Technomathematics Group

Prof. Dr. Axel Klar

Address

Gottlieb-Daimler-Straße
Building: 48, Room: 575
67663 Kaiserslautern

P.O. Box: 3049
67653 Kaiserslautern

Contact

+49 631 205 4986

klar(at)mathematik.uni-kl.de

Research interests

Methods:

  • Asymptotic-induced numerical methods for kinetic and hyperbolic equations 
  • Dynamics on networks
  • Mesh-free particle methods in fluid dynamics
  • Moment methods for  kinetic and transport equations 
  • Interacting particle systems and mean-field limits


Applications:

  • Socioeconomics: modeling and simulation of traffic flow and pedestrian dynamics  
  • Biology: cell motion in tissues and radiation therapy
  • Technology: : nanotechnology, semiconductor manufacturing, fiber dynamics and non-woven textiles

Publications

MathSciNet:  List of publications

MathSciNet:  Author ID

Web of Knowledge: Researcher ID

Scopus: Scopus ID

Google scholar: Google scholar ID

 

Links to my publications and preprints:

2027

  1. G. Dimarco, A. Klar, T. Köfler, L. Pareschi, Asymptotic preserving methods for the low mach limit in discrete velocity models approximating kinetic equation, Comm. Comp. Phys. 41,2,383-414, 2027
  2. A. Klar, Y. Zhou, Error Estimates for Hyperbolic Scaling Limits of Linear Kinetic Models on Networks, arXiv

  3. G. Dimarco, A. Klar, T. Köfler, L. Pareschi, S. Tiwari, High order asymptotic-preserving schemes for kinetic equations from rarefied to incompressible regimes, arXiv 

  4. K. Willems, E. Arlemark, G. Samaey, A. Klar, A Semi-Lagrangian method for the polyatomic ESBGK model, arXiv 

  5. G. Dimarco, A. Klar, T. Köfler, L. Pareschi, S. Tiwari, Y. Zhou, A relaxation system for the low Mach limit of kinetic equations: stability and higher order asymptotic-preserving schemes, arXiv

  6.  

2026

  1. K. Willems, A. Klar, G. Russo, G. Samaey, S.Tiwari, A meshless MUSCL method for the BGK-Boltzmann equation, JCP 563, 115111,  2026.
  2. R. Borsche, T. Damm, A. Klar, Y. Zhou, A spectral approach to interface layers on networks for the linearized kinetic BGK equation with hyperbolic scaling, KRM 24, 51-74,2026.
  3. Willems, Klaas, Tiwari, Sudarshan, Klar, Axel, Higher order mesh-free methods for BGK equation with moving boundaries, Springer Aerospace Technology,Part F1507, 411–419, 2026.
  4. P. Goatin, A.Klar, C. Mezquita, Discrete adjoint gradient computation for multiclass traffic flow models on road networks, Optimization and Engineering,2026
  5. R. Borsche, T. Damm, A. Klar, Y. Zhou, Interface layers and coupling conditions for kinetic equations on networks: a spectral approach, to appear in M3AS, 2026.

 

2025

  1. K. Willems, A. Klar, G. Samaey, Higher order meshless schemes for hyperbolic equations, 105, 90, JSC 2025. 
  2. A. D. Fome, W. Bock, A. Klar, Analysis of a competitive respiratory disease system with quarantine: epidemic thresholds and cross-immunity effects, Appl. Math. Comp. 485, 128968,  2025
  3. A.D. Fome, I. Rodiah, W. Bock, B. Lange, A. Klar, The interplay of influenza and COVID-19 in Germany: a study of competitive disease dynamics with quarantine measures and partial cross-immunity, BMC Public Health, 25, 3044, 2025

2024

  1.  R. Borsche, A. Klar, Moment methods for kinetic traffic flow and a class of macroscopic traffic models, M3AS, 34, 6, 1077-1105, 2024
  2. R. Borsche, A. Klar, A Hierarchy of Kinetic Discrete-Velocity Models for Traffic Flow Derived from a Non-local Prigogine-Herman Model,  SIAM Appl. Math. 84, 1, 139-164, 2024
  3. S. Tiwari, A. Klar, A mesh-free particle method for continuum modelling of granular flow, Journal of Computational and Applied Mathematics 438, 115529, 2024

