The purpose of this paper is to introduce a new strategy to improve the convergence and efficiency of the class of domain decomposition known as Schur complement techniques related to interface variables for the simulation of mechanical, electrical and thermal problems in presence of cross points. More precisely, we are interested not only in domain decomposition with two equal parts having the same physical properties but rather in more general splitting components. It is known that in the first case, the optimal convergence with good pre-conditioner is obtained in two iterations and the problem is still challenging in the second case. The primary goal then is to fill part of the gap in such problem domain decomposition techniques and to contribute to solve extremely difficult industrial problems of large scale by using parallel sparse direct solver of the multi-core environment of the whole system and handling each part of the system independently of the change of the mesh or the shifting of the mathematical method of resolution and subsequently, we treat the interface as boundary conditions. The numerical experiments of our algorithm are performed on few models arising from discretization of partial differential equations using Finite Element Method (FEM).
- Quarteroni A., Valli A. Domain Decomposition Methods for Partial Differential Equation. Clarendon Press, Oxford (1999).
- Barboteu M. Contact, frottement et techniques de calcul parallèle. Thèse de doctorat, Université Montpellier II (1999).
- Barboteu M., Alart P., Vidrascu M. A domain decomposition strategy for non classical frictional multi-contact problems. Computer Methods in Applied Mechanics and Engineering. 190 (37–38), 4785–4803 (2001).
- Marceau D. Modélisation du contact tridimensionnel avec frottement en grandes transformations et son application à l'étude des dispositifs d'ancrage multitorons. Thèse de doctorat, Département de génie civil, Université Laval (2001).
- Marceau D., Fafard M., Bastien J. Constitutive law for wedge-tendon gripping interface in anchorage device-numerical modeling and parameters identification. Structural Engineering and Mechanics. 15 (6), 609–628 (2003).
- Goulet P. Modélisation du comportement thermo-électro-mécanique des interfacesde contact d'une cuve de Hall-Héroult. Thèse de doctorat, Département de génie chimique, Université Laval (2003).
- Richard D. Aspects thermomécaniques de la modélisation par éléments finis dupréchauffage électrique d'une cuve de Hall-Héroult: Lois constitutives, conception orientée objet et validation. Thè}se de doctorat, Département de génie civil, Université Laval (2004).
- Farhat C., Roux F.-X. A method of finite element tearing and interconnecting its parallel solution algorithm. International Journal for Numerical Methods in Engineering. 32 (6), 1205–1227 (1991).
- Avery P., Rebel G., Lesoinne M., Farhat C. A numerically scalabel dual-primalsubstructuring method for the solution of contact problems – part I: the frictionless case. Computer Methods in Applied Mechanics and Engineering. 193 (23–26), 2403–2426 (2004).
- Dostál Z., Horák D., Kučera R., Vondrák V., Haslinger J., Dobiáš J., Pták S. FETI based algorithms for contact problems: scalability, large displacements and 3D Coulomb friction. Computer Methods in Applied Mechanics and Engineering. 194 (2–5), 395–409 (2005).
- Kalantzis V. A spectral Newton–Schur algorithm for the solution of symmetric generalized eigenvalue problems. Electronic Transactions on Numerical Analysis. 52, 132–153 (2020).
- Saad Y. Method for Sparse Linear Systems. Second ed. with corrections (2000).
- Xing H. L., Fujumoto T., Makinouchi A. Static-explicit fe modeling of 3-D large deformation multibody contact problems on parallel computer. Simulation of Materials Processing: theory Methods and Applications. 207–212 (1998).
- Mandel M. Balancing domain decomposition. Communications in Applied Numerical Methods. 9 (3), 233–241 (1993).