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See detailA hyper-reduction method using adaptivity to cut the assembly costs of reduced order models
Hale, Jack UL; Schenone, Elisa; Baroli, Davide UL et al

E-print/Working paper (2019)

At every iteration or timestep of the online phase of some reduced-order modelling schemes, large linear systems must be assembled and then projected onto a reduced order basis of small dimension. The ... [more ▼]

At every iteration or timestep of the online phase of some reduced-order modelling schemes, large linear systems must be assembled and then projected onto a reduced order basis of small dimension. The projected small linear systems are cheap to solve, but assembly and projection are now the dominant computational cost. In this paper we introduce a new hyper-reduction strategy called reduced assembly (RA) that drastically cuts these costs. RA consists of a triangulation adaptation algorithm that uses a local error indicator to con- struct a reduced assembly triangulation specially suited to the reduced order basis. Crucially, this reduced assembly triangulation has fewer cells than the original one, resulting in lower assembly and projection costs. We demonstrate the efficacy of RA on a Galerkin-POD type reduced order model (RAPOD). We show performance increases of up to five times over the baseline Galerkin-POD method on a non-linear reaction-diffusion problem solved with a semi-implicit time-stepping scheme and up to seven times for a 3D hyperelasticity problem solved with a continuation Newton-Raphson algorithm. The examples are implemented in the DOLFIN finite element solver using PETSc and SLEPc for linear algebra. Full code and data files to produce the results in this paper are provided as supplementary material. [less ▲]

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See detailPOD-based reduction methods, the Quasicontinuum Method and their Resemblance
Beex, Lars UL; Schenone, Elisa; Hale, Jack UL

Scientific Conference (2016, June 27)

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See detailPOD-based Reduction Methods, the Quasicontinuum Method and their Resemblance
Schenone, Elisa; Hale, Jack UL; Beex, Lars UL

Scientific Conference (2016, June)

POD-based reduction methods and the quasicontinuum method share two similar reduction steps to increase the computational speed of large mechanical models. Here, they are compared with each other.

Detailed reference viewed: 64 (8 UL)
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See detailReducing non-linear PDEs using a reduced integration proper orthogonal decomposition method
Schenone, Elisa; Hale, Jack UL; Beex, Lars UL et al

Scientific Conference (2016)

Detailed reference viewed: 124 (14 UL)