FE2 multiscale in linear elasticity based on parametrized microscale models using proper generalized decomposition

Multiscale structural topology optimization with an approximate constitutive model for local material microstructure

“…Note that, by simultaneous use of parallel computing and ROM [22], a further reduction in computational time can be achieved in multiscale analysis [23]. Most of the existing ROMs constructed using reduction strategies such as Proper Orthogonal Decomposition (POD) [24,25], Proper Generalized Decomposition (PGD) [26][27][28], material map model [29,30], eigendeformation-based reduction [31,32], Nonuniform Transformation Field Analysis (NTFA) [33][34][35][36], and Numerical EXplicit Potentials (NEXP) [37,38] are developed intending to represent the effective constitutive law of nonlinear heterogeneous materials.…”

Computational analysis of damage in hybrid composite structure

“…These types solve a damage progression in micro-models at every integration point of an FEM macro-model. A substantial reduction of sometimes enormous computational time can be effected using a high level of parallelisation [20]. The mean field approaches are further typical methods of nonlinear homogenisation, [8].…”

Computational vademecums for real‐time simulation of surgical cutting in haptic environments

“…More recently, proper generalized decomposition (PGD) methods further simplify this approach by eliminating the need for the offline computation of snapshots of the system. In essence, PGD determines on the fly the best basis for the simulation of the system (although results are often not optimal as in POD) and, notably, allow to solve efficiently high‐dimensional problems .…”