6 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…