Parametric solutions involving geometry integrated with computer-aided design
arXiv:1902.09248 · doi:10.1016/j.cma.2019.112631
Abstract
The main objective of this work is to describe a general and original approach for computing an off-line solution for a set of parameters describing the geometry of the domain. That is, a solution able to include information for different geometrical parameter values and also allowing to compute readily the sensitivities. Instead of problem dependent approaches, a general framework is presented for standard engineering environments where the geometry is defined by means of NURBS. The parameters controlling the geometry are now the control points characterising the NURBS curves or surfaces. The approach proposed here, valid for 2D and 3D scenarios, allows a seamless integration with CAD preprocessors. The proper generalised decomposition (PGD), which is applied here to compute explicit geometrically parametrised solutions, circumvents the curse of dimensionality. Moreover, optimal convergence rates are shown for PGD approximations of incompressible flows.
arXiv comment45 pages, 34 figures
References in corpus (2)
Cited by in corpus (8)
- Nonintrusive proper generalised decomposition for parametrised incompressible flow problems in OpenFOAM
- Separated response surfaces for flows in parametrised domains: comparison of a priori and a posteriori PGD algorithms
- Hybridisable discontinuous Galerkin solution of geometrically parametrised Stokes flows
- An overlapping domain decomposition method for the solution of parametric elliptic problems via proper generalized decomposition
- State Estimation with Model Reduction and Shape Variability. Application to biomedical problems
- A surrogate model for topology optimisation of elastic structures via parametric autoencoders
- Parametric solutions of turbulent incompressible flows in OpenFOAM via the proper generalised decomposition
- Nonintrusive reduced order model for parametric solutions of inertia relief problems