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We present a finite element discretization to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of displacement and ...

Full waveform inversion is a seismic imaging method which requires solving a large-scale minimization problem, typically through local optimization techniques. Most local optimization methods can basically be built up from two choices: the update ...

• Unified presentation and comparison of line search and trust-region globalization methods.
• Innovative introduction of preconditioning through the inner product.
• Comprehensive comparison of the steepest, the l-BFGS and the Newton ...

In this paper we advance the analysis of discretizations for a fluid-structure interaction model of the monolithic coupling between the free flow of a viscous Newtonian fluid and a deformable porous medium separated by an interface. A ...

• Well-posedness of the coupled problem is proved treating the problem as a perturbed saddle-point system.

Using the framework of operator or Calderón preconditioning, uniform preconditioners are constructed for elliptic operators discretized with continuous finite (or boundary) elements. The preconditioners are constructed as the ...

We extend the operator preconditioning framework Hiptmair (2006) [10] to Petrov-Galerkin methods while accounting for parameter-dependent perturbations of both variational forms and their preconditioners, as occurs when performing ...

Operator preconditioning based on decomposition into subspaces has been developed in early 90’s in the works of Nepomnyaschikh, Matsokin, Oswald, Griebel, Dahmen, Kunoth, Rüde, Xu, and others, with inspiration from particular applications, e.g., ...

Least squares methods are effective for solving systems of partial differential equations. In the case of nonlinear systems the equations are usually linearized by a Newton iteration or successive substitution method, and then treated as a linear least ...

Operator preconditioning offers a general recipe for constructing preconditioners for discrete linear operators that have arisen from a Galerkin approach. The key idea is to employ matching Galerkin discretizations of operators of complementary mapping ...