NON-SYMMETRIC FRACTIONAL DIFFUSION NON-SYMMETRIC FRACTIONAL - - PowerPoint PPT Presentation

▶
non symmetric fractional diffusion non symmetric
SMART_READER_LITE
LIVE PREVIEW

NON-SYMMETRIC FRACTIONAL DIFFUSION NON-SYMMETRIC FRACTIONAL - - PowerPoint PPT Presentation

Oct 27, 2022 361 likes •1.13k views

NON-SYMMETRIC FRACTIONAL DIFFUSION NON-SYMMETRIC FRACTIONAL DIFFUSION AS A SPECIAL CASE OF AS A SPECIAL CASE OF NONLOCAL CONVECTION-DIFFUSION NONLOCAL CONVECTION-DIFFUSION Marta D'Elia, Center for Computing Research, SNL, mdelia@sandia.gov M.

slide-1
SLIDE 1

NON-SYMMETRIC FRACTIONAL DIFFUSION NON-SYMMETRIC FRACTIONAL DIFFUSION AS A SPECIAL CASE OF AS A SPECIAL CASE OF NONLOCAL CONVECTION-DIFFUSION NONLOCAL CONVECTION-DIFFUSION

Marta D'Elia, Center for Computing Research, SNL, mdelia@sandia.gov

  • M. Gunzburger (FSU), R. Lehoucq (SNL), Q. Du (Columbia)

Fractional PDEs: Theory, Algorithms and Applications ICERM, Providence, RI – June 20th 2018

Sandia National Labs, NM – Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525.

slide-2
SLIDE 2

Introduction

slide-3
SLIDE 3
  • M. D'Elia – mdelia@sandia.gov

NONLOCAL MODELS

slide-4
SLIDE 4
  • M. D'Elia – mdelia@sandia.gov

NONLOCAL MODELS

slide-5
SLIDE 5
  • M. D'Elia – mdelia@sandia.gov

NONLOCAL MODELS

slide-6
SLIDE 6
  • M. D'Elia – mdelia@sandia.gov

NONLOCAL MODELS

slide-7
SLIDE 7
  • M. D'Elia – mdelia@sandia.gov

NONLOCAL MODELS

slide-8
SLIDE 8
  • M. D'Elia – mdelia@sandia.gov

FRACTIONAL (NONLOCAL) MODELS

slide-9
SLIDE 9
  • M. D'Elia – mdelia@sandia.gov

FRACTIONAL (NONLOCAL) MODELS

slide-10
SLIDE 10
  • M. D'Elia – mdelia@sandia.gov

FRACTIONAL (NONLOCAL) MODELS

slide-11
SLIDE 11
  • M. D'Elia – mdelia@sandia.gov

FRACTIONAL (NONLOCAL) MODELS

slide-12
SLIDE 12
  • M. D'Elia – mdelia@sandia.gov

FRACTIONAL (NONLOCAL) MODELS

slide-13
SLIDE 13
  • M. D'Elia – mdelia@sandia.gov

FRACTIONAL (NONLOCAL) MODELS

slide-14
SLIDE 14

NOT ONLY STOCHASTIC PROCESSES

  • M. D'Elia – mdelia@sandia.gov
slide-15
SLIDE 15

Outline

slide-16
SLIDE 16

NONLOCAL VECTOR CALCULUS

  • M. D'Elia – mdelia@sandia.gov
slide-17
SLIDE 17

NONLOCAL VECTOR CALCULUS

  • M. D'Elia – mdelia@sandia.gov
slide-18
SLIDE 18

NONLOCAL VECTOR CALCULUS

  • M. D'Elia – mdelia@sandia.gov
slide-19
SLIDE 19

NONLOCAL VECTOR CALCULUS

  • M. D'Elia – mdelia@sandia.gov
slide-20
SLIDE 20

NONLOCAL VECTOR CALCULUS

  • M. D'Elia – mdelia@sandia.gov
slide-21
SLIDE 21

NONLOCAL VECTOR CALCULUS

  • M. D'Elia – mdelia@sandia.gov
slide-22
SLIDE 22

NONLOCAL VECTOR CALCULUS

  • M. D'Elia – mdelia@sandia.gov
slide-23
SLIDE 23

NONLOCAL VECTOR CALCULUS

  • M. D'Elia – mdelia@sandia.gov
slide-24
SLIDE 24

NONLOCAL VECTOR CALCULUS

  • M. D'Elia – mdelia@sandia.gov
slide-25
SLIDE 25

NONLOCAL VECTOR CALCULUS

  • M. D'Elia – mdelia@sandia.gov
slide-26
SLIDE 26

THE FRACTIONAL LAPLACIAN AS A NONLOCAL OPERATOR

– M.D., M. Gunzburger, The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator, Computers and Mathematics with applications, 66, 1245–1260, 2013

