Best N-term GPC approximations for a class of stochastic linear elasticity equations
We consider a class of stochastic linear elasticity problems whose elastic moduli depend linearly on a countable set of random variables. The stochastic equation is studied via a deterministic parametric problem on an infinite-dimensional parameter space. We first study the best N-term approximat...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2014
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| Online Access: | https://hdl.handle.net/10356/101359 http://hdl.handle.net/10220/18707 |
| _version_ | 1826120254488576000 |
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| author | Xia, Bingxing. Hoang, Viet Ha. |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Xia, Bingxing. Hoang, Viet Ha. |
| author_sort | Xia, Bingxing. |
| collection | NTU |
| description | We consider a class of stochastic linear elasticity problems whose elastic moduli depend
linearly on a countable set of random variables. The stochastic equation is studied via a
deterministic parametric problem on an infinite-dimensional parameter space. We first
study the best N-term approximation of the generalized polynomial chaos (gpc) expansion
of the solution to the displacement formula by considering a Galerkin projection
onto the space obtained by truncating the gpc expansion. We provide sufficient conditions
on the coefficients of the elastic moduli’s expansion so that a rate of convergence
for this approximation holds. We then consider two classes of stochastic and parametric
mixed elasticity problems. The first one is the Hellinger–Reissner formula for approximating
directly the gpc expansion of the stress. For isotropic problems, the multiplying
constant of the best N-term convergence rate for the displacement formula grows with
the ratio of the Lame constants. We thus consider stochastic and parametric mixed problems
for nearly incompressible isotropic materials whose best N-term approximation rate
is uniform with respect to the ratio of the Lame constants. |
| first_indexed | 2024-10-01T05:13:30Z |
| format | Journal Article |
| id | ntu-10356/101359 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:13:30Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | ntu-10356/1013592020-03-07T12:34:43Z Best N-term GPC approximations for a class of stochastic linear elasticity equations Xia, Bingxing. Hoang, Viet Ha. School of Physical and Mathematical Sciences DRNTU::Science::Mathematics We consider a class of stochastic linear elasticity problems whose elastic moduli depend linearly on a countable set of random variables. The stochastic equation is studied via a deterministic parametric problem on an infinite-dimensional parameter space. We first study the best N-term approximation of the generalized polynomial chaos (gpc) expansion of the solution to the displacement formula by considering a Galerkin projection onto the space obtained by truncating the gpc expansion. We provide sufficient conditions on the coefficients of the elastic moduli’s expansion so that a rate of convergence for this approximation holds. We then consider two classes of stochastic and parametric mixed elasticity problems. The first one is the Hellinger–Reissner formula for approximating directly the gpc expansion of the stress. For isotropic problems, the multiplying constant of the best N-term convergence rate for the displacement formula grows with the ratio of the Lame constants. We thus consider stochastic and parametric mixed problems for nearly incompressible isotropic materials whose best N-term approximation rate is uniform with respect to the ratio of the Lame constants. 2014-01-27T06:34:48Z 2019-12-06T20:37:09Z 2014-01-27T06:34:48Z 2019-12-06T20:37:09Z 2013 2013 Journal Article Xia, B., & Hoang, V. H. (2013). Best N-Term GPC Approximations for a Class of Stochastic Linear Elasticity Equations. Mathematical Models And Methods In Applied Sciences, 24(3), 1-40. https://hdl.handle.net/10356/101359 http://hdl.handle.net/10220/18707 10.1142/S0218202513500589 en Mathematical models and methods in applied sciences © 2013 World Scientific Publishing Company. 40 p. |
| spellingShingle | DRNTU::Science::Mathematics Xia, Bingxing. Hoang, Viet Ha. Best N-term GPC approximations for a class of stochastic linear elasticity equations |
| title | Best N-term GPC approximations for a class of stochastic linear elasticity equations |
| title_full | Best N-term GPC approximations for a class of stochastic linear elasticity equations |
| title_fullStr | Best N-term GPC approximations for a class of stochastic linear elasticity equations |
| title_full_unstemmed | Best N-term GPC approximations for a class of stochastic linear elasticity equations |
| title_short | Best N-term GPC approximations for a class of stochastic linear elasticity equations |
| title_sort | best n term gpc approximations for a class of stochastic linear elasticity equations |
| topic | DRNTU::Science::Mathematics |
| url | https://hdl.handle.net/10356/101359 http://hdl.handle.net/10220/18707 |
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