Domain decomposition involving subdomain separable space representations for solving parametric problems in complex geometries

Mohammad Javad Kazemzadeh-Parsi (1, 2) , Amine Ammar (1) , Francisco Chinesta (3)

1 LAMPA - Laboratoire Angevin de Mécanique, Procédés et InnovAtion
2 Islamic Azad University
3 PIMM - Laboratoire Procédés et Ingénierie en Mécanique et Matériaux

A domain decomposition technique combined with an enhanced geometry mapping based on the use of NURBS is considered for solving parametrized models in complex geometries (non simply connected) within the so-called proper generalized decomposition (PGD) framework, enabling the expression of the solution in each subdomain in a fully separated form, involving both the space and the model parameters. NURBS allow a compact and powerful domain mapping into a fully separated reference geometry, while the PGD allows recovering an affine structure of the problem in the reference domain, facilitating the use of the standard PGD solver for computing the parametric solution in each subdomain first, and then by enforcing the interface transmission conditions, in the whole domain.

Mots clés: Space separated representation; Domain decomposition; PGD; NURBS

Domaines: Analyse numérique [math.NA]; Autre

Mohammad Javad Kazemzadeh-Parsi, Amine Ammar, Francisco Chinesta. Domain decomposition involving subdomain separable space representations for solving parametric problems in complex geometries. Advanced Modeling and Simulation in Engineering Sciences, 2022, 9, pp.2. ⟨10.1186/s40323-022-00216-w⟩. ⟨hal-03708814⟩