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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.

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

  2. Introduction

  3. NONLOCAL MODELS M. D'Elia – mdelia@sandia.gov

  4. NONLOCAL MODELS M. D'Elia – mdelia@sandia.gov

  5. NONLOCAL MODELS M. D'Elia – mdelia@sandia.gov

  6. NONLOCAL MODELS M. D'Elia – mdelia@sandia.gov

  7. NONLOCAL MODELS M. D'Elia – mdelia@sandia.gov

  8. FRACTIONAL (NONLOCAL) MODELS M. D'Elia – mdelia@sandia.gov

  9. FRACTIONAL (NONLOCAL) MODELS M. D'Elia – mdelia@sandia.gov

  10. FRACTIONAL (NONLOCAL) MODELS M. D'Elia – mdelia@sandia.gov

  11. FRACTIONAL (NONLOCAL) MODELS M. D'Elia – mdelia@sandia.gov

  12. FRACTIONAL (NONLOCAL) MODELS M. D'Elia – mdelia@sandia.gov

  13. FRACTIONAL (NONLOCAL) MODELS M. D'Elia – mdelia@sandia.gov

  14. NOT ONLY STOCHASTIC PROCESSES M. D'Elia – mdelia@sandia.gov

  15. Outline

  16. NONLOCAL VECTOR CALCULUS M. D'Elia – mdelia@sandia.gov

  17. NONLOCAL VECTOR CALCULUS M. D'Elia – mdelia@sandia.gov

  18. NONLOCAL VECTOR CALCULUS M. D'Elia – mdelia@sandia.gov

  19. NONLOCAL VECTOR CALCULUS M. D'Elia – mdelia@sandia.gov

  20. NONLOCAL VECTOR CALCULUS M. D'Elia – mdelia@sandia.gov

  21. NONLOCAL VECTOR CALCULUS M. D'Elia – mdelia@sandia.gov

  22. NONLOCAL VECTOR CALCULUS M. D'Elia – mdelia@sandia.gov

  23. NONLOCAL VECTOR CALCULUS M. D'Elia – mdelia@sandia.gov

  24. NONLOCAL VECTOR CALCULUS M. D'Elia – mdelia@sandia.gov

  25. NONLOCAL VECTOR CALCULUS M. D'Elia – mdelia@sandia.gov

  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

  27. FRACTIONAL and TRUNCATED FRACTIONAL M. D'Elia – mdelia@sandia.gov

  28. FRACTIONAL and TRUNCATED FRACTIONAL M. D'Elia – mdelia@sandia.gov

  29. FRACTIONAL and TRUNCATED FRACTIONAL M. D'Elia – mdelia@sandia.gov

  30. NUMERICAL APPROXIMATION M. D'Elia – mdelia@sandia.gov

  31. NUMERICAL APPROXIMATION M. D'Elia – mdelia@sandia.gov

  32. NUMERICAL APPROXIMATION M. D'Elia – mdelia@sandia.gov

  33. NUMERICAL APPROXIMATION M. D'Elia – mdelia@sandia.gov

  34. NUMERICAL APPROXIMATION M. D'Elia – mdelia@sandia.gov

  35. NUMERICAL APPROXIMATION M. D'Elia – mdelia@sandia.gov

  36. NUMERICAL APPROXIMATION M. D'Elia – mdelia@sandia.gov

  37. NUMERICAL APPROXIMATION M. D'Elia – mdelia@sandia.gov

  38. NUMERICAL APPROXIMATION M. D'Elia – mdelia@sandia.gov

  39. NUMERICAL APPROXIMATION M. D'Elia – mdelia@sandia.gov

  40. NUMERICAL APPROXIMATION M. D'Elia – mdelia@sandia.gov

  41. NUMERICAL APPROXIMATION M. D'Elia – mdelia@sandia.gov

  42. NUMERICAL APPROXIMATION M. D'Elia – mdelia@sandia.gov

  43. NUMERICAL APPROXIMATION M. D'Elia – mdelia@sandia.gov

  44. NONLOCAL CONVECTION-DIFFUSION – MD, Q. Du, M. Gunzburger, R. Lehoucq, Nonlocal convection-diffusion problems on bounded domains and finite-range jump processes, Computational Methods in Applied Mathematics , 29, 2017

  45. NONLOCAL VECTOR CALCULUS – CONVECTION M. D'Elia – mdelia@sandia.gov

  46. NONLOCAL VECTOR CALCULUS – CONVECTION M. D'Elia – mdelia@sandia.gov

  47. NONLOCAL VECTOR CALCULUS – CONVECTION M. D'Elia – mdelia@sandia.gov

  48. NONLOCAL CONVECTION DIFFUSION PROBLEMS M. D'Elia – mdelia@sandia.gov

  49. NONLOCAL CONVECTION DIFFUSION PROBLEMS M. D'Elia – mdelia@sandia.gov

  50. NONLOCAL CONVECTION DIFFUSION PROBLEMS M. D'Elia – mdelia@sandia.gov

  51. NONLOCAL CONVECTION DIFFUSION PROBLEMS M. D'Elia – mdelia@sandia.gov

  52. NONLOCAL CONVECTION DIFFUSION PROBLEMS M. D'Elia – mdelia@sandia.gov

  53. NONLOCAL CONVECTION DIFFUSION PROBLEMS M. D'Elia – mdelia@sandia.gov

  54. NONLOCAL CONVECTION DIFFUSION PROBLEMS M. D'Elia – mdelia@sandia.gov

  55. TIME-DEPENDENT PROBLEMS M. D'Elia – mdelia@sandia.gov

  56. TIME-DEPENDENT PROBLEMS M. D'Elia – mdelia@sandia.gov

  57. TIME-DEPENDENT PROBLEMS M. D'Elia – mdelia@sandia.gov

  58. APPLICATION: MARKOV PROCESSES M. D'Elia – mdelia@sandia.gov

  59. APPLICATION: MARKOV PROCESSES M. D'Elia – mdelia@sandia.gov

  60. APPLICATION: MARKOV PROCESSES M. D'Elia – mdelia@sandia.gov

  61. EXPECTED EXIT TIME M. D'Elia – mdelia@sandia.gov

  62. EXPECTED EXIT TIME M. D'Elia – mdelia@sandia.gov

  63. SPECIAL CASES OF THE NONLOCAL OPERATOR M. D'Elia – mdelia@sandia.gov

  64. SPECIAL CASES OF THE NONLOCAL OPERATOR M. D'Elia – mdelia@sandia.gov

  65. SPECIAL CASES OF THE NONLOCAL OPERATOR M. D'Elia – mdelia@sandia.gov

  66. SPECIAL CASES OF THE NONLOCAL OPERATOR M. D'Elia – mdelia@sandia.gov

  67. CURRENT AND FUTURE WORK

  68. M. D'Elia – mdelia@sandia.gov

  69. M. D'Elia – mdelia@sandia.gov

  70. M. D'Elia – mdelia@sandia.gov

  71. M. D'Elia – mdelia@sandia.gov

  72. M. D'Elia – mdelia@sandia.gov

  74. DEFINITION M. D'Elia – mdelia@sandia.gov

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