Max Firmbach M.Sc.

Professur für Computergestützte Simulation im Bauingenieurwesen

Academic Education

04/2021 -                         Doctoral Researcher, Institute for Mathematics and Computer-Based Simulation, University of the Bundeswehr Munich, Germany
10/2018 - 03/2021 Master of Science, Computational Science and Engineering, TU Munich, Germany
09/2014 - 05/2018 Bachelor of Engineering, Aerospace Engineering, University of Applied Sciences Aachen, Germany
   

Stays abroad

09/2024 - 12/2024 Visiting Researcher, Computational Science Research Institute, Sandia National Laboratories, USA
03/2019 Computational Mechanics, MINES ParisTech, France
   

Research Interests

Numerical linear algebra · Multigrid methods · Preconditioning · Scientific computing · High-performance computing · Computational mechanics · Multiphysics simulation

My research focuses on scalable numerical methods for multiphysics simulations, particularly block preconditioning and algebraic multigrid methods for multi-field and mixed-dimensional problems in computational mechanics. Application areas include the simulation of beam-solid interaction and heterogeneous materials. 

Current projects I contribute to:

  • Efficient numerical algorithms for solving systems of linear equations (Zentrum für Digitalisierungs- und Technologieforschung der Bundeswehr (dtec.bw) - Project HPC.bw)
  • Stable discretization methods and scalable solvers for embedded fiber/solid coupling (Deutsche Forschungsgemeinschaft (DFG) - Project number 528397555)

Software

In my research and teaching, I work extensively with open-source software frameworks for scientific computing and multiphysics simulation. Most of my software development is done in C++, complemented by Python and MATLAB.

The most important software frameworks and libraries I currently work with include:

  • 4C Multiphysics GitHub: An open-source multiphysics simulation code (in collaboration with the Institute for Computational Mechanics (TUM))
  • Trilinos GitHub: An open-source software project providing scalable algorithms and solvers for large-scale multiphysics applications
  • MueLu: The next-generation multigrid framework within Trilinos
  • Teko: The framework within Trilinos for the development and implementation of block preconditioners.
  • BeamMe GitHub: An open-source framework for 3D beam finite element model generation.

Libraries I used or/and contributed to in the past:

  • preCICE GitHub: coupling library for partitioned multi-physics simulations
  • DUNE: distributed and unified numerics environment for solving partial differential equations

Publications

Below is an overview of my research contributions.

Preprints and Articles Submitted for Publication
  1. Firmbach M, Steinbrecher I, Popp A, Mayr M (2026): Modified augmented Lagrangian preconditioning for mixed-dimensional beam-solid coupling, Preprint, submitted for publication, arXiv web-logo.png
  2. Firmbach M, Phillips M, Glusa C, Popp A, Siefert C M, Mayr M (2026): Smoothed aggregation algebraic multigrid for problems with heterogeneous and anisotropic materials, Preprint, submitted for publication, arXiv web-logo.png
Articles in Peer-Reviewed International Journals
  1. Firmbach M, Steinbrecher I, Popp A, Mayr M (2024): An approximate block factorization preconditioner for mixed-dimensional beam-solid interaction, Computer Methods in Applied Mechanics and Engineering, 431:117256, DOI (Open Access) doi.png, arXiv web-logo.png
Conference Proceedings and Book Contributions (with Peer-Review)
  1. Firmbach M, Steinbrecher I, Popp A, Mayr M (2023): Computational challenges in mixed-dimensional beam/solid coupling. Proceedings in Applied Mathematics and Mechanics, 23(1): e202200227, DOI (Open Access) doi.png

