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math.NA2025
Adaptive meshfree approximation for linear elliptic partial differential equations with PDE-greedy kernel methods
Tizian Wenzel, Daniel Winkle, Gabriele Santin +1
We consider meshless approximation for solutions of boundary value problems (BVPs) of elliptic Partial Differential Equations (PDEs) via symmetric kernel collocation. We discuss th…
math.NA2024
Error Analysis of Randomized Symplectic Model Order Reduction for Hamiltonian systems
Robin Herkert, Patrick Buchfink, Bernard Haasdonk +2
Solving high-dimensional dynamical systems in multi-query or real-time applications requires efficient surrogate modelling techniques, as e.g., achieved via model order reduction (…
math.NA2024
Model reduction on manifolds: A differential geometric framework
Patrick Buchfink, Silke Glas, Bernard Haasdonk +1
Using nonlinear projections and preserving structure in model order reduction (MOR) are currently active research fields. In this paper, we provide a novel differential geometric f…