ME 597A Lecture 5: Generalized Polynomial Chaos for UQ II - The Collocation Approach

By Dongbin Xiu1, Akil Narayan2

1. Mathematics, Purdue University, West Lafayette, IN 2. Purdue University, West Lafayette, IN

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Researchers should cite this work as follows:

  • Dongbin Xiu, Akil Narayan (2015), "ME 597A Lecture 5: Generalized Polynomial Chaos for UQ II - The Collocation Approach," http://nanohub.org/resources/22237.

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Birck Nanotechnology Center, Room 1001, Purdue University, West Lafayette, IN

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  1. UQ
ME 597A Lecture 5: Generalized Polynomial Chaos for UQ II - The Collocation Approach
  • Lecture 5: Generalized Polynomial Chaos for UQ II - The Collocation Approach 1. Lecture 5: Generalized Polynom… 0
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  • Generalized Polynomial Chaos (gPC) 2. Generalized Polynomial Chaos (… 57.8244911578245
    00:00/00:00
  • gPC Galerkin properties 3. gPC Galerkin properties 326.22622622622623
    00:00/00:00
  • gPC Setup 4. gPC Setup 446.946946946947
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  • Tensor-Product Polynomials 5. Tensor-Product Polynomials 550.08341675008342
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  • Tensor-Product Polynomials 6. Tensor-Product Polynomials 666.56656656656662
    00:00/00:00
  • Problems with Galerkin 7. Problems with Galerkin 742.24224224224224
    00:00/00:00
  • gPC - Collocation 8. gPC - Collocation 1026.1594928261595
    00:00/00:00
  • Reconstruction 9. Reconstruction 1287.0870870870872
    00:00/00:00
  • gPC - Collocation recap 10. gPC - Collocation recap 1391.257924591258
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  • Interpolation 11. Interpolation 1555.9559559559559
    00:00/00:00
  • Interpolation vs. quadrature 12. Interpolation vs. quadrature 1755.4554554554554
    00:00/00:00
  • High dimensionality 13. High dimensionality 2383.6503169836506
    00:00/00:00
  • Sparse grids 14. Sparse grids 2472.2389055722392
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  • Sparse grids - 3 dimensions 15. Sparse grids - 3 dimensions 2536.1027694361028
    00:00/00:00
  • Sparse grids 16. Sparse grids 2585.5188521855189
    00:00/00:00
  • gPC Collocation procedure 17. gPC Collocation procedure 2791.157824491158
    00:00/00:00
  • Collocation example - Human arterial network 18. Collocation example - Human ar… 2963.863863863864
    00:00/00:00
  • 1D Stochastic Model of the Human Arterial Tree 19. 1D Stochastic Model of the Hum… 3158.5251918585254
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  • Summary 20. Summary 3237.1705038371706
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  • Summary 21. Summary 3333.833833833834
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  • References 22. References 3432.032032032032
    00:00/00:00