Lattice Boltzmann methods on the way to exascale Ulrich Rüde LSS Erlangen and CERFACS Toulouse ulrich.ruede@fau.de Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique www.cerfacs.fr Lehrstuhl für Simulation Universität Erlangen-Nürnberg www10.informatik.uni-erlangen.de 1
Outline Motivation Building Blocks for the Direct Simulation of Complex Flows 1. Supercomputing: scalable algorithms, efficient software 2. Solid phase - rigid body dynamics 3. Fluid phase - Lattice Boltzmann method 4. Electrostatics - finite volume 5. Fast implicit solvers - multigrid 6. Gas phase - free surface tracking, volume of fluids Multi-physics applications Coupling Examples Perspectives 2
Motivation Simulating Additive Manufacturing Bikas, H., Stavropoulos, P., & Chryssolouris, G. (2015). Additive manufacturing methods and modelling approaches: a critical review. The International Journal of Advanced Manufacturing Technology, 1-17. Klassen, A., Scharowsky, T., & Körner, C. (2014). Evaporation model for beam based additive manufacturing using free surface lattice Boltzmann methods. Journal of Physics D: Applied Physics, 47(27), 275303. 3
Electron Beam Melting Process 3D printing EU-Project Fast- EBM ARCAM (Gothenburg) TWI (Cambridge) FAU Erlangen Generation of powder bed Energy transfer by electron beam penetration depth heat transfer Flow dynamics melting melt flow surface tension wetting capillary forces contact angles solidification Ammer, R., Markl, M., Ljungblad, U., Körner, C., & UR (2014). Simulating fast electron beam melting with a parallel thermal free surface lattice Boltzmann method. Computers & Mathematics with Applications, 67(2), 318-330. Ammer, R., UR, Markl, M., Jüchter V., & Körner, C. (2014). Validation experiments for LBM simulations of electron beam melting. International Journal of Modern Physics C. 4
SuperMuc: 3 PFlops Building Block I: Current and Future High Performance Supercomputers 5
Multi-PetaFlops Supercomputers Sunway TaihuLight JUQUEEN SuperMUC (phase 1) SW26010 processor 10,649,600 cores 260 cores (1.45 GHz) per node 32 GiB RAM per node 125 PFlops Peak Power consumption: 15.37 MW TOP 500: #1 Blue Gene/Q architecture 458,752 PowerPC A2 cores 16 cores (1.6 GHz) per node 16 GiB RAM per node 5D torus interconnect 5.8 PFlops Peak TOP 500: #13 Intel Xeon architecture 147,456 cores 16 cores (2.7 GHz) per node 32 GiB RAM per node Pruned tree interconnect 3.2 PFlops Peak TOP 500: #27 What is the problem? LBM Methods Ulrich Rüde
Only optimal algorithms qualify TERRA Thought experiment with O(N 2 ) algorithm Energy computer generation gigascale: 10 9 FLOPS terascale 10 12 FLOPS petascale 10 15 FLOPS exascale 10 18 FLOPS desired problem size DoF=N 10 6 10 9 10 12 10 15 energy estimate (kwh) 1 NJoule N 2 all-to-all communication 0.278 Wh 10 min of LED light 278 kwh 2 weeks blow drying hair 278 GWh 1 month electricity for Hamburg 278 PWh 100 years world electricity production TerraNeo prototype (kwh) 0.13 Wh 0.03 kwh 27 kwh? At extreme scale: optimal complexity is a must! 7
Building block II: The Lagrangian View: Granular media simulations with the physics engine 1 250 000 spherical particles 256 processors 300 300 time steps runtime: 48 h (including data output) texture mapping, ray tracing Pöschel, T., & Schwager, T. (2005). Computational granular dynamics: models and algorithms. Springer Science & Business Media. 8
Lagrangian Particle Presentation Single particle described by state variables (position x, orientation φ, translational and angular velocity v and ω) a parameterization of its shape S (e.g. geometric primitive, composite object, or mesh) and its inertia properties (mass m, principle moments of inertia I xx, I yy and I zz ). The Newton-Euler equations of motion for rigid bodies describe the rate of change of the state variables: ẋ(t) = '(t) v(t) M('(t)) =!(t) v(t) Q('(t))!(t) f(s(t),t) (s(t),t)!(t) I('(t))!(t) 9
