# Numerical and Parallel Scalability of Feti Algorithm for Variational Inequalities

## Ing. David Horak

**Nov. 6, 2001, 2:30 p.m. T 811**

The objective of this talk is to explain the basic principles of recently suggested efficient domain decomposition algorithm for the solution of variational inequalities arising from elliptic problems with inequality boundary conditions (suggested by Dostal, Gomes Neto and Santos) and to present the parallelization strategy that has been employed for implementation of this FETI related solver in PETSc and the numerical experiments. Discretized problem is first turned by duality theory of convex programming into a quadratic programming problem and modified by means of orthogonal projectors to the natural coarse space (suggested by Mandel, Farhat and Roux). The problem is then solved by augmented Lagrangian algorithm with an outer loop for Lagrange multipliers for equality constraints ensuring continuity among nonoverlapping subdomains and inner loop for solution of bound constrained quadratic programming problems. Theoretical results and numerical experiments with parallel solution of a model problem discretized by up to more than eight million of nodal variables give an evidence of both numerical and parallel scalability of the algorithm presented.