Max Firmbach M.Sc.

Academic Education

Stays abroad

Research Interests

• Preconditioning and efficient algorithms for the mixed-dimensional modelling of the interaction of solid continua with embedded beams

Sparsity pattern of the system matrix                     Model of a concrete wall with steel rebar

• Partitioned and monolithic coupling approaches for fluid-structure interaction

Deformation of a flexible pipe due to a traveling pressure wave

Software Development

I mostly do programming in C++, but also work with Python and Matlab.

The most important software libraries I currently work with:

• 4C: in-house multiphysics code (in collaboration with the Institute for Computational Mechanics (TUM))
• Trilinos: open-source project for algorithms for large-scale multiphsyics applications
• MueLu: next-generation multigrid framework within Trilinos

Libraries I used or/and contributed to:

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

Preprints and Articles Submitted for Publication

1. 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 

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 , arXiv 

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) 

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
   

Courses & Exercises

Supervised Student Projects / Theses

1. Strength-of-connection for materials with several 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)