Hard Contacts alternative to the discrete element method Hard contacts require impulses, exhibit non-differentiable but continuous trajectories, contact reactions are defined implicitly in general, have non-unique solutions, and can be solved numerically by methods from two classes. ) measure differential inclusions 100% 80% 60% 40% 20% 0% -20% -1 soft contacts hard contacts -0.5 0 0.5 1 1.5 2 2.5 3 Fig.: Bouncing ball with a soft and a hard contact model. Moreau, J., Panagiotopoulos P. (1988): Nonsmooth mechanics and applications, vol 302. Springer, Wien-New York Popa, C., Preclik, T., & UR (2014). Regularized solution of LCP problems with application to rigid body dynamics. Numerical Algorithms, 1-12. Preclik, T. & UR (2015). Ultrascale simulations of non-smooth granular dynamics; Computational Particle Mechanics, DOI: 10.1007/s40571-015-0047-6 Extreme Scale LBM Methods - Ulrich Rüde 10
Newton-Euler Equations for Rigid Bodies ẋ(t) v(t) = '(t) Q('(t))!(t) v(t) f(s(t),t) M('(t)) =!(t) (s(t),t)!(t) I('(t))!(t) Contact detection minimizing signed distance function Time-continuous non-penetration constraint for hard contacts Coulomb friction Parallelization via domain partitioning Parallel data structures for contact detection Protocol for synchronization (t) 0? n (t) 0 11
Nonlinear Complementarity and Time Stepping Non-penetration conditions Coulomb friction conditions continuous forces =0 + =0 0? n 0 k to k 2 apple µ n + 0? n 0 k v + tok 2 to = µ n v + to + 0? n 0 k v + tok 2 to = µ n v+ to k v + to k 2 =0 impulses =0 0? n 0 k to k 2 apple µ n + 0? n 0 k v + tok 2 to = µ n v + to discrete t + v0 n( ) 0? n 0 k to k 2 apple µ n k v 0 to( )k 2 to = µ n v 0 to( ) Signorini condition impact law friction cone condition frictional reaction opposes slip Moreau, J., Panagiotopoulos P. (1988): Nonsmooth mechanics and applications, vol 302. Springer, Wien-New York Popa, C., Preclik, T., & UR (2014). Regularized solution of LCP problems with application to rigid body dynamics. Numerical Algorithms, 1-12. Preclik, T. & UR (2015). Ultrascale simulations of non-smooth granular dynamics; Computational Particle Mechanics, DOI: 10.1007/s40571-015-0047-6 12
Regularizing Multi-Contact Problems 13
Parallel Computation Key features of the parallelization: domain partitioning distribution of data contact detection synchronization protocol subdomain NBGS accumulators and corrections aggressive message aggregation nearest-neighbor communication Iglberger, K., & UR (2010). Massively parallel granular flow simulations with non-spherical particles. Computer Science-Research and Development, 25(1-2), 105-113 Iglberger, K., & UR (2011). Large-scale rigid body simulations. Multibody System Dynamics, 25(1), 81-95 14
Shaker scenario with sharp edged hard objects 864 000 sharp-edged particles with a diameter between 0.25 mm and 2 mm. 15
PE marble run - rigid objects in complex geometry Animation by Sebastian Eibl and Christian Godenschwager 16
Scaling Results Solver algorithmically not optimal for dense systems, hence cannot scale unconditionally, but is highly efficient in many cases of practical importance Strong and weak scaling results for a constant number of iterations performed on SuperMUC and Juqueen Largest ensembles computed 2.8 10 10 non-spherical particles 1.1 10 10 contacts granular gas: scaling results Breakup up of compute times on Erlangen RRZE Cluster Emmy av. time per time step and 1000 particles in s 0.116 0.114 0.112 0.11 0.108 0.106 0.104 0.102 0.1 av. time per time step ( rst series) 0.098 av. time per time step (second series) parallel e ciency (second series) 0.096 1 4 16 64 256 1024 4096 16384 number of nodes (b) Weak-scaling graph on the Juqueen supercomputer. 1.2 1 0.8 0.6 0.4 0.2 0 parallel e ciency 9.5% 25.9% 8.0% 12.6% (a) Time-step profile of the granular gas executed with 5 2 2 = 20 processes on a single node. 25.8% 18.1% 8.3% 5.9% 22.7% 30.6% 16.5% 16.0% (b) Time-step profile of the granular gas executed with 8 8 5 = 320 processes on 16 nodes. 17
