2 citations · 7 across the 8 of their papers we have counts for
9 papers
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…
Neural Green's Operators for Parametric Partial Differential Equations
Hugo Melchers, Joost Prins, Michael Abdelmalik
This work introduces a paradigm for constructing parametric neural operators that are derived from finite-dimensional representations of Green's operators for linear partial differ…
Moment Methods for the 3D Radiative Transfer Equation Based on -Divergences
Michael R. A. Abdelmalik, Zhenning Cai, Teddy Pichard
The method of moments is widely used for the reduction of kinetic equations into fluid models. It consists in extracting the moments of the kinetic equation with respect to a veloc…
A conservative Galerkin solver for the quasilinear diffusion model in magnetized plasmas
Kun Huang, Michael Abdelmalik, Boris Breizman +1
The quasilinear theory describes the resonant interaction between particles and waves with two coupled equations: one for the evolution of the particle probability density function…
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…