Partial moment entropy approximation to radiative heat transfer. - Martin Frank 004; Bruno Dubroca; Axel Klar (J. Comput. Phys., 2006)

Toward Fast and Accurate Deterministic Methods for Dose Calculation in Electron Radiotherapy. - Martin Frank 004; Hartmut Hensel; Axel Klar (IMECS, 2007)

Time-dependent simplified PN approximation to the equations of radiative transfer. - Martin Frank 004; Axel Klar; Edward W. Larsen; Shugo Yasuda (J. Comput. Phys., 2007)

A Fast and Accurate Moment Method for the Fokker-Planck Equation and Applications to Electron Radiotherapy. - Martin Frank 004; Hartmut Hensel; Axel Klar (SIAM J. Appl. Math., 2007)

A realizability-preserving discontinuous Galerkin method for the M1 model of radiative transfer. - Edgar Olbrant; Cory D. Hauck; Martin Frank 004 (J. Comput. Phys., 2012)

Higher Order Mixed-Moment Approximations for the Fokker-Planck Equation in One Space Dimension. - Florian Schneider 004; Graham W. Alldredge; Martin Frank 004; Axel Klar (SIAM J. Appl. Math., 2014)

A comparative study of limiting strategies in discontinuous Galerkin schemes for the M1 model of radiation transport. - Prince Chidyagwai; Martin Frank 004; Florian Schneider 004; Benjamin Seibold (J. Comput. Appl. Math., 2018)

Ray Effect Mitigation for the Discrete Ordinates Method Using Artificial Scattering. - Martin Frank 004; Jonas Kusch; Thomas Camminady; Cory D. Hauck (CoRR, 2019)

Ray effect mitigation for the discrete ordinates method through quadrature rotation. - Thomas Camminady; Martin Frank 004; Kerstin Küpper; Jonas Kusch (J. Comput. Phys., 2019)

A Regularized Entropy-Based Moment Method for Kinetic Equations. - Graham W. Alldredge; Martin Frank 004; Cory D. Hauck (SIAM J. Appl. Math., 2019)

A Positive Asymptotic-Preserving Scheme for Linear Kinetic Transport Equations. - M. Paul Laiu; Martin Frank 004; Cory D. Hauck (SIAM J. Sci. Comput., 2019)

Massively Parallel Stencil Strategies for Radiation Transport Moment Model Simulations. - Marco Berghoff; Martin Frank 004; Benjamin Seibold (ICCS (7), 2020)

Robust Mathematical formulation and Probabilistic Description of Agent-based Computational Economic Market Models. - Maximilian Beikirch; Simon Cramer; Martin Frank 004; Philipp Otte; Emma Pabich; Torsten Trimborn (Adv. Complex Syst., 2020)

A structured approach to the construction of stable linear Lattice Boltzmann collision operator. - Philipp Otte; Martin Frank 004 (Comput. Math. Appl., 2020)

Filtered stochastic Galerkin methods for hyperbolic equations. - Jonas Kusch; Ryan G. McClarren; Martin Frank 004 (J. Comput. Phys., 2020)

Intrusive acceleration strategies for uncertainty quantification for hyperbolic systems of conservation laws. - Jonas Kusch; Jannick Wolters; Martin Frank 004 (J. Comput. Phys., 2020)

A low-rank method for two-dimensional time-dependent radiation transport calculations. - Zhuogang Peng; Ryan G. McClarren; Martin Frank 004 (J. Comput. Phys., 2020)

Dynamical low-rank approximation for Burgers' equation with uncertainty. - Jonas Kusch; Gianluca Ceruti; Lukas Einkemmer; Martin Frank 004 (CoRR, 2021)

On the convergence of the regularized entropy-based moment method for kinetic equations. - Graham W. Alldredge; Martin Frank 004; Jan Giesselmann (CoRR, 2021)

A structure-preserving surrogate model for the closure of the moment system of the Boltzmann equation using convex deep neural networks. - Steffen Schotthöfer; Tianbai Xiao; Martin Frank 004; Cory D. Hauck (CoRR, 2021)

