I am developing, as member of the chair for High-Perfomance Scientific Computing, algorithms and software for scientific computing in the following research fields:

• high-performance computing: matrix-free computations, dynamic sparse communication patterns, node-level optimization

• iterative solvers: multigrid, block preconditioners

• efficient algorithms for high-dimensional partial differential equations (e.g. 6D Vlasov-Poisson)

• discontinuous Galerkin methods

• computational fluid dynamics

• simulation of additive manufacturing processes including solid-state sintering (in collaboration with Vladimir Ivannikov) and melt-pool modeling (in collaboration with Magdalena Schreter)

Furthermore, I am one of the principal developers of the general-purpose finite-element library  deal.II, of the Navier-Stokes solver  ExaDG, and of the finite-element library  hyper.deal for high-dimensional applications. I have participated in writing deal.II's tutorials:  step-19,  step-70 (both demonstrating the particle infrastructure), step-75 (matrix-free multigrid for hp-FEM), step-76 (matirix-free Euler solver exploiting MPI-3.0 shared-memory features). 

For more details on my current projects, see my GitHub page:  https://github.com/peterrum.

Articles in peer-reviewed international journals

• J. Heinz, P. Munch, M. Kaltenbacher. High-Order Non-Conforming Discontinuous Galerkin Methods for the Acoustic Conservation Equations, 2022, accepted for publication in International Journal for Numerical Methods in Engineering.  PDF
• D. Arndt, W. Bangerth, M. Feder, M. Fehling, R. Gassmöller, T. Heister, L. Heltai, M. Kronbichler, M. Maier, P. Munch, JP. Pelteret, S. Sticko, B. Turcksin, D. Wells. The deal.II library, version 9.4. Journal of Numerical Mathematics, vol. 30, no. 3, pp. 231-246, 2022.  DOI
• M. Kronbichler, D. Sashko, P. Munch, Enhancing data locality of the conjugate gradient method for high-order matrix-free finite-element implementations, The International Journal of High Performance Computing Applications, SAGE Publications, 2022,  DOI
• P. Munch, I. Dravins, M. Kronbichler, M. Neytcheva, Stage-parallel fully implicit Runge-Kutta implementations with optimal multilevel preconditioners at the scaling limit, 2022, accepted for publication in SIAM Journal on Scientific Computing (SISC),  PDF
• P. Munch, T. Heister, LP. Saavedra, M. Kronbichler, Efficient distributed matrix-free multigrid methods on locally refined meshes for FEM computations, 2022, accepted for publication in ACM Transactions on Parallel Computing (TOPC),  PDF
• D. Arndt, W. Bangerth, B. Blais, M. Fehling, R. Gassmöller, T. Heister, L. Heltai, U. Köcher, M. Kronbichler, M. Maier, P. Munch, JP. Pelteret, S. Proell, K. Simon, B. Turcksin, D. Wells, J. Zhang. The deal.II library, version 9.3. Journal of Numerical Mathematics, vol. 29, no. 3, pp. 171-186, 2021.  DOI
• S. Golshan, P. Munch, R. Gassmoller, M. Kronbichler, B. Blais. Lethe-DEM : An open-source parallel discrete element solver with load balancing, Computational Particle Mechanics, 2022.  DOI
• N. Fehn, M. Kronbichler, P. Munch, W. A. Wall, Numerical evidence of anomalous energy dissipation in incompressible Euler flows: Towards grid-converged results for the inviscid Taylor-Green problem, Journal of Fluid Mechanics, vol. 932, A40, 2021.  DOI
• D. Arndt, W. Bangerth, B. Blais, T. C. Clevenger, M. Fehling, A. V. Grayver, T. Heister, L. Heltai, M. Kronbichler, M. Maier, P. Munch, JP. Pelteret, R. Rastak, I. Thomas, B. Turcksin, Z. Wang, D. Wells. The deal.II library, version 9.2. Journal of Numerical Mathematics 28(3):131-146, 2020,  DOI
• P. Munch, K. Kormann, M. Kronbichler, hyper.deal: An efficient, matrix-free finite-element library for high-dimensional partial differential equations, ACM Transactions on Mathematical Software, vol. 47(4), pp. 1–34, 2021.  DOI
• N. Fehn, P. Munch, W. A. Wall, M. Kronbichler, Hybrid multigrid methods for high-order discontinuous Galerkin discretizations, Journal of Computational Physics 415 (2020) 109538. DOI
• M. Kronbichler, K. Kormann, N. Fehn, P. Munch, J. Witte, A Hermite-like basis for faster matrix-free evaluation of interior penalty discontinuous Galerkin operators, 2019, submitted. PDF

