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Panel Discussion on V&V/UQ

N. R. Aluru

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V&V Challenges

Approach: Identify key phenomena and rank their importance; Verification using tier-1 (single physics), tier-2 (coupled physics), and tier-3 (system level)Challenges: Lack of modules/codes/analytical expressions for some physical phenomena; Verification can be challenging for tier-2 and tier-3

Verification

Approach: Identify key phenomena and rank their importance; Validation using tier-1 (single physics), tier-2 (coupled physics), and tier-3 (system level); Use experimental data from literature, Sandia and in-house experiments Challenges: Lack of data for some physical phenomena; Validation can be challenging for many examples

Validation

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UQ ChallengesQuestions:What input uncertainties are the most important?How does uncertainty in microstructure affect macroscopic membrane response? Uncertainty in dimensions?How does uncertainty in microstructure propagate into the force-history response and thus into structural response?

Criterion for success: Comparison to uncertainty experiments

Challenges: Propagating uncertainty across scales and physics, computational size and cost, careful control of number of uncertain variables Young’s modulus for polysilicon as

measured by various research group over the years [J. V. Clark, Ph.D. thesis, 2005].

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Verification Techniques Structural-Thermal-ElectrostaticsStructural-Thermal-Electrostatics

Coupling Coupling Tier III ExampleTier III Example

FVM + MPM Solver:domain discretization; solution

algorithms; time-marching

ANSYS:domain discretization; solution

algorithm; time-marching

Verification:Define criteria

structureAssumptionsa. specified geometry;b. specified boundary conditions;c. specified applied voltaged. linear elastic materiale. heat generation in metal

Electrostaticfield

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Validation Techniques

Phenomena Source of Validation Data

Tier 3 (System-Level Validation)

1. Electro-mechanical response with dielectric charging and environmental effects

2. Shock response

3. Materials characterization and surface roughness evolution

1. Purdue experiments with actual RF MEMS in the range of 25-125C and different humidity levels

2. Purdue experiments on actual RF MEMS structures for a range of accelerations and temperatures from -55C to 75C.

3. Purdue experiments with TEM and AFM on evolution of grain size, orientation, defects, and surface roughness

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UQ Techniques

Generalized Polynomial Chaos

Stochastic Collocation Methods

+ Easy to implement

+ Minor changes to code

─ Not as efficient as Galerkin

─ Harder to implement

─ Significant changes to code

+ More efficient than collocation

Choice of inputs from collocation

Solver

Stochastic Galerkin Methods

Solver

Good solution for LAMMPS

Good starting point for other codes

Better for FVM / MPM codes

Optimization beyond collocation

realizations

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How we will use V&V and UQ to guide and set priorities for research activities

Identifying key phenomena and ranking their importance is largely driven by V&V and UQ

Sensitivity/UQ will determine what inputs are important to models – example: role of accomodation coefficients in rarefied gas damping

Modeled Phenomena Algorithm or Solver

Test Problems

Tier I (Individual)1. Drift diffusion charge transport

2. Atomistic-level computation of mechanics

FVM

MD/LAMMPS

Analytic solutions for drift -diffusion for known potential fieldComparison of wire/beam bending with in-house MD codes, GRASP

Tier II (Coupled)1. Electrostatics+linear mech. response2. Fluid-structure interaction

FVM+MPM

FVM+MPM

Published solutions (44 - 47)

Comparison with ADINA

Modeled Phenomena Importance Model Adequacy

Comments

1. Electrostatics High Adequate Large microelectronics literature and adequate data

2. Stiction:a. Roughness evolutionb. Capillary condensation

HighHigh

InadequateInadequate

Few detailed models or simulations for roughness evolution, condensation.

3. Electro-thermo-mech. response:

a. Linearb. Nonlinear

HighHigh

AdequateInadequate

Classical electro-mech. response well understood

Interaction of microstruct with continuum not well understood.

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Far-Reaching V&V/UQ Issues

Electrostatic pull-in in MEMS leads to discontinuities in the random domain; Need to develop efficient stochastic algorithms for non-smooth functions in the random domain

Explore easier ways of implementing UQ

New software paradigms for automating UQ implementation

Extensive experimental data is needed for UQ /Validation

Education, teaching and training new generation of students in V&V/UQ