Building Block III: Scalable Flow Simulations with the Lattice Boltzmann Method Lallemand, P., & Luo, L. S. (2000). Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability. Physical Review E, 61(6), 6546. Feichtinger, C., Donath, S., Köstler, H., Götz, J., & Rüde, U. (2011). WaLBerla: HPC software design for computational engineering simulations. Journal of Computational Science, 2(2), 105-112. Extreme Scale LBM Methods - Ulrich Rüde 18
The Eulerian View : Lattice-Boltzmann Discretization in squares or cubes (cells) Particles Distribution Functions (PDF) in 2D: 9 numbers (2DQ9) in 3D: D3Q19 (alternatives D3Q27, etc) Repeat (many times) stream collide Extreme Scale LBM Methods - Ulrich Rüde 19
Basic Lattice Boltzmann Method Single Relaxation Time (SRT) Macroscopic quantities Equilibrium distribution function Extreme Scale LBM Methods - Ulrich Rüde
The stream step Move PDFs into neighboring cells Non-local part, Linear propagation to neighbors (stream step) Local part, Non-linear operator, (collide step) Extreme Scale LBM Methods - Ulrich Rüde 21
The collide step Compute new PDFs modeling molecular collisions Most collision operators can be expressed as Equilibrium function: non-linear, depending on the conserved moments,, and. Extreme Scale LBM Methods - Ulrich Rüde 22
Performance on Coronary Arteries Geometry Color coded proc assignment Godenschwager, C., Schornbaum, F., Bauer, M., Köstler, H., & UR (2013). A framework for hybrid parallel flow simulations with a trillion cells in complex geometries. In Proceedings of SC13: International Conference for High Performance Computing, Networking, Storage and Analysis (p. 35). ACM. Weak scaling 458,752 cores of JUQUEEN over a trillion (10 12 ) fluid lattice cells cell sizes 1.27µm diameter of red blood cells: 7µm 2.1 10 12 cell updates per second 0.41 PFlops Strong scaling 32,768 cores of SuperMUC cell sizes of 0.1 mm 2.1 million fluid cells 6000+ time steps per second Extreme Scale LBM Methods - Ulrich Rüde
Single Node Performance JUQUEEN SuperMUC vectorized optimized standard Pohl, T., Deserno, F., Thürey, N., UR, Lammers, P., Wellein, G., & Zeiser, T. (2004). Performance evaluation of parallel largescale lattice Boltzmann applications on three supercomputing architectures. Proceedings of the 2004 ACM/IEEE conference on Supercomputing (p. 21). IEEE Computer Society. Donath, S., Iglberger, K., Wellein, G., Zeiser, T., Nitsure, A., & UR (2008). Performance comparison of different parallel lattice Boltzmann implementations on multi-core multi-socket systems. International Journal of Computational Science and Engineering, 4(1), 3-11. Extreme Scale LBM - Ulrich Rüde
Weak scaling for TRT lid driven cavity - uniform grids JUQUEEN 16 processes per node 4 threads per process 2.1 10 12 cell updates per second (TLups) SuperMUC 4 processes per node 4 threads per process 0.837 10 12 cell updates per second (TLups) Körner, C., Pohl, T., UR., Thürey, N., & Zeiser, T. (2006). Parallel lattice Boltzmann methods for CFD applications. In Numerical Solution of Partial Differential Equations on Parallel Computers (pp. 439-466). Springer Berlin Heidelberg. Feichtinger, C., Habich, J., Köstler, H., UR, & Aoki, T. (2015). Performance modeling and analysis of heterogeneous lattice Boltzmann simulations on CPU GPU clusters. Parallel Computing, 46, 1-13. Extreme Scale LBM - Ulrich Rüde
Partitioning and Parallelization static block-level refinement ( forest of octrees) static load balancing DISK compact (KiB/MiB) binary MPI IO DISK allocation of block data ( grids) separation of domain partitioning from simulation (optional) 26
