Preconditioning iterative solvers via the Empirical Interscale Finite Element Method (EIFEM)
This work explores the use of the Empirical Interscale Finite Element Method (EIFEM) as a novel preconditioner for iterative solvers in the linear elastic regime. Originally developed as a multiscale Reduced Order Model (ROM), EIFEM captures the kinematics of a unit cell and leverages static condens...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:dnet:upcommonspor::576fa22755e9b2f533fb428127174b61 |
| Acceso en línea: | https://hdl.handle.net/2117/461030 https://dx.doi.org/10.1016/j.cma.2025.118257 |
| Access Level: | acceso embargado |
| Palabra clave: | Preconditioning Reduced-Order Modeling Architected materials Multiscale mechanics Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics |
| Sumario: | This work explores the use of the Empirical Interscale Finite Element Method (EIFEM) as a novel preconditioner for iterative solvers in the linear elastic regime. Originally developed as a multiscale Reduced Order Model (ROM), EIFEM captures the kinematics of a unit cell and leverages static condensation with a reduced basis to construct a coarse approximation. We integrate EIFEM as a coarse space within a preconditioned conjugate gradient solver, incorporating pre- and post-smoothing steps. Numerical experiments confirm that EIFEM-based preconditioning significantly reduces iteration counts, particularly for near-solid structures. Although non-solid structures also benefit from reduced iteration counts, the convergence rate is lower compared to solid or nearly-solid cases. This behavior stems from the sensitivity of the solver to the accuracy of the ROM approximation, and we show discontinuous edge functions and discuss other potential strategies as a way to enhance this accuracy. In terms of scalability, the preconditioner is robust, maintaining a nearly constant iteration count as the problem size increases. This work is the first application of EIFEM for preconditioning purposes, demonstrating its potential as a scalable and efficient preconditioner for iterative solvers in 2D and 3D geometries. |
|---|