arXiv subjects

Magne Nordaas

Publications and source records attributed to Magne Nordaas.

3 recordsLinked to original sources

arXiv2017

Solving Poisson's Equation on the Microsoft HoloLens

We present a mixed reality application (HoloFEM) for the Microsoft HoloLens. The application lets a user define and solve a physical problem governed by Poisson's equation with the surrounding real world geometry as input data. Holograms are used to visualise both the problem and the solution. The finite element method is used to solve Poisson's equation. Solving and visualising partial differential equations in mixed reality could have potential usage in areas such as building planning and safety engineering.

cs.GR↗

arXiv2016

Efficient preconditioners for saddle point systems with trace constraints coupling 2D and 1D domains

We study preconditioners for a model problem describing the coupling of two elliptic subproblems posed over domains with different topological dimension by a parameter dependent constraint. A pair of parameter robust and efficient preconditioners is proposed and analyzed. Robustness and efficiency of the preconditioners is demonstrated by numerical experiments.

math.NA↗

arXiv2015

Robust preconditioners for PDE-constrained optimization with limited observations

Regularization robust preconditioners for PDE-constrained optimization problems have been successfully developed. These methods, however, typically assume that observation data is available throughout the entire domain of the state equation. For many inverse problems, this is an unrealistic assumption. In this paper we propose and analyze preconditioners for PDE-constrained optimization problems with limited observation data, e.g. observations are only available at the boundary of the solution domain. Our methods are robust with respect to both the regularization parameter and the mesh size. That is, the condition number of the preconditioned optimality system is uniformly bounded, independently of the size of these two parameters. We first consider a prototypical elliptic control problem and thereafter more general PDE-constrained optimization problems. Our theoretical findings are illuminated by several numerical results.

math.OC↗