Flow through structure of thin crystals (filter) work with Jose Pedro Galache and Antonio Gil CMT-Motores Termicos, Universitat Politecnica de Valencia 27
Parallel AMR load balancing different views on domain partitioning 2:1 balanced grid (used for the LBM) distributed graph: nodes = blocks edges explicitly stored as < block ID, process rank > pairs forest of octrees: octrees are not explicitly stored, but implicitly defined via block IDs 28
AMR and Load Balancing with walberla Isaac, T., Burstedde, C., Wilcox, L. C., & Ghattas, O. (2015). Recursive algorithms for distributed forests of octrees. SIAM Journal on Scientific Computing, 37(5), C497-C531. Meyerhenke, H., Monien, B., & Sauerwald, T. (2009). A new diffusion-based multilevel algorithm for computing graph partitions. Journal of Parallel and Distributed Computing, 69(9), 750-761. Schornbaum, F., & Rüde, U. (2016). Massively Parallel Algorithms for the Lattice Boltzmann Method on NonUniform Grids. SIAM Journal on Scientific Computing, 38(2), C96-C126. Extreme Scale LBM Methods - Ulrich Rüde 29
AMR Performance Benchmark Environments: JUQUEEN (5.0 PFLOP/s) Blue Gene/Q, 459K cores, 1 GB/core compiler: IBM XL / IBM MPI SuperMUC (2.9 PFLOP/s) Intel Xeon, 147K cores, 2 GB/core compiler: Intel XE / IBM MPI Benchmark (LBM D3Q19 TRT): avg. blocks/process (max. blocks/proc.) level initially after refresh after load balance 0 0.383 (1) 0.328 (1) 0.328 (1) 1 0.656 (1) 0.875 (9) 0.875 (1) 2 1.313 (2) 3.063 (11) 3.063 (4) 3 3.500 (4) 3.500 (16) 3.500 (4) Extreme Scale LBM Methods - Ulrich Rüde 30
AMR Performance Benchmark Environments: JUQUEEN (5.0 PFLOP/s) Blue Gene/Q, 459K cores, 1 GB/core compiler: IBM XL / IBM MPI SuperMUC (2.9 PFLOP/s) Intel Xeon, 147K cores, 2 GB/core compiler: Intel XE / IBM MPI Benchmark (LBM D3Q19 TRT): during this refresh process all cells on the finest level are coarsened and coarsen refine the same amount of fine cells is created by splitting coarser cells 72 % of all cells change their size Extreme Scale LBM Methods - Ulrich Rüde 31
AMR Performance JUQUEEN space filling curve: Morton 12 197 billion cells seconds 10 8 6 4 58 billion cells 14 billion cells hybrid MPI+OpenMP version with SMP 1 process 2 cores 8 threads #cells per core 31,062 127,232 429,408 2 0 256 4096 32,768 458,752 cores Extreme Scale LBM Methods - Ulrich Rüde 32
AMR Performance JUQUEEN diffusion load balancing 12 197 billion cells seconds 10 8 6 4 58 billion cells 14 billion cells time almost independent of #processes! #cells per core 31,062 127,232 429,408 2 0 256 4096 32,768 458,752 cores Extreme Scale LBM Methods - Ulrich Rüde 33
Pore scale resolved flow in porous media Direct numerical simulation of flow through sphere packings Beetstra, R., Van der Hoef, M. A., & Kuipers, J. A. M. (2007). Drag force of intermediate Reynolds number flow past monoand bidisperse arrays of spheres. AIChE Journal, 53(2), 489-501. Tenneti, S., Garg, R., & Subramaniam, S. (2011). Drag law for monodisperse gas solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres. International journal of multiphase flow, 37(9), 1072-1092. 34
Flow field and vorticity 2D slice visualized Domain size: Re = 300 Volume fraction:
Macroscopic drag correlation Finally, the drag correlation reads Average absolute percentage error: 9.7 % Bogner, S., Mohanty, S., & UR (2015). Drag correlation for dilute and moderately dense fluid-particle systems using the lattice Boltzmann method, International Journal of Multiphase Flow 68, 71-79. 36
Setup of random spherical structure for porous media with the PE Massively Parallel Multiphysics Simulations - Ulrich Rüde
