A new algorithm of proper generalized decomposition for parametric symmetric elliptic problems. (English) Zbl 1447.35145
The work is a really technical one with very abstract formulations. The authors build an iterative deflation algorithm to approximate the solution of a parametric family of elliptic problems, and show its convergence. They explain why this algorithm is a genuine extension of both POD (proper orthogonal decomposition) and PGD (proper generalized decomposition) algorithms. Actually they prove the strong convergence in the parametric elliptic norm of the deflation algorithm for quite general parametric elliptic operators.
Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca)
MSC:
| 35J35 | Variational methods for higher-order elliptic equations |
| 35Pxx | Spectral theory and eigenvalue problems for partial differential equations |
| 47A80 | Tensor products of linear operators |
Keywords:
proper orthogonal decomposition; proper generalized decomposition; online computation; reduced order modeling; symmetric elliptic problems; deflation algorithmReferences:
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