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

Numerical simulation of endovascular treatment options for cerebral aneurysms. - Frank, Martin; Holzberger, Fabian; Horvat, Medeea; Kirschke, Jan; Mayr, Matthias; Muhr, Markus; Nebulishvili, Natalia; Popp, Alexander; Schwarting, Julian; Wohlmuth, Barbara I. (CoRR, 2024)

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

Asymptotic-preserving and energy stable dynamical low-rank approximation for thermal radiative transfer equations. - Patwardhan, Chinmay; Frank, Martin; Kusch, Jonas (CoRR, 2024)

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

Energy-aware operation of HPC systems in Germany. - Suarez, Estela; Bockelmann, Hendryk; Eicker, Norbert; Eitzinger, Jan; Sayed, Salem El; Fieseler, Thomas; Frank, Martin; Frech, Peter; Giesselmann, Pay; Hackenberg, Daniel; Hager, Georg; Herten, Andreas; et al. (CoRR, 2024)

Numerical Robustness of PINNs for Multiscale Transport Equations. - Jesser, Alexander; Krycki, Kai; McClarren, Ryan G.; Frank, Martin (CoRR, 2024)

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

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

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

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

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

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

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

A low-rank power iteration scheme for neutron transport criticality problems. - Kusch, Jonas; Whewell, Benjamin; McClarren, Ryan G.; Frank, Martin (J. Comput. Phys., 2022)

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

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

A low-rank power iteration scheme for neutron transport criticality problems. - Kusch, Jonas; Whewell, Benjamin; McClarren, Ryan G.; Frank, Martin (CoRR, 2022)

Constructing relaxation systems for lattice Boltzmann methods. - Simonis, Stephan; Frank, Martin; Krause, Mathias J. (CoRR, 2022)

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

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

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

A parallel implementation of a diagonalization-based parallel-in-time integrator. - Caklovic, Gayatri; Speck, Robert; Frank, Martin (CoRR, 2021)

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

A Realizable Filtered Intrusive Polynomial Moment Method. - Alldredge, Graham W.; Frank, Martin; Kusch, Jonas; McClarren, Ryan G. (CoRR, 2021)

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

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

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

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

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

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

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

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

Miniaturized Ultra-Wideband Antenna Design for Human Implants. - Frank, Martin; Lurz, Fabian; Kempf, Markus; Röber, Jürgen; Weigel, Robert; Koelpin, Alexander (2020)

Universal low-cost Transmitarray Antenna Design at 61 GHz for Beam Steering with different Feed Antennas. - Frank, Martin; Lurz, Fabian; Weigel, Robert; Koelpin, Alexander (2020)

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

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

Glycosciences.DB: an annotated data collection linking glycomics and proteomics data (2018 update). - Böhm, Michael; Bohne-Lang, Andreas; Frank, Martin; Loß, Alexander; Rojas-Macias, Miguel A.; Lütteke, Thomas (Nucleic Acids Res., 2019)

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

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

122 GHz Low-cost Substrate Integrated Waveguide based Leaky-Wave Antenna Design. - Frank, Martin; Lurz, Fabian; Weigel, Robert; Koelpin, Alexander (2019)

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

Intrusive acceleration strategies for Uncertainty Quantification for hyperbolic systems of conservation laws. - Kusch, Jonas; Wolters, Jannick; Frank, Martin (CoRR, 2019)

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

Design and characterization of antenna arrays in eWLB package for 61 GHz radar applications. - Frank, Martin; Ghesquière, Pol; Kiefl, Stefan; Weigel, Robert; Koelpin, Alexander (2018)

An Approximation of the M2 Closure: Application to Radiotherapy Dose Simulation. - Pichard, Teddy; Alldredge, Graham W.; Brull, Stéphane; Dubroca, Bruno; Frank, Martin (J. Sci. Comput., 2017)

Derivation and analysis of Lattice Boltzmann schemes for the linearized Euler equations. - Otte, Philipp; Frank, Martin (Comput. Math. Appl., 2016)

Augmenting Mathematics Courses by Problem-Based Learning. - Frank, Martin; Roeckerrath, C. (Int. J. Eng. Pedagog., 2016)

Comparison of different approaches applied in Analytic Hierarchy Process - an example of information needs of patients with rare diseases. - Pauer, Frédéric; Schmidt, Katharina; Babac, Ana; Damm, Kathrin; Frank, Martin; Schulenburg, Johann-Matthias Graf von der (BMC Medical Informatics Decis. Mak., 2016)

An Asymptotic Preserving Two-dimensional Staggered Grid Method for Multiscale Transport Equations. - Küpper, Kerstin; Frank, Martin; Jin, Shi (SIAM J. Numer. Anal., 2016)

Heliostat Field Layout Optimization with Evolutionary Algorithms. - Richter, Pascal; Laukamp, David; Gerdes, Levin; Frank, Martin; Ábrahám, Erika (2016)

Binding energy calculations for hevein-carbohydrate interactions using expanded ensemble molecular dynamics simulations. - Koppisetty, Chaitanya A. K.; Frank, Martin; Lyubartsev, Alexander; Nyholm, Per-Georg (J. Comput. Aided Mol. Des., 2015)

