A new domain decomposition strategy based on the hybrid FE-MESHLESS method

A new strategy for improving the convergence and efficiency of the class of domain decomposition known as interface variable related Schur complement techniques for simulating mechanical, electrical and thermal problems in the presence of cross points is examined in this work. To be more precise, we're not just interested in domain decomposition into two parts with the same physical properties, but rather in more general splitting components. In the first case, we obtain optimal convergence with a good pre-conditioner in two iterations, while the problem remains difficult in the second case. The primary objective is therefore to fill in some of the gaps in these problem domain decomposition techniques and to contribute to the solution of extremely difficult large-scale industrial problems. A parallel sparse direct solver of the multi-core environment of the whole system is used and each part of the system is handled independently of the change of the mesh or the shifting of the mathematical method of resolution, and subsequently, the interface is treated as boundary condition. The numerical experiments of our algorithm are performed on a few models arising from discretizations of partial differential equations using the finite element method and a meshless method.