Proper Generalized Decomposition with time adaptive space separation for transient wave propagation problems in separable domains

Abstract

Transient wave propagation problems may involve rich discretizations, both in space and in time, leading to computationally expensive simulations, even for simple spatial domains. The Proper Generalized Decomposition (PGD) is an attractive model order reduction technique to address this issue, especially when the spatial domain is separable. In this work, we propose a space separation with a time adaptive number of modes to efficiently capture transient wave propagation in separable domains. We combine standard time integration schemes with this original space separated representation for empowering standard procedures. The numerical behavior of the proposed method is explored through several 2D wave propagation problems involving radial waves, propagation on long time analyses, and wave conversions. We show that the PGD solution approximates its standard finite element solution counterpart with acceptable accuracy, while reducing the storage needs and the computation time (CPU time). Numerical results show that the CPU time per time step linearly increases when refining the mesh, even with implicit time integration schemes, which is not the case with standard procedures.