Conference
A robust preconditioner for saddle-point problems in an industrial context
| العنوان: | A robust preconditioner for saddle-point problems in an industrial context |
|---|---|
| المؤلفون: | Bacq, Pierre-Loïc, Ndjinga, Michael, Gerschenfeld, Antoine |
| المساهمون: | Service de Thermo-hydraulique et de Mécanique des Fluides (STMF), Département de Modélisation des Systèmes et Structures (DM2S), Institut des Sciences Appliquées et de la Simulation pour les énergies bas carbone (ISAS), CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Institut des Sciences Appliquées et de la Simulation pour les énergies bas carbone (ISAS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay |
| المصدر: | CANUM 2024 - '-ème Congrès national d’Analyse Numérique ; https://cea.hal.science/cea-04841864 ; CANUM 2024 - '-ème Congrès national d’Analyse Numérique, May 2024, Le Bois-Plage-En-Ré, France ; https://canum2024.math.cnrs.fr/fr/ |
| بيانات النشر: | CCSD |
| سنة النشر: | 2024 |
| المجموعة: | HAL-CEA (Commissariat à l'énergie atomique et aux énergies alternatives) |
| مصطلحات موضوعية: | [INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA] |
| جغرافية الموضوع: | Le Bois-Plage-En-Ré, France |
| الوصف: | International audience ; We consider the linear resolution of saddle-point systems arising from the discretisation of coupled or constrained systems. In many cases, such systems are challenging to solve by iterative methods and the developments of efficient preconditioners is an active field of research [2]. In this presentation, we present a robust block-preconditioner for a 2 × 2 block-system. In this talk, we highlight a problematic that has not been much investigated to the extent of our knowledge. In an industrial context, theoretical hypotheses are often not satisfied. Even the most simple systems of the form of Equation (1) can become challenging to solve for state-of-the-art linear solvers when the diagonal dominance of the block A is lost. Such a difficulty occurs for instance on distorted meshes. Industrial solvers then resort to direct solvers with all the ensuing limitations. To tackle this difficulty, we present an algebraic preconditioner with increased robustness for systems such as Equation (1). The key idea involves an algebraic transformation of the system that compensates the loss of diagonal dominance. Since the approach we propose is algebraic in nature, it can be applied to a broad class of problems. In the context of the talk, we focus on systems encountered during the resolution of the incompressible Navier-Stokes equations discretised on general meshes with PolyMAC [1]. We first highlight the loss of robustness of classical approaches when considering distorted meshes. In a second time, we describe an innovative preconditioner based on an algebraic transformation of the linear system. Numerical results show impressive convergence on problems of industrial complexity. |
| نوع الوثيقة: | conference object |
| اللغة: | English |
| الاتاحة: | https://cea.hal.science/cea-04841864 https://cea.hal.science/cea-04841864v1/document https://cea.hal.science/cea-04841864v1/file/abstract_bacq_canum2024.pdf |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.31595491 |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |