Biochips are physically and/or electronically controllable miniaturized labs. They are used for combinatorial chemical and biological analysis in environmental and medical studies. The precise positioning of the samples on the surface of the chip in picoliter to nanoliter volumes can be done...

We use a nonoverlapping iterative domain decomposition procedure based on the Robin interface condition to develop a new multiscale mixed method to compute the velocity field in heterogeneous porous media. Hybridized mixed finite elements are used for the spatial discretization of the equations....

The neutronic simulation of a nuclear reactor core is performed using the neutron transport equation, and leads to an eigenvalue problem in the steady-state case. Among the deterministic resolution methods, simplified transport (SPN) or diffusion approximations are often used. The MINOS solver...

The method of balanced domain decomposition by constraints is an iterative algorithm for numerical solution of partial differential equations which exploits a non-overlapping partition of a domain. As an essential part of each step, restricted problems are solved on every subdomain and a certain...

The numerical solution of very large three-dimensional electromagnetic field problems are challenging for various applications in the industry. In this paper, we propose a nonoverlapping domain decomposition approach for solving the three-dimensional Maxwell equations on MIMD computers, based on...

A non-overlapping domain decomposition algorithm of Neumann–Neumann type for solving variational inequalities arising from the elliptic boundary value problems in two dimensions with unilateral boundary condition is presented. We suppose that boundary with inequality condition is...

Hydro-thermo-mechanical analysis of reactor vessels based on the finite element method is a very demanding task due to its complexity as well as the large number of unknowns. This contribution deals with efficient computer implementation of the coupled analysis and attention is also devoted to...

The adaptive BDDC method is extended to the selection of face constraints in three dimensions. A new implementation of the BDDC method is presented based on a global formulation without an explicit coarse problem, with massive parallelism provided by a multifrontal solver. Constraints are...

A parallel implementation of the Balancing Domain Decomposition based on Constraints (BDDC) method using the frontal solver is employed to solve systems of linear equations from finite element analysis, and incorporated into a standard finite element system for engineering analysis by linear...

The point of this paper is to review recent theoretical and experimental results related to scalability of the FETI based domain decomposition algorithm that was proposed recently by Dostál, Friedlander, Santos and Gomes for numerical solution of discretized variational inequalities. After...