1887

Abstract

Summary

This work presents an a priori MOR strategy where the multidimensional model equations, with some parameters set as new variables of the problem, are solved. Neither SVD nor previous precomputed solutions are used to build the surrogate model. Instead, the proper generalized decomposition (PGD) is applied. More precisely, the generalized solution is a priori represented using products of separated functions defined in low-dimensional spaces. Each of these functions is evaluated within a greedy algorithm and a Gauss-Seidel approach during the offline phase, reducing the high-dimensional complexity of the original equations. Compared to POD-based methods, multiple crucial benefits appear when using a PGD approximation: (i) a database of solutions for realistic applications is available to the user for any required combination of parameter values, (ii) the access to this database is immediate, and (iii) inversion techniques can be drastically accelerated since all the derivatives with respect to any parameter are also readily available.

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/content/papers/10.3997/2214-4609.201601514
2016-05-31
2020-04-04
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