International Conference Contributions with Abstract

  1. Firmbach M, Steinbrecher I, Popp A, Mayr M: A modified augmented Lagrangian preconditioner for mixed-dimensional beam-solid coupling, 17th World Congress on Computational Mechanics, Munich, Germany, July 19 - 24, 2026
  2. Firmbach M, Phillips M, Glusa C, Popp A, Siefert C, Mayr M: Smoothed aggregation algebraic multigrid for problems with heterogeneous and anisotropic material behavior, GAMM 96th Annual Meeting of the International Association of Applied Mathematics and Mechanics, Stuttgart, Germany, March 16 - 20, 2026
  3. Firmbach M, Steinbrecher I, Popp A, Mayr M: Block preconditioning for mixed-dimensional beam/solid coupling, 11th International Conference on Coupled Problems in Science and Engineering, Villasimus/Sardinia, Italy, May 26 - 29, 2025
  4. Firmbach M, Phillips M, Glusa C, Tuminaro R, Siefert C, Mayr M: Smoothed aggregation algebraic multigrid for problems with heterogeneous and anisotropic material behavior, GAMM 95th Annual Meeting of the International Association of Applied Mathematics and Mechanics, Poznań, Poland, April 7 - 11, 2025
  5. Firmbach M, Mayr M: An open-source framework for physics-based algebraic multigrid block preconditioners in MueLu, ECCOMAS 2024 European Congress on Computational Methods in Applied Sciences and Engineering, Lisbon, Portugal, June 3 - 7, 2024
  6. Firmbach M, Popp A, Mayr M: Physics-based block preconditioning for beam/solid coupling, ECCOMAS 2024 European Congress on Computational Methods in Applied Sciences and Engineering, Lisbon, Portugal, June 3 - 7, 2024
  7. Firmbach M, Popp A, Mayr M: Physics-based block preconditioning for mixed-dimensional beam/solid coupling, 36th Chemnitz Finite Element Symposium, Leibnitz, Austria, September 11 - 13, 2023
  8. Firmbach M, Popp A, Mayr M: Multigrid preconditioning for mixed-dimensional beam/solid coupling, 10th International Conference on Coupled Problems in Science and Engineering, Chania/Crete, Greece, June 5 - 7, 2023
  9. Firmbach M, Popp A, Mayr M: Physics-Based Algebraic Multigrid Block-Preconditioning for Beam/Solid Interaction, 9th GACM Colloqium on Computational Mechanics 2022, Essen, Germany, September 21 - 23, 2022
  10. Firmbach M, Popp A, Mayr M: Algebraic multigrid block-preconditioning for beam/solid meshtying, 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics, Aachen, Germany, August 15 - 19, 2022
  11. Firmbach M, Popp A, Mayr M: Physics-based block preconditioning for beam/solid interaction, invited, 15th World Congress on Computational Mechanics & 8th Asian Pacific Congress on Computational Mechanics, Yokohama, Japan, July 31 - August 5, 2022 (virtual)
  12. Firmbach M, Callies R: Aeroelastic simulation of slender wings for electric aircraft: a partitioned approach with DUNE and preCICE,  invited, 9th International Conference on Coupled Problems in Science and Engineering, Chia Laguna/Sardinia, Italy, June 13 - 16, 2021 (virtual)

 

Workshops

  1. Firmbach M: Trilinos use in 4C-multiphysics, Trilinos User Group Meeting, Albuquerque, USA, October 22-24, 2024
  2. Firmbach M: Block preconditioning for fluid-structure interaction in Trilinos: Teko vs. MueLu, European Trilinos User Group Meeting, Hamburg, Germany, June 24-26, 2024
  3. Firmbach M, Popp A, Mayr M: An open-source framework for physics-based algebraic multigrid block preconditioners, GAMM CSE Workshop, November 10/17, 2023 (virtual)
  4. Firmbach M: Trilinos User Group Meeting, Albuquerque, USA, October/November 31-02, 2023 (virtual)
  5. Firmbach M: Development of physics-based multi-level block preconditioners in Trilinos/MueLu, European Trilinos User Group Meeting, Delft, Netherlands, June 28-30, 2023
  6. Firmbach M, Popp A, Mayr M: Physics based block preconditioning with sparse approximate inverses in MueLu: An application to beam/solid interaction, Trilinos User Group Meeting, Albuquerque, USA, October 25-27, 2022 (virtual)
  7. Firmbach M: Physics based block preconditioning with sparse approximate inverses in MueLu - An application to beam solid interaction, invited, European Trilinos User Group Meeting, Munich, Germany, September 12-14, 2022 (virtual)
  8. Firmbach M: 3rd preCICE Workshop, Stuttgart, Germany, February 21-23, 2022 (virtual)

 

Monographs

  1. Firmbach (2021): Aeroelastic simulation of slender wings for electric aircraft: a partitioned approach with DUNE and preCICE, Master's thesis, TU Munich
  2. Firmbach (2018): Evaluation and modification of a finite element material model for structural adhesives during electrophoretic deposition, Bachelor's thesis, University of Applied Sciences Aachen

Teaching

I contribute to exercises in programming, statistics, and uncertainty modeling, while supervising student theses and research projects in computational mechanics.

 

Courses & Exercises
HT 21, 22, 23

Programmieren (Exercise)
WT 22, 23, 24

Statistik (Exercise)
FT 24 Modeling of Uncertainties and Data (Exercise, Stand-In)

 
Supervised Student Projects / Theses
  1. Strength-of-connection for materials with multiple parameters, Bachelor's Thesis (2026)
  2. Optimization algorithms in MATLAB, Term Paper (2025)
  3. Smoothed aggregation algebraic multigrid for heterogeneous and anisotropic problems from computational solid mechanics, Master's Thesis (2025)
  4. Evaluation of a geometric search algorithm for mixed dimensional modeling approaches, Bachelor's Thesis (2024)
  5. Comparison of smoothers for algebraic multigrid preconditioning in fluid-structure interaction , Term Paper (2023)
  6. Algebraic multigrid block preconditioning for fluid-structure interaction using MueLu, Master's Thesis (2023)
  7. Enhancement of algorithms for beam/solid interaction, Student Project (2023)
  8. Implementation of truss elements inside the DUNE framework, Bachelor's Thesis (2021)