The Nonclassical Boltzmann Equation and DIffusion-Based Approximations to the Boltzmann Equation. - Frank, Martin; Krycki, Kai; Larsen, Edward W.; Vasques, Richard (SIAM J. Appl. Math., 2015)

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

Computational Aspects of Models for Minimizing the Effects of Ectopic Beats on Heart Rate Variability. - Frank, Martin; Bachler, Martin; Wassertheurer, Siegfried; Mayer, Christopher C. (Simul. Notes Eur., 2014)

StaRMAP - A Second Order Staggered Grid Method for Spherical Harmonics Moment Equations of Radiative Transfer. - Seibold, Benjamin; Frank, Martin (ACM Trans. Math. Softw., 2014)

Computation of Binding Energies Including Their Enthalpy and Entropy Components for Protein-Ligand Complexes Using Support Vector Machines. - Koppisetty, Chaitanya A. K.; Frank, Martin; Kemp, Graham J. L.; Nyholm, Per-Georg (J. Chem. Inf. Model., 2013)

Asymptotic derivation and numerical investigation of time-dependent simplified PN equations. - Olbrant, Edgar; Larsen, Edward W.; Frank, Martin; Seibold, Benjamin (J. Comput. Phys., 2013)

Spiral search based fast rotation estimation for efficient HEVC compression of navigation video sequences. - Springer, Dominic; Frank, Martin; Simmet, Franz; Niederkorn, Dieter; Kaup, André (2013)

Optimal radiotherapy treatment planning using minimum entropy models. - Barnard, Richard C.; Frank, Martin; Herty, Michael (Appl. Math. Comput., 2012)

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

Adaptive Finite Element Simulation of the Time-dependent Simplified P N Equations. - Frank, Martin; Lang, Jens; Schäfer, Matthias (J. Sci. Comput., 2011)

Diffusive Corrections to PN Approximations. - Schäfer, Matthias; Frank, Martin; Levermore, C. David (Multiscale Model. Simul., 2011)

GlycomeDB - a unified database for carbohydrate structures. - Ranzinger, René; Herget, Stephan; Lieth, Claus-Wilhelm von der; Frank, Martin (Nucleic Acids Res., 2011)

Generalized Fokker-Planck Theory for Electron and Photon Transport in Biological Tissues: Application to Radiotherapy. - Olbrant, Edgar; Frank, Martin (Comput. Math. Methods Medicine, 2010)

The coolest path problem. - Frank, Martin; Fügenschuh, Armin; Herty, Michael; Schewe, Lars (Networks Heterog. Media, 2010)

Forschungsarbeiten zur Simulation Diskreter Prozesse und zu objektorientierter Simulationssoftware an der IHD. - Frank, Martin (2008)

Existence and bounds for the half-moment entropy approximation to radiative transfer. - Frank, Martin; Pinnau, René (Appl. Math. Lett., 2007)

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

GlycoMapsDB: a database of the accessible conformational space of glycosidic linkages. - Frank, Martin; Lütteke, Thomas; Lieth, Claus-Wilhelm von der (Nucleic Acids Res., 2007)

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

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

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

Carbohydrate Structure Suite (CSS): analysis of carbohydrate 3D structures derived from the PDB. - Lütteke, Thomas; Frank, Martin; Lieth, Claus-Wilhelm von der (Nucleic Acids Res., 2005)

Bioinformatics for glycomics: Status, methods, requirements and perspectives. - Lieth, Claus-Wilhelm von der; Bohne-Lang, Andreas; Lohmann, Klaus Karl; Frank, Martin (Briefings Bioinform., 2004)

glycosciences.de: An Internet Portal for Glyco-related Data from Open Access Resources. - Götz, Thomas; Bohne-Lang, Andreas; Frank, Martin; Lohmann, Klaus Karl; Loß, Alexander; Lütteke, Thomas; Lieth, Claus-Wilhelm von der (2004)

Knowledge-based approach for the rapid generation of a representative ensemble of N-glycan conformations. - Frank, Martin; Bohne, Andreas; Wetter, Thomas; Lieth, Claus-Wilhelm von der (Silico Biol., 2002)

Proceedings of the WWW2002 International Workshop on the Semantic Web, Hawaii, May 7, 2002 (CEUR-WS.org, 2002)

Glycosylation of Proteins: A Computer-Based Method for Rapid Exploration of Conformational Space of N-Glycans. - Bohne, Andreas; Frank, Martin; Wetter, Thomas; Lieth, Claus-Wilhelm von der (2001)

AN intelligent user interface for mixed-initiative multi-source travel planning. - Frank, Martin; Muslea, Maria; Oh, Jean; Minton, Steven; Knoblock, Craig A. (2001)

Mixed-initiative, multi-source information assistants. - Knoblock, Craig A.; Minton, Steven; Ambite, José Luis; Muslea, Maria; Oh, Jean; Frank, Martin (2001)

Das objektorientierte Modellierungskonzept des Simulationssystems TOMAS. - Frank, Martin (1990)

Tools for Computer Aided Design of Production Processes. - Frank, Martin (1984)