Peer-reviewed proceedings and book contributions

• P. Munch, K. Ljungkvist, M. Kronbichler, Efficient Application of Hanging-Node Constraints for Matrix-Free High-Order FEM Computations on CPU and GPU, In: Varbanescu, AL., Bhatele, A., Luszczek, P., Marc, B. (eds) High Performance Computing. ISC High Performance 2022. Lecture Notes in Computer Science, vol 13289. pp. 133-152, Springer, Cham, 2022.  DOI
• M. Kronbichler, N. Fehn, P. Munch, M. Bergbauer, K. R. Wichmann, C. Geitner, M. Allalen, M. Schulz, W. A. Wall. A Next-Generation Discontinuous Galerkin Fluid Dynamics Solver with Application to High-Resolution Lung Airflow Simulations. TIn: SC '21: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, Article No.: 21, pp. 1–15, 2021.  DOI
• D. Arndt, N. Fehn, G. Kanschat, K. Kormann, M. Kronbichler, P. Munch, W. A. Wall, J. Witte, ExaDG: High-Order Discontinuous Galerkin for the Exa-Scale, In H.-J. Bungartz, S. Reiz, B. Uekermann, P. Neumann, and W. E. Nagel (eds.), Software for Exascsale Computing - SPPEXA 2016-2019, Lecture Notes in Computational Science and Engineering, vol 136. pp. 189-224, Springer, Cham, 2020.  DOI

International conference contributions with abstract

• N. Fehn, M. Kronbichler, P. Munch, W. A. Wall, On numerical evidence of anomalous energy dissipation, 14th European Fluid Mechanics Conference (EFMC14), Athens, Greece, September 13 - 16, 2022.  Abstract

• M. Kronbichler, P. Munch, I. Dravins, M. Neytcheva, Performance of Stage-Parallel Implicit Runge-Kutta Methods with Fast Multigrid Methods, International Conference on Scientific Computation and Differential Equations (SciCADE) 2022, Reykjavik, Island, July 25-29, 2022.  Abstract

• M. Bergbauer, P. Munch, A. Massing, M. Kronbichler, WA. Wall, Comparison of stabilization techniques for CutDG methods, 8th European Congress on Computational Methods in Applied Sciences and Engineering, Oslo, Norway, June 5-9 June, 2022.  Abstract

• I. Dravins, M. Neytcheva, O. Axelsson, P. Munch, M. Kronbichler, On stage-parallel preconditioning of implicit Runge-Kutta methods, Preconditioning 2022, Chemnitz, Germany, June 8-10, 2022.  Abstract

• P. Munch, T. Heister, LP. Saavedra and M. Kronbichler, A comparative study of global coarsening and local smoothing multigrid methods on locally refined meshes for distributed matrix-free FEM computations, 17th Copper Mountain Conference On Iterative Methods, virtual, April 4-8, 2022.  Abstract 

• M. Kronbichler, P. Munch, N. Fehn, Efficient multigrid solvers for high-order discontinuous Galerkin discretizations via matrix-free operator evaluation, 6th ECCOMAS Young Investigators Conference YIC2021, Valencia, Spain, July 7-9, 2021.  Abstract
• P. Munch, N. Fehn, W. A. Wall, M. Kronbichler, SIMD vectorization for high-order matrix-free finite element computations in CFD, SIAM Conference on Computational Science and Engineering (CSE19), Spokane, Washington, USA, February 25 - March 1, 2019.  Abstract