Flow over porous structure Porosity 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 Setup Height of the channel 0.8 0.6 0.4 0.2 Porosity Velocity Profile 0 0 0.2 0.4 0.6 0.8 1 Streamwise velocity Pore geometry and streamlines Fattahi, E., Waluga, C., Wohlmuth, B., & Rüde, U. (2015). Large scale lattice Boltzmann simulation for the coupling of free and porous media flow. arxiv preprint arxiv:1507.06565. To appear in LNCS, Proceedings of HPCSE 2015. Massively Parallel Multiphysics Simulations - Ulrich Rüde 38
Turbulent flow over a permeable region Re 3000 direct numerical simulation Volume rendering of velocity magnitude Periodic in X and Y direction I10 cluster, 7x32x19=4256 core hours 1,300,000 timesteps 8 times more time steps on the finest level 39
Multi-Physics Simulations for Particulate Flows Parallel Coupling with walberla and PE Ladd, A. J. (1994). Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. Journal of Fluid Mechanics, 271(1), 285-309. Tenneti, S., & Subramaniam, S. (2014). Particle-resolved direct numerical simulation for gas-solid flow model development. Annual Review of Fluid Mechanics, 46, 199-230. Bartuschat, D., Fischermeier, E., Gustavsson, K., & UR (2016). Two computational models for simulating the tumbling motion of elongated particles in fluids. Computers & Fluids, 127, 17-35. 40
Fluid-Structure Interaction direct simulation of Particle Laden Flows (4-way coupling) Götz, J., Iglberger, K., Stürmer, M., & UR (2010). Direct numerical simulation of particulate flows on 294912 processor cores. In Proceedings of Supercomputing 2010, IEEE Computer Society. Götz, J., Iglberger, K., Feichtinger, C., Donath, S., & UR (2010). Coupling multibody dynamics and computational fluid dynamics on 8192 processor cores. Parallel Computing, 36(2), 142-151. 41
Simulation of sediment transport 42
Heterogenous CPU-GPU Simulation Particles: 31250, Domain: 400x400x200, Timesteps: 400 000 Devices: 2 x M2070 + 1 Intel Westmere, Runtime: 17.5 h Fluidized Beds: Direct numerical simulation fully resolved particles Fluid-structureinteraction 4-way-coupling C. Feichtinger, J. Habich, H. Köstler, U. Rüde, T. Aoki, Performance modeling and analysis of heterogeneous lattice Boltzmann simulations on CPU GPU clusters, Parallel Computing, Volume 46, July 2015, Pages 1-13 C. Feichtinger, J. Habich, H. Köstler, G. Hager, U. Rüde, G. Wellein, A flexible Patch-based lattice Boltzmann parallelization approach for heterogeneous GPU CPU clusters, Parallel Computing, Volume 37, Issue 9, September 2011, Pages 536-549. 43
Weak Scaling experiment Götz, J., Iglberger, K., Stürmer, M., & Rüde, U. (2010, November). Direct numerical simulation of particulate flows on 294912 processor cores. In Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis (pp. 1-11). IEEE Computer Society. Efficiency 1 0.9 0.8 0.7 0.6 0.5 Jugene Blue Gene/P Jülich Supercomputer Center 40x40x40 lattice cells per core 80x80x80 lattice cells per core 100 1000 10000 300000 Number of Cores Largest simulation on Jugene: 8 Trillion (10 12 ) variables per time step (LBM alone) Scaling 64 to 294 912 cores Densely packed particles 150 994 944 000 lattice cells 264 331 905 rigid spherical objects Massively Parallel Multiphysics Simulations - Ulrich Rüde 44
Building Block IV (electrostatics) Direct numerical simulation of charged particles in flow Positive and negatively charged particles in flow subjected to transversal electric field Masilamani, K., Ganguly, S., Feichtinger, C., & UR (2011). Hybrid lattice-boltzmann and finite-difference simulation of electroosmotic flow in a microchannel. Fluid Dynamics Research, 43(2), 025501. Bartuschat, D., Ritter, D., & UR (2012). Parallel multigrid for electrokinetic simulation in particle-fluid flows. In High Performance Computing and Simulation (HPCS), 2012 International Conference on (pp. 374-380). IEEE. Bartuschat, D. & UR (2015). Parallel Multiphysics Simulations of Charged Particles in Microfluidic Flows, Journal of Computational Science, Volume 8, May 2015, Pages 1-19 45
