2 citations · 7 across the 8 of their papers we have counts for
6 papers · 1 filter
Analysis of Moment Closures Using -Divergences for Rarefied Dynamics with Binary Collisions and Their Galerkin Discretizations
Michael R. A. Abdelmalik, Irene M. Gamba, Torsten Keßler +1
This work introduces a robust deterministic framework for approximating solutions of the Boltzmann equation with binary collisions by discretizing their dependence on time, positio…
Wigner-Eckart Factorization of the Polyatomic Boltzmann Collision Operator
Torsten Keßler, Bas W. T. Gieling, René R. Hiemstra +1
We extend the Wigner-Eckart factorization of the spectral Boltzmann collision operator to polyatomic gases with continuous internal energy. Because internal energies are invariant…
When can a neural operator replace a coarse solve? Architectural principles for two-level preconditioning
Hugo Melchers, Victorita Dolean, Michael Abdelmalik
Neural operators are increasingly used as accelerators inside classical numerical methods, but it is rarely clear which architectural ingredients matter for which application. We a…
An optimal Petrov-Galerkin framework for operator networks
Philip Charles, Deep Ray, Yue Yu +7
The optimal Petrov-Galerkin formulation to solve partial differential equations (PDEs) recovers the best approximation in a specified finite-dimensional (trial) space with respect…
Variationally Mimetic Operator Networks
Dhruv Patel, Deep Ray, Michael R. A. Abdelmalik +2
In recent years operator networks have emerged as promising deep learning tools for approximating the solution to partial differential equations (PDEs). These networks map input fu…
Goal-Oriented Adaptive THB-Spline Schemes for PDE-Based Planar Parameterization
Jochen Hinz, Michael Abdelmalik, Matthias Möller
This paper presents a PDE-based planar parameterization framework with support for Truncated Hierarchical B-Splines (THB-splines). For this, we adopt the a posteriori refinement st…