Abstract
First, the effectivity of classical Proper Generalized Decomposition (PGD) computational methods is analyzed on a one dimensional transient diffusion benchmark problem, with a moving load. Classical PGD methods refer to Galerkin, Petrov–Galerkin and Minimum Residual formulations. A new and promising PGD computational method based on the Constitutive Relation Error concept is then proposed and provides an improved, immediate and robust reduction error estimation. All those methods are compared to a reference Singular Value Decomposition reduced solution using the energy norm. Eventually, the variable separation assumption itself (here time and space) is analyzed with respect to the loading velocity.
Highlights
Nowadays, numerical simulations constitute a common tool in science and engineering activities
The first goal of this paper is to compare the effectivity of the classical Proper Generalized Decomposition (PGD) computational methods which are all built on a progressive algorithm [20], rather than solving the m basis functions at once
Minimal CRE performances In “Minimisation of the Constitutive Relation Error” we proposed a new PGD computational method based on the minimization of CRE, with two variants
Summary
Numerical simulations constitute a common tool in science and engineering activities. In order to give an accurate representation of the real world, a large set of parameters and nonlinearities may need to be introduced in the mathematical models involved in the simulation, leading to important and often overwhelming computational effort. This results in a huge number of degrees of freedom, a drawback for such complex models, so that they cannot be tackled with classical brute force methods. These methods exploit the fact that the response of complex models can often be approximated with a reasonable accuracy by the response of a surrogate model, seen as the projection of the initial one on a lower dimensional
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