DeepAI AI Chat
Log In Sign Up

Bi-Parametric Operator Preconditioning

by   Paul Escapil-Inchauspé, et al.

We extend the general operator preconditioning framework [R. Hiptmair, Comput. Math. with Appl. 52 (2006), pp. 699-706] to account for parameter-dependent perturbations of variational forms and their preconditioning. These perturbations can arise, for example, from quadrature approximation or machine precision, when solving variational formulations as in standard finite or boundary element methods. By explicitly considering different perturbation parameters for the original equation and its preconditioning, our bi-parametric abstract setting leads to endomorphisms. Furthermore, thanks to this novel approach, new techniques to enhance iterative linear solvers performance are deduced. Further implications of our results for elliptic operators and second-kind Fredholm operators are given.


page 1

page 2

page 3

page 4


Operator preconditioning: the simplest case

Using the framework of operator or Calderón preconditioning, uniform pre...

An iterative method for solving elliptic Cauchy problems

We investigate the Cauchy problem for elliptic operators with C^∞-coeffi...

Padé-parametric FEM approximation for fractional powers of elliptic operators on manifolds

This paper focuses on numerical approximation for fractional powers of e...

Coercive second-kind boundary integral equations for the Laplace Dirichlet problem on Lipschitz domains

We present new second-kind integral-equation formulations of the interio...

Accelerated Calderón preconditioning for Maxwell transmission problems

We investigate a range of techniques for the acceleration of Calderón (o...

Multilevel approximation of Gaussian random fields: Covariance compression, estimation and spatial prediction

Centered Gaussian random fields (GRFs) indexed by compacta such as smoot...

Automatic stabilization of finite-element simulations using neural networks and hierarchical matrices

Petrov-Galerkin formulations with optimal test functions allow for the s...