1 citations · 2 across the 7 of their papers we have counts for
8 papers
Model reduction of port-Hamiltonian systems via neural networks
Silke Glas, Alexander Heinlein, Harald Monsuur +1
In this paper, we consider structure-preserving model reduction of port-Hamiltonian (pH) systems which extend classical Hamiltonian systems with dissipation and an input-output por…
A least squares finite element method for backward parabolic problems
Harald Monsuur
Backward parabolic equations, such as the backward heat equation, are classical examples of ill-posed problems where solutions may not exist or depend continuously on the data. In…
Preconditioning of a pollution-free discretization of the Helmholtz equation
Harald Monsuur
We present a pollution-free first order system least squares (FOSLS) formulation for the Helmholtz equation, solved iteratively using a block preconditioner. This preconditioner co…
Quasi-Optimal Least Squares: Inhomogeneous boundary conditions, and application with machine learning
Harald Monsuur, Robin Smeets, Rob Stevenson
We construct least squares formulations of PDEs with inhomogeneous essential boundary conditions, where boundary residuals are not measured in unpractical fractional Sobolev norms,…
Ultra-weak least squares discretizations for unique continuation and Cauchy problems
Harald Monsuur, Rob Stevenson
In this paper, conditional stability estimates are derived for unique continuation and Cauchy problems associated to the Poisson equation in ultra-weak variational form. Numerical…
A pollution-free ultra-weak FOSLS discretization of the Helmholtz equation
Harald Monsuur, Rob Stevenson
We consider an ultra-weak first order system discretization of the Helmholtz equation. When employing the optimal test norm, the `ideal' method yields the best approximation to the…
Minimal residual methods in negative or fractional Sobolev norms
Harald Monsuur, Rob Stevenson, Johannes Storn
For numerical approximation the reformulation of a PDE as a residual minimisation problem has the advantages that the resulting linear system is symmetric positive definite, and th…
Least squares solvers for ill-posed PDEs that are conditionally stable
Wolfgang Dahmen, Harald Monsuur, Rob Stevenson
This paper is concerned with the design and analysis of least squares solvers for ill-posed PDEs that are conditionally stable. The norms and the regularization term used in the le…