Presentations and invited talks

• N. Much, M. Schreter, P. Munch, M Kronbichler, WA. Wall, C Meier, A Novel Finite Element Formulation for Thermal Multi-phase Flow Including Melting and Evaporation: Application to Additive Manufacturing Melt Pool Modeling, 9th GACM Colloquium on Computational Mechanics, Essen, Germany, September 21-23, 2022
• M. Kronbichler, P. Munch. Recent advances in matrix-free, multigrid, non-matching, and simplex support in deal.II.,  9th deal.II Users and Developers Workshop, virtual one-day meeting, June 18, 2021.  PDF
• P. Munch, D. Paukner, I. Scheider, deal.II workshop, virtual three-day workshop at Helmholtz-Zentrum Hereon and Technical University of Hamburg, April 19-21, 2021,  Day 1,  Day 2,  Day 3
• P. Munch, Current status of simplex support in deal.II, deal.II Simplex Workshop 2021, virtual three-day workshop, January 13-15, 2021,  PDF
• P. Munch, K. Kormann, M. Kronbichler, Solving the high-dimensional Vlasov equation with deal.II and hyper.deal, 8th deal.II Users and Developers Workshop, virtual one-day meeting, May 26, 2020.  PDF,  VIDEO
• P. Munch, M. Allalen, M. Kronbichler , P. Ó. Conbhuı́, P. Kanduri, deal.II on GPU, final presentation at EuroHack19, Lugano, Switzerland, September 29 - October 4, 2019.  PDF
• P. Munch, M. Kronbichler, Efficient, large-scale simulations on complex geometries - using a hybrid multigrid solver and a fully distributed triangulation, 7th deal.II Users and Developers Workshop, Fort Collins, Colorado, USA, August 6 - 9, 2019.  PDF

Supervised student projects

• Analysis of surface tension in two-phase flows, Master's Thesis (Department of Mathematics, TUM), Judith Pauen, 2021, in cooperation with  Magdalena Schreter and  Martin Kronbichler

• Efficient shock-capturing approaches for matrix-free high-order discontinuous Galerkin methods, Master's Thesis (Department of Mechanical Engineering, TUM), David Schneider, 2020, in cooperation with  Martin Kronbichler

• Massively parallel PDE solutions: coupling the sparse-grid combination technique with an efficient matrix-free finite element solver, Project (University of Stuttgart), Marius Goehring, 2021, in cooperation with  Theresa Pollinger

• An efficient hybrid multigrid solver for adaptive meshes, Master's Thesis (Computational Science and Engineering, Department of Informatics, TUM), Laura Prieto Saavedra, 2020, in cooperation with  Martin Kronbichler

• Cache-efficient enumeration of degrees of freedom for high-order FEM on modern CPU hardware, IDP (Interdisciplinary Project, Department of Informatics, TUM), Alex Roschlaub, 2019, in cooperation with  Martin Kronbichler

• High-order discontinuous Galerkin simulations of Joukowsky and NACA airfoils, Bachelor's Thesis (Department of Mechanical Engineering, TUM), Elias Dejene, 2019

• Implementation and validation of a quasistatic elasticity FEM-solver, student project (Department of Mechanical Engineering, TUM), Daniel Dengler

• Performance analysis of high-order finite element algorithms, IDP (Interdisciplinary Project, Department of Informatics, TUM), Karlo Kraljic, 2019, in cooperation with  Martin Kronbichler

• Numerical investigations on the efficiency of an in-house high-order discontinuous Galerkin flow solver compared to OpenFOAM, Master's Thesis (Department of Mechanical Engineering, TUM), Yingxian Wang, 2019, in cooperation with  Niklas Fehn