5 papers · 1 filter
Metric-driven numerical methods
Patrick Henning, Laura Huynh, Daniel Peterseim
In this paper, we explore the concept of metric-driven numerical methods as a powerful tool for solving various types of multiscale partial differential equations. Our focus is on…
A Simple Collocation-Type Approach to Numerical Stochastic Homogenization
Moritz Hauck, Hannah Mohr, Daniel Peterseim
This paper proposes a novel collocation-type numerical stochastic homogenization method for prototypical stochastic homogenization problems with random coefficient fields of small…
Hierarchical Super-Localized Orthogonal Decomposition Method
Jose C. Garay, Hannah Mohr, Daniel Peterseim +1
We present the construction of a sparse-compressed operator that approximates the solution operator of elliptic PDEs with rough coefficients. To derive the compressed operator, we…
Riemannian Newton methods for energy minimization problems of Kohn-Sham type
R. Altmann, D. Peterseim, T. Stykel
This paper is devoted to the numerical solution of constrained energy minimization problems arising in computational physics and chemistry such as the Gross-Pitaevskii and Kohn-Sha…
Positivity preserving finite element method for the Gross-Pitaevskii ground state: discrete uniqueness and global convergence
Moritz Hauck, Yizhou Liang, Daniel Peterseim
We propose a positivity preserving finite element discretization for the nonlinear Gross-Pitaevskii eigenvalue problem. The method employs mass lumping techniques, which allow to t…