Product design optimization

Process optimization

Reduced experimentation

Physical system

Process Process modelmodel

Product Product modelmodel

Product

Market need

Multiscale Modeling Methods

Why Multiscale Models ?

Solid State Lighting

Spatial ScaleSpatial Scale1nm 1m 1mm 1cm

Coupled Coupled Physical Physical

PhenomenaPhenomena

Light Emission

In

h

Clustering/ Diffusion

nano m

icro m

eso m

acro

1 nm

1 m

1 cm

1 m

Solid State Lighting Application

LED

Atomic structure

Photonic crystal

Solid state bulb

Light Extraction

Photonic Crystal

Heat Transport Stress

nano m

icro m

eso

macro

1 nm

1 m

1 cm

1 m

Solid State Lighting Application

LED

Atomic structure

Photonic crystal

Solid state bulb

Solid State Bulb

(a)

In0.23

Ga0.77

N

n-A

l 0.15

Ga 0.

85N

p-GaN

p-A

l 0.15

Ga 0.

85N

0.05 m

n-GaN

Band gap Lattice LED device

The Building Blocks Electronic Structure Calculations

Solve Schrodinger’s equation for ground states of electrons:

Affinities

Sensors Solid state lighting

LED

Band gap calculations

i

2

i2

2

ti2

hV

m

1

8

h

(a)

In0.23

Ga0.77

N

n-A

l 0.15

Ga 0.

85N

p-GaN

p-A

l 0.15

Ga 0.

85N

0.05 m

n-GaN

Band gap

Scale ~ 0.1nm

The Building Blocks Atomistic Simulations

Molecular dynamics Monte Carlo

Nanostructured materials Thin film growth

Polymer nanocomposites

Nanocrystalline materials

Discrete model of island nucleation

Mapping to continuum

Scale ~ 10nm

Enzyme in octane

The Building Blocks Discrete Mesoscale Simulations

Coarse grained polymer models

Discrete dislocation dynamics (metals)

Discrete dislocation dynamics

Polymer models

ContinuumAtomistically informed constitutive equations

Scale ~ 1m

Polycrystal plasticity

Atomistic Coarse grained

The Building Blocks Continuum Simulations

Single scale models – Integrate the relevant system of PDEs.

Multiscale models – Sequential methods: Variational multiscale Time/space assymptotic expansion

– Embedded methods: Multigrid Domain decomposition

Scale > 0.1m (system specific)

Linking the Building Blocks Across Scales

Electronic Electronic structurestructure

AtomisticsAtomistics

MesoscaleMesoscale

Continuum Continuum micromicro

Discrete m

odels

Discrete m

odels

Continuum m

odels

Continuum m

odels

Coupled atomistic-continuum

Interatomic potentials

Calibration of higher order continuum based on

atomistics

and Continuum Continuum macromacro

Calibration of continuum constitutive laws based on discrete

models

Continuum multiscale models

Stochastic Nature of Physical Problems

• Multiple sources of uncertainty on all scales.

• Scale linking or system reduction must account for uncertainty.

Discrete systems – Statistical Mechanics Methods

Continuum systems – Stochastic Partial Differential Equations

Product design optimization

Process optimization

Reduced experimentation

Physical system

Process Process modelmodel

Product Product modelmodel

Product

Market need

Multiscale Modeling Methods

System Level Methods

• Construct a reduced order model to be used in control and system/process optimization. The reduced order model is calibrated based on input from the full multiscale model and the physical system.

Control Optimization

• System level modeling handled as a hierarchical multilevel optimization problem

-Optimization methods provide compatibility in models at different scales

- Desirable system level attributes communicated to bottom level

Feed forward control

Controller

Reduced order model

Physical system

disturbance

noise

Modeling Challenges

• Usually, no more than 2 scales are linked. Most models refer to a single spatial scale.

• This requires assumptions to be made about the gross behavior (constitutive laws) of the smaller scale.

• The time scale linking problem is much more difficult; consistent procedures with high degree of generality are lacking.

• The various physical phenomena are intimately coupled at the atomic scale. They are usually treated as being decoupled in continuum models.

Temporal scale linking

Spatial scale linking

Multiple physical phenomena

Summary of MSERC Modeling Requirements

• Need hierarchies of physical models ranging from electronic structure to reduced order system models.

• Modeling methods must include procedures to link models across spatial and temporal scales.

• The model hierarchies must include models appropriate for answering the pertinent questions arising at the various stages of multiscale systems engineering design.