A Schur-complement model-order-reduction technique for the finite element solution of transient elastohydrodynamic lubrication problems. (January 2019)

• Record Type: Journal Article
• Authors: Habchi, W.
• Is Part Of: Advances in engineering software. Volume 127(2019)
• Page Start: 28
• Page End: 37
• Publication Date: 2019-01
• Subjects: Transient elastohydrodynamic lubrication -- Finite elements -- Model order reduction -- Schur-complement method; Computer-aided engineering -- Periodicals; Engineering -- Computer programs -- Periodicals; Engineering -- Software -- Periodicals; Periodicals; 620.0028553
• DOI: 10.1016/j.advengsoft.2018.10.007
• Languages: English
• ISSNs: 0965-9978

Abstract

Highlights: Reduced order finite element modeling of transient elastohydrodynamic lubrication problems. Model order reduction technique is based on Schur-complement method. Model order reduction technique is exact and introduces no additional errors. Model order reduction technique speeds up computational times by an order of 15:1. Model is based on full-coupling of involved physics, leading to fast convergence characteristics. Abstract: The current work presents a reduced order finite element modeling framework for the solution of transient elastohydrodynamic lubrication (EHL) problems. The model order reduction technique is based on a Schur-complement method, applied to the elastic part within EHL problems. As such, it is exact and introduces no additional errors to the solution, with respect to the standard non-reduced finite element model. The technique reduces by one, the dimension of the linear elasticity part within the EHL problem. The use of the Schur-complement method however leads to a semi-dense Jacobian matrix. This is why the technique is complemented with a splitting procedure, allowing it to retrieve a standard finite-element-like sparsity pattern. In terms of computational performance, it is shown through a set of numerical experiments that the proposed reduced model offers a speed-up in computational times of the order of 15:1, compared to the equivalent full model, without any compromise on the accuracy of the solution.