2023

  1. I. Akramov, R. Borsche, N. Eckhard and A. Klar, Interface layers and coupling conditions on networks for linearized kinetic BGK equation, Kinetic and related models, doi: 10.3934/krm.2023029, 2023
  2. P.S. Abdul Salam, S. Tiwari, A. Klar, S. Sundar, A numerical investigation of pedestrian dynamics based on rational behaviour in different density scenarios, Physica A:  Statistical mechanics and its applications, 624, 128933, 2023
  3. P.S. Abdul Salam, W. Bock, A. Klar, S. Tiwari, Coupling pedestrian flow and disease contagion models, Crowd dynamics 4,  Modelling and simulation in Science, engineering and technology, edts. N. Bellomo, L. Gibelli, Springer Nature 2023

2022

  1. S. Tiwari, A. Klar, G. Russo, A meshfree arbitrary Lagrangian-Eulerian method for the BGK model of the Boltzmann equation with moving boundaries, J. Comp. Phys. 458, 111088, 2022
  2. S. Tiwari, A. Klar, G. Russo, Modeling and simulations of moving droplet in a rarefied gas, International Journal of Computational Fluid Dynamics 35, 666-684, 2022
  3. R. Borsche, A. Klar, M. Zanella, Kinetic-controlled hydrodynamics for multilane traffic flow with driver-assist vehicles, Physica A 587, 126486, 2022
  4. M.W. Hlawitschka, S. Tiwari, J. Kwizera, H.-J. Bart, A. Klar, Simulation of fluid particle cutting: validation and case study, Differ. Equ. Dyn. Syst. 30, 363-382, 2022.

2021

  1. P.S. Abdul Salam, W. Bock, A. Klar, S. Tiwari, Disease contagion models coupled to crowd motion and mesh-free simulation, M3AS, 2021
  2. R. Borsche, A. Klar, Asymptotic methods for kinetic and macroscopic equations on networks, Trails in kinetic theory, Sema-Semai, 2021
  3. M. Rein, J. Mohring, T. Damm, and A. Klar, Model order reduction of hyperbolic systems focusing on district heating networks, J. Franklin Institute, 2021
  4. G. Corbin, A. Klar, C. Surulescu, C. Engwer, M. Wenske, J. Nieto, J. Soler, Modeling glioma invasion with anisotropy and hypoxia-triggered motility enhancement: from subcellular dynamics to macroscopic PDEs with multiple taxis, M3AS, 31(1), 177-222, 2021

2020

  1. M. Rein, J. Mohring, T. Damm, and A. Klar, Optimal control of district heating networks using a reduced order model, Optimal control, applications and methods 41 (4), 1352-1370, 2020
  2. S. Tiwari, A. Klar, G. Russo, Interaction of rigid body motion and rarefied gas dynamics based on the BGK model, Mathematics in Engineering, 2,2, 203-229, 2020
  3. P. Goswami, T. Baier, S. Tiwari, C. Lv, S. Hardt and A. Klar, Drag force on spherical particle near a plane wall in rarefied gas. J. Fluid Dyn. 883, A47, 2020
  4. M. Rein, J. Mohring, T. Damm, and A. Klar, Stability preserving model order reduction for district heating networks, Progress in Industrial Mathematics at ECMI 2018, Springer 2020
  5. M.K. Mahato, A. Klar, S. Tiwari, Modelling and Simulation of macroscopic pedestrian flow models, Progress in Industrial Mathematics at ECMI 2018, Springer 2020
  6. A. Meurer, A. Weber, H.-J. Bart, A. Klar, Experimental Validation of a Microscopic Ellipsoidal Particle Model immersed in Fluid Flow, The Nepali Mathematical Science Report, 36 (1-2), 27-37, 2020.

2019

  1. A. Klar, Interacting fiber structures: mathematical aspects and applications, Rivista di Matematica della Università di Parma, 10, 2, 199-268, 2019
  2. F. Baus, A. Klar, N. Marheineke, R. Wegener, Low-Mach and slenderness limit for elastic Cosserat rods and its numerical investigation, Asymptotic Analysis, 2019
  3. A.Klar, S.Tiwari, A multi-scale particle methods for mean-field equations: the general case,  SIAM Multiscale Mod. Simul. 17 (1), 233-259, 2019
  4. L. Müller, A. Klar, F. Schneider, A numerical comparison of the method of moments for the population balance equation, Mathematics and Computers in Simulation 65,  26-55, 2019
  5. R. Borsche, A. Klar, F. Schneider, Numerical methods for mean field and moment models for pedestrian flow, Crowd Dynamics Volume 1 - Theory, Models, and Safety Problems, N. Bellomo and L. Gibelli Eds., Birkhäu

Students

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