A Study on the LATIN-PGD Method: Analysis of Some Variants in the Light of the Latest Developments

The LATIN-PGD method is a powerful alternative to the Newton–Raphson scheme for solving non-linear time-dependent problems in combination with reduced-order modeling methods. Many developments have been carried out over the last few decades and have led to some variants of the LATIN-PGD method. However, only few comparisons have been made between these variants and none using the digital resources now available. In this article, a comparison between the two major variants of the LATIN-PGD method, as well as with the Newton–Raphson one, is performed using a unified software which highlights the assets of the LATIN-PGD. Various test cases dealing with elasto-visco-plastic problems are undertaken, including comparison with commercial solvers, which reveals the interesting time saving in favor of the LATIN-PGD method.