ME 597A Lecture 4: Generalized Polynomial Chaos for UQ I - The Galerkin Approach

By Dongbin Xiu1, Akil Narayan2

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

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Researchers should cite this work as follows:

  • Dongbin Xiu, Akil Narayan (2015), "ME 597A Lecture 4: Generalized Polynomial Chaos for UQ I - The Galerkin Approach," http://nanohub.org/resources/22236.

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

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  1. UQ
ME 597A Lecture 4: Generalized Polynomial Chaos for UQ I - The Galerkin Approach
  • Lecture 4: Generalized Polynomial Chaos for UQ, part 1 The Galerkin Approach 1. Lecture 4: Generalized Polynom… 0
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  • Generalized Polynomial Chaos (gPC) 2. Generalized Polynomial Chaos (… 88.321654988321654
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  • Technical summary 3. Technical summary 235.03503503503504
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  • A Simple Example 4. A Simple Example 349.44944944944945
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  • A Simple Example 5. A Simple Example 490.9242575909243
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  • A Simple Example 6. A Simple Example 872.03870537203875
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  • Computing a mean and variance 7. Computing a mean and variance 1726.3263263263264
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  • Accuracy of gPC 8. Accuracy of gPC 1960.8942275608943
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  • Accuracy of gPC 9. Accuracy of gPC 2074.507841174508
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  • Non-smooth dependence 10. Non-smooth dependence 2546.57991324658
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  • Non--smooth dependence 11. Non--smooth dependence 2588.355021688355
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  • Observations about gPC - Galerkin 12. Observations about gPC - Galer… 2684.150817484151
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  • Probability distribution 13. Probability distribution 2753.3867200533869
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  • Polynomial Families 14. Polynomial Families 2808.0080080080079
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  • More observations about gPC - Galerkin 15. More observations about gPC - … 2842.4424424424424
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  • Tensor - Product polynomials 16. Tensor - Product polynomials 2933.6002669336003
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  • Summary 17. Summary 2998.4984984984985
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  • Improvements? 18. Improvements? 3065.0316983650318
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  • 19. 3138.6720053386721
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