic
  differentiation (AD)
• Evolution of adifor tool AD for F90 with
  Truchas code and Ubiksolve linear solver library
  as initial target
• PI Mike Fagan, Rice Dept of Computational and
  Applied Mathematics

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Steady-State Diffusion
Continuous Diffusion
Discrete Diffusion
will be symmetric and positive definite. (A key
goal)
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Theoretical Motivation
First a way to discretize the divergence is
invented (i.e., we invent D). Second, that D is
inserted into the above equation, along with
other approximations for the integrals, to derive
a G.
More detail The above formula demonstrates that
the inner products using the divergence and
gradient operators are equal, which is the
definition of adjointess.
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Handling Polyhedra
Handling General Polyhedrons
The New Problem
For general polyhedra, discretizing the volume
integral presents difficulties. This was the
major focus of the UH effort How can the mimetic
approach be extended to this case?
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Handling Polyhedra
Success
Break the polyhedron into tets. Establish new
constraints to ensure 2nd-order spatial
convergence. This new idea is what is now being
tested by T-7/X-3.
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2D Results Tensor Diffusion
Polygonal Mesh
AMR Mesh
Results by Konstantin Lipnikov
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Status
Capabilities have been preserved for very general
meshes.
Accurate (2nd order) Easy-to-solve matrix (SPD)
No restrictions Any polygon/polyhedron Any
connectivity
Details
Source Scott Runnels, X-3

• Developed in Shavano architecture
• gt 90 pages of documentation
• All goals met Parallel, transient, 3D, 2D
  Cartesian and r-z.
• Strong SQA
• Technical success and programmatically relevant

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Tight Collaboration with LANL
Cooperation and Information Flow
UH
T-7
X-3
Guidance
Guidance
Academic Investigation New, Risky
Liaison Co-Development Academic
Testing Application Requirements
Feasible Ideas
Technology
CCS
LAMG linear solver
Keys to success

• X-3 leadership who sets clear requirements and
  supports interaction (Burton)
• An X-3 person dedicated to ensuring success
  (Runnels)
• X-3 (Shavano) team buy-in and expertise
  (Kenamond, Gianakon, Berry)
• CCS T-7 support and integrated technology
  (Morel, Berndt)
• A T-7 technical expert who contributes to the
  X-3 program (Lipnikov)
• A T-7 person who guides and collaborates with UH
  (Shashkov)
• An effective and responsive academician
  (Kuznetsov)

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Future Directions/Needs
Conserving and robust method for enforcing bound
preservation
More general grids and non-planar 3-D cell faces
Cells of mixed materials
A
B
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MFD Efforts Success and Impact

• Success metrics
• Evolution of algorithm accuracy/robustness
• More efficient as well?
• Staff development
• Students -gt postdoc -gt new LANL staff
• Education/training of existing LANL staff
• Impact
• Now Implementation in Shavano Project software
  available in FY05 releases
• Future Truchas code, AMR mesh codes

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AD work at Rice

• PI Mike Fagan
• Usefulness of AD?
• Code sensitivities relation of output to input
• Narrows focus to relevant models/algorithms
• Optimization use derivatives for searching
• Interface with SNLs Dakota tool?
• Nonlinear methods approximate the Jacobian?
• Verification facilitating the use of MMS
• Key question Can an AD tool be used on the large
  ASC codes?
• If not, can it be applied on key kernels?
• ASC is entering a phase where the codes are more
  mature and stable
• Therefore ready for this tool

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ASC Computational Science Needs

• PDE discretization methods
• For unstructured and Eulerian/AMR meshes
• VV tools/methodologies UQ, sensitivities
• Methods for nonlinear multi-physics time
  integration
• Linear and nonlinear solvers
• Interface kinematics and dynamics
• Motion and physics around interfaces bounding N
  materials
• Mesh management (for ALE, setup)
• Generation, motion, smoothing, remap/rezone
• Methods for computational mechanics
• Material damage/failure on Eulerian meshes
• Methods for turbulence/mix _at_ interfaces
• Homogenization techniques for mixed materials
• Transport methods quicker, more
  efficient/accurate
• Modeling unresolved scales

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LACSI FY06 Computational Science Efforts

• Advanced Polyhedral Discretization Methods for
  Diffusion-Type Problems in Strongly Heterogeneous
  Media
• PI Yuri Kuznetsov (UH)
• Continuation of FY05 work presence of material
  discontinuities, monotonicity constraints,
  homogenization, performance
• Application of AD tools
• PI Mike Fagan (Rice)
• Targets Telluride,

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Computational Science Considerations

• Metrics
• Staff recruitment, sabbatical opportunities,
  capability search/identification
• Evaluation criteria
• Matching with requirements, approach for
  collaboration
• Match with thrust areas (still TBD) on Weapons
  Science (WS) Foundation, e.g.
• PDE discretization
• Interfacial physics models and methods
• Transport models and methods
• Multi-physics coupling
• VV methodologies
• Added value
• Have an Adv. Apps Project customer
• Close partnering with CS community (performance,
  SQE)
• Find out about planned WS proposals from X/T/CCS