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TerraNeo
Integrated Co-Design of an Exascale Earth Mantle Modeling Framework

Collaborators

Funding

BMBF EU

Work on TerraNeo continues as it forms an integral part of our new project CoMPS: Multi-physics simulations for Geodynamics on heterogeneous Exascale Systems. The latter is one of 15 projects funded by the German Federal Ministry of Education and Research (BMBF) via its SCALEXA (New Methods and Technologies for Exascale Computing) initiative.

Funded by the European Union - NextGenerationEU. The views and opinions expressed are solely those of the author(s) and do not necessarily reflect the views of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them.

SPPEXA

From 2013 to 2019 the development of TerraNeo was funded by the German Research Foundation. Our project of the same name was part of the German Priority Programme 1648: Software for Exascale Computing. The 2020 article TerraNeo - Mantle Convection Beyond a Trillion Degrees of Freedom summarizes the project results.

Software


HyTeG

The TerraNeo project is powered by the HyTeG (Hybrid Tetrahedral Grids) framework for extreme-scale high performance finite element simulations. It is tailored towards matrix-free geometric multigrid solvers.

HyTeG is built upon the concept of hierarchical hybrid grids (HHG) to enable the solution of extreme-scale linear systems with up to multiple trillion (1012) unknowns. The article Textbook Efficiency: Massively Parallel Matrix-Free Multigrid for the Stokes System studies the efficiency of HyTeG's geometric multigrid solver applied to extreme-scale saddle point problems.

News

Recent activities of the TerraNeo research group.

2024

2023

2022

Research Goals


Mantle Convection

Mantle convection is a central component of the Earth system. The slow but ceaseless deformation of rocks through viscous creep taking place in the mantle has a far greater impact on our planet than might immediately be evident. Immense forces are at work deep below our feet and continuously reshape Earth’s surface. It is convective motion in the mantle that generates the enormous driving forces leading to large scale horizontal motion, in the form of plate tectonics and associated earthquake and mountain building activity. At the same time mantle convection also induces substantial vertical motion in the form of dynamically maintained topography through pressure gradients beneath tectonic plates. This vertical motion is perhaps the most spectacular manifestation of mantle convection - and its most defining and enduring impact upon the entire Earth system.

Mantle convection modelling relies upon sophisticated computational modelling and is a classical grand challenge application requiring extremely large grids and many time steps. These are necessary to represent the system with spatial and temporal resolutions fine enough to allow for the use of earth-like physical parameters. The mantle is characterized