Abstract
A numerical study is presented on reduced order modeling of low and high-dimensional partial differential equations using a new B-spline Galerkin proper generalized decomposition (PGD) method. Galerkin-PGD schemes based on B-splines are numerically investigated for various benchmark problems, including the Poisson equation, linear/nonlinear advection–diffusion equations, and the Navier–Stokes equations. The treatment of inhomogeneous boundary conditions, non-separable terms and nonlinearities is numerically investigated. Numerical errors for high-fidelity B-spline solutions and reduced order solutions are provided to demonstrate the effectiveness and accuracy of the proposed method. Computational costs are reported to illustrate the efficiency of the developed approaches.
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