6-way coupling charge distribution velocity BCs Finite volumes MG treat BCs V-cycle iter at. object motion hydrodynam. force LBM treat BCs stream-collide step electrostat. force Newtonian mechanics collision response object distance correction force Lubrication correction 46
Separation experiment 240 time steps fully 6-way coupled simulation 400 sec on SuperMuc weak scaling up to 32 768 cores 7.1 Mio particles Total runtimes [] 400 300 200 100 0 1 2 4 8 16 32 64 Number of nodes 128 256 512 1024 2048 LBM Map Lubr HydrF pe MG SetRHS PtCm ElectF 10 3 MFLUPS (LBM) 90 80 70 60 50 40 30 20 10 0 0 250 500 750 1000 1250 1500 1750 2000 Number of nodes 47 LBM Perform. MG Perform. 120 100 80 60 40 20 10 3 MLUPS (MG)
Building Block V Volume of Fluids Method for Free Surface Flows joint work with Regina Ammer, Simon Bogner, Martin Bauer, Daniela Anderl, Nils Thürey, Stefan Donath, Thomas Pohl, C Körner, A. Delgado Körner, C., Thies, M., Hofmann, T., Thürey, N., & UR. (2005). Lattice Boltzmann model for free surface flow for modeling foaming. Journal of Statistical Physics, 121(1-2), 179-196. Donath, S., Feichtinger, C., Pohl, T., Götz, J., & UR. (2010). A Parallel Free Surface Lattice Boltzmann Method for Large- Scale Applications. Parallel Computational Fluid Dynamics: Recent Advances and Future Directions, 318. Anderl, D., Bauer, M., Rauh, C., UR, & Delgado, A. (2014). Numerical simulation of adsorption and bubble interaction in protein foams using a lattice Boltzmann method. Food & function, 5(4), 755-763. Bogner, S., Ammer, R., & Rüde, U. (2015). Boundary conditions for free interfaces with the lattice Boltzmann method. Journal of Computational Physics, 297, 1-12. 48
Free Surface Flows Volume-of-Fluids like approach Flag field: Compute only in fluid Special free surface conditions in interface cells Reconstruction of curvature for surface tension 49
Simulation of Metal Foams Example application: Engineering: metal foam simulations Based on LBM: Free surfaces Surface tension Disjoining pressure to stabilize thin liquid films Parallelization with MPI and load balancing Other applications: Food processing Fuel cells Körner, C., Thies, M., Hofmann, T., Thürey, N., & UR (2005). Lattice Boltzmann model for free surface flow for modeling foaming. Journal of Statistical Physics, 121(1-2), 179-196. Donath, S., Mecke, K., Rabha, S., Buwa, V., & UR (2011). Verification of surface tension in the parallel free surface lattice Boltzmann method in walberla. Computers & Fluids, 45(1), 177-186. Thürey, N., &UR. (2009). Stable free surface flows with the lattice Boltzmann method on adaptively coarsened grids. Computing and Visualization in Science, 12(5), 247-263. 50
Simulation for hygiene products (for Procter&Gamble) capillary pressure surface tension inclination contact angle 51
Additive Manufacturing Fast Electron Beam Melting Ammer, R., Markl, M., Ljungblad, U., Körner, C., & UR (2014). Simulating fast electron beam melting with a parallel thermal free surface lattice Boltzmann method. Computers & Mathematics with Applications, 67(2), 318-330. Ammer, R., UR, Markl, M., Jüchter V., & Körner, C. (2014). Validation experiments for LBM simulations of electron beam melting. International Journal of Modern Physics C. 52
Simulation of Electron Beam Melting Simulating powder bed generation using the PE framework High speed camera shows melting step for manufacturing a hollow cylinder WaLBerla Simulation 53
Conclusions 54
Research in Computational Science is done by teams Harald Köstler Christian Godenschwager Kristina Pickl Regina Ammer Simon Bogner Ehsan Fattahi Florian Schornbaum Sebastian Kuckuk Christoph Rettinger Dominik Bartuschat Martin Bauer Christian Kuschel 55
Thank you for your attention! Videos, preprints, slides at https://www10.informatik.uni-erlangen.de 56