MULTISCALE COMPUTATION:

From Fast Solvers
To Systematic Upscaling

Major scaling bottlenecks:
computing

Scale-born obstacles:

Moving one particle at a time


fast local ordering

Slide 5

Scale-born obstacles:

Slide 7

Slide 8

Slide 9

Scale-born obstacles:

Slide 11

Slide 12

Multigrid solvers
Cost: 25-100 operations per unknown

Multigrid solvers
Cost: 25-100 operations per unknown

Multigrid solvers
Cost: 25-100 operations per unknown

Slide 16

Multigrid solvers
Cost: 25-100 operations per unknown

"Same fast solver"

Multigrid solvers
Cost: 25-100 operations per unknown

Slide 20

Multigrid solvers
Cost: 25-100 operations per unknown

Slide 22

Slide 23

Slide 24

SWA

Detected Lesions

Multigrid solvers
Cost: 25-100 operations per unknown

Slide 28

Multigrid solvers
Cost: 25-100 operations per unknown

N eigenfunctions

Multigrid solvers
Cost: 25-100 operations per unknown

Integro-differential Equation

Slide 33

Slide 34

Multigrid solvers
Cost: 25-100 operations per unknown

Slide 36

Scale-born obstacles:

Repetitive systems
e.g., same equations everywhere

Systematic Upscaling

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Fluids

Windows

Fluids

Lower Temperature T

Optimization by
Multiscale annealing

Systematic Upscaling

Upscaling Projects

THANK YOU

Slide 54

Aggregating Regions Adaptively