slide-27
SLIDE 27
  • M. D'Elia – mdelia@sandia.gov

FRACTIONAL and TRUNCATED FRACTIONAL

slide-28
SLIDE 28
  • M. D'Elia – mdelia@sandia.gov

FRACTIONAL and TRUNCATED FRACTIONAL

slide-29
SLIDE 29
  • M. D'Elia – mdelia@sandia.gov

FRACTIONAL and TRUNCATED FRACTIONAL

slide-30
SLIDE 30
  • M. D'Elia – mdelia@sandia.gov

NUMERICAL APPROXIMATION

slide-31
SLIDE 31
  • M. D'Elia – mdelia@sandia.gov

NUMERICAL APPROXIMATION

slide-32
SLIDE 32
  • M. D'Elia – mdelia@sandia.gov

NUMERICAL APPROXIMATION

slide-33
SLIDE 33

NUMERICAL APPROXIMATION

  • M. D'Elia – mdelia@sandia.gov
slide-34
SLIDE 34

NUMERICAL APPROXIMATION

  • M. D'Elia – mdelia@sandia.gov
slide-35
SLIDE 35

NUMERICAL APPROXIMATION

  • M. D'Elia – mdelia@sandia.gov
slide-36
SLIDE 36

NUMERICAL APPROXIMATION

  • M. D'Elia – mdelia@sandia.gov
slide-37
SLIDE 37

NUMERICAL APPROXIMATION

  • M. D'Elia – mdelia@sandia.gov
slide-38
SLIDE 38

NUMERICAL APPROXIMATION

  • M. D'Elia – mdelia@sandia.gov
slide-39
SLIDE 39
  • M. D'Elia – mdelia@sandia.gov

NUMERICAL APPROXIMATION

slide-40
SLIDE 40

NUMERICAL APPROXIMATION

  • M. D'Elia – mdelia@sandia.gov
slide-41
SLIDE 41

NUMERICAL APPROXIMATION

  • M. D'Elia – mdelia@sandia.gov
slide-42
SLIDE 42

NUMERICAL APPROXIMATION

  • M. D'Elia – mdelia@sandia.gov
slide-43
SLIDE 43

NUMERICAL APPROXIMATION

  • M. D'Elia – mdelia@sandia.gov
slide-44
SLIDE 44

NONLOCAL CONVECTION-DIFFUSION

– MD, Q. Du, M. Gunzburger, R. Lehoucq, Nonlocal convection-diffusion problems

  • n bounded domains and finite-range jump processes, Computational Methods in

Applied Mathematics, 29, 2017

slide-45
SLIDE 45

NONLOCAL VECTOR CALCULUS – CONVECTION

  • M. D'Elia – mdelia@sandia.gov
slide-46
SLIDE 46

NONLOCAL VECTOR CALCULUS – CONVECTION

  • M. D'Elia – mdelia@sandia.gov
slide-47
SLIDE 47

NONLOCAL VECTOR CALCULUS – CONVECTION

  • M. D'Elia – mdelia@sandia.gov
slide-48
SLIDE 48

NONLOCAL CONVECTION DIFFUSION PROBLEMS

  • M. D'Elia – mdelia@sandia.gov
slide-49
SLIDE 49

NONLOCAL CONVECTION DIFFUSION PROBLEMS

  • M. D'Elia – mdelia@sandia.gov
slide-50
SLIDE 50

NONLOCAL CONVECTION DIFFUSION PROBLEMS

  • M. D'Elia – mdelia@sandia.gov
slide-51
SLIDE 51

NONLOCAL CONVECTION DIFFUSION PROBLEMS

  • M. D'Elia – mdelia@sandia.gov
slide-52
SLIDE 52

NONLOCAL CONVECTION DIFFUSION PROBLEMS

  • M. D'Elia – mdelia@sandia.gov
slide-53
SLIDE 53

NONLOCAL CONVECTION DIFFUSION PROBLEMS

  • M. D'Elia – mdelia@sandia.gov
slide-54
SLIDE 54

NONLOCAL CONVECTION DIFFUSION PROBLEMS

  • M. D'Elia – mdelia@sandia.gov
slide-55
SLIDE 55

TIME-DEPENDENT PROBLEMS

  • M. D'Elia – mdelia@sandia.gov
slide-56
SLIDE 56

TIME-DEPENDENT PROBLEMS

  • M. D'Elia – mdelia@sandia.gov
slide-57
SLIDE 57

TIME-DEPENDENT PROBLEMS

  • M. D'Elia – mdelia@sandia.gov
slide-58
SLIDE 58

APPLICATION: MARKOV PROCESSES

  • M. D'Elia – mdelia@sandia.gov
slide-59
SLIDE 59

APPLICATION: MARKOV PROCESSES

  • M. D'Elia – mdelia@sandia.gov
slide-60
SLIDE 60

APPLICATION: MARKOV PROCESSES

  • M. D'Elia – mdelia@sandia.gov
slide-61
SLIDE 61

EXPECTED EXIT TIME

  • M. D'Elia – mdelia@sandia.gov
slide-62
SLIDE 62

EXPECTED EXIT TIME

  • M. D'Elia – mdelia@sandia.gov
slide-63
SLIDE 63

SPECIAL CASES OF THE NONLOCAL OPERATOR

  • M. D'Elia – mdelia@sandia.gov
slide-64
SLIDE 64

SPECIAL CASES OF THE NONLOCAL OPERATOR

  • M. D'Elia – mdelia@sandia.gov
slide-65
SLIDE 65

SPECIAL CASES OF THE NONLOCAL OPERATOR

  • M. D'Elia – mdelia@sandia.gov
slide-66
SLIDE 66

SPECIAL CASES OF THE NONLOCAL OPERATOR

  • M. D'Elia – mdelia@sandia.gov
slide-67
SLIDE 67

CURRENT AND FUTURE WORK

slide-68
SLIDE 68
  • M. D'Elia – mdelia@sandia.gov
slide-69
SLIDE 69
  • M. D'Elia – mdelia@sandia.gov
slide-70
SLIDE 70
  • M. D'Elia – mdelia@sandia.gov
slide-71
SLIDE 71
  • M. D'Elia – mdelia@sandia.gov
slide-72
SLIDE 72
  • M. D'Elia – mdelia@sandia.gov
slide-73
SLIDE 73
slide-74
SLIDE 74

DEFINITION

  • M. D'Elia – mdelia@sandia.gov
slide-75
SLIDE 75