28 citations · 56 across the 11 of their papers we have counts for
11 papers
A robust and time-parallel preconditioner for parabolic reconstruction problems using Isogeometric Analysis
Kent-Andre Mardal, Jarle Sogn, Stefan Takacs
We consider a PDE-constrained optimization problem of tracking type with parabolic state equation. The solution to the problem is characterized by the Karush-Kuhn-Tucker (KKT) syst…
Variational Formulations of the Strong Formulation -- Forward and Inverse Modeling using Isogeometric Analysis and Physics-Informed Networks
Kent-Andre Mardal, Jarle Sogn, Marius Zeinhofer
The recently introduced Physics-Informed Neural Networks (PINNs) have popularized least squares formulations of both forward and inverse problems involving partial differential equ…
Isogeometric Tearing and Interconnecting Solvers for Linearized Elasticity in multi-patch Isogeometric Analysis
Jarle Sogn, Stefan Takacs
We consider the linearized elasticity equation, discretized with multi-patch Isogeometric Analysis. A standard discretization error analysis is based on Korn's inequality, which de…
Stable discretizations and IETI-DP solvers for the Stokes system in multi-patch Isogeometric Analysis
Jarle Sogn, Stefan Takacs
We are interested in a fast solver for the Stokes equations, discretized with multi-patch Isogeometric Analysis. In the last years, several inf-sup stable discretizations for the S…
Multigrid solvers for isogeometric discretizations of the second biharmonic problem
Jarle Sogn, Stefan Takacs
We develop a multigrid solver for the second biharmonic problem in the context of Isogeometric Analysis (IgA), where we also allow a zero-order term. In a previous paper, the autho…
Dual-Primal Isogeometric Tearing and Interconnecting methods for the Stokes problem
Jarle Sogn, Stefan Takacs
We are interested in a fast solver for linear systems obtained by discretizing the Stokes problem with multi-patch Isogeometric Analysis. We use Dual-Primal Isogeometric Tearing an…
Robust preconditioning and error estimates for optimal control of the convection-diffusion-reaction equation with limited observation in Isogeometric analysis
Kent-Andre Mardal, Jarle Sogn, Stefan Takacs
In this paper we analyze an optimization problem with limited observation governed by a convection--diffusion--reaction equation. Motivated by a Schur complement approach, we arriv…
Robust Preconditioners for Multiple Saddle Point Problems and Applications to Optimal Control Problems
Alexander Beigl, Jarle Sogn, Walter Zulehner
In this paper we consider multiple saddle point problems with block tridiagonal Hessian in a Hilbert space setting. Well-posedness and the related issue of preconditioning are disc…
Preconditioning Inverse Problems for Hyperbolic Equations with Applications to Photoacoustic Tomography
Alexander Beigl, Otmar Scherzer, Jarle Sogn +1
This paper is concerned with robust preconditioning of wave equations constrained linear inverse problems from boundary observation data. The main result of this paper is a concept…
Robust multigrid solvers for the biharmonic problem in isogeometric analysis
Jarle Sogn, Stefan Takacs
In this paper, we develop multigrid solvers for the biharmonic problem in the framework of isogeometric analysis (IgA). In this framework, one typically sets up B-splines on the un…
Schur complement preconditioners for multiple saddle point problems of block tridiagonal form with application to optimization problems
Jarle Sogn, Walter Zulehner
The importance of Schur complement based preconditioners are well-established for classical saddle point problems in . In this paper we extend the…