A stochastic kinetic scheme for multi-scale plasma transport with uncertainty quantification. - Tianbai Xiao; Martin Frank 004 (J. Comput. Phys., 2021)

A stochastic kinetic scheme for multi-scale flow transport with uncertainty quantification. - Tianbai Xiao; Martin Frank 004 (J. Comput. Phys., 2021)

Using neural networks to accelerate the solution of the Boltzmann equation. - Tianbai Xiao; Martin Frank 004 (J. Comput. Phys., 2021)

Structure Preserving Neural Networks: A Case Study in the Entropy Closure of the Boltzmann Equation. - Steffen Schotthöfer; Tianbai Xiao; Martin Frank 004; Cory D. Hauck (ICML, 2022)

Neural network-based, structure-preserving entropy closures for the Boltzmann moment system. - Steffen Schotthöfer; Tianbai Xiao; Martin Frank 004; Cory D. Hauck (CoRR, 2022)

A realizable filtered intrusive polynomial moment method. - Graham W. Alldredge; Martin Frank 004; Jonas Kusch; Ryan G. McClarren (J. Comput. Appl. Math., 2022)

Constructing relaxation systems for lattice Boltzmann methods. - Stephan Simonis; Martin Frank 004; Mathias J. Krause (Appl. Math. Lett., 2023)

Implicit propagation of directly addressed grids in lattice Boltzmann methods. - Adrian Kummerländer; Márcio Dorn; Martin Frank 004; Mathias J. Krause (Concurr. Comput. Pract. Exp., 2023)

Multivariate error modeling and uncertainty quantification using importance (re-)weighting for Monte Carlo simulations in particle transport. - Pia Stammer; Lucas Burigo; Oliver Jäkel; Martin Frank 004; Niklas Wahl (J. Comput. Phys., 2023)

RelaxNet: A structure-preserving neural network to approximate the Boltzmann collision operator. - Tianbai Xiao; Martin Frank 004 (J. Comput. Phys., 2023)

Predicting continuum breakdown with deep neural networks. - Tianbai Xiao; Steffen Schotthöfer; Martin Frank 004 (J. Comput. Phys., 2023)

A Flux Reconstruction Stochastic Galerkin Scheme for Hyperbolic Conservation Laws. - Tianbai Xiao; Jonas Kusch; Julian Koellermeier; Martin Frank 004 (J. Sci. Comput., 2023)

Structure-Preserving Operator Learning: Modeling the Collision Operator of Kinetic Equations. - Jae Yong Lee; Steffen Schotthöfer; Tianbai Xiao; Sebastian Krumscheid; Martin Frank 004 (CoRR, 2024)

Structure-preserving neural networks for the regularized entropy-based closure of the Boltzmann moment system. - Steffen Schotthöfer; M. Paul Laiu; Martin Frank 004; Cory D. Hauck (CoRR, 2024)

A stochastic Galerkin lattice Boltzmann method for incompressible fluid flows with uncertainties. - Mingliang Zhong; Tianbai Xiao; Mathias J. Krause; Martin Frank 004; Stephan Simonis (J. Comput. Phys., 2024)

Structure-preserving neural networks for the regularized entropy-based closure of a linear, kinetic, radiative transport equation. - Steffen Schotthöfer; M. Paul Laiu; Martin Frank 004; Cory D. Hauck (J. Comput. Phys., 2025)

OpenLB-UQ: An Uncertainty Quantification Framework for Incompressible Fluid Flow Simulations. - Mingliang Zhong; Adrian Kummerländer; Shota Ito; Mathias J. Krause; Martin Frank 004; Stephan Simonis (CoRR, 2025)

Uncertain data assimilation for urban wind flow simulations with OpenLB-UQ. - Mingliang Zhong; Dennis Teutscher; Adrian Kummerländer; Mathias J. Krause; Martin Frank 004; Stephan Simonis (CoRR, 2025)