An explicit-implicit projection approach for solving saddle-point systems arising from parameter identification problems

This paper proposes a new approach to solve sparse linear saddle-point systems arising in large scale parameter estimation approach using energy functionals. The constraints of those systems involve kinematic constraints and sensors ones. The approach is based on a double projection of the generated saddle point system onto the nullspace of the constraints. The first projection onto the kinematic constraints is proposed as an explicit process through the computation of a sparse null basis. Then, we detail the application of a constraint preconditioner within a Krylov subspace solver, as an implicit second projection of the system onto the nullspace of the sensors constraints. We further present and compare approximations of the constraint preconditioner. The approach is implemented in a parallel distributed environment. Significant gains in computational cost and memory are illustrated on several industrial applications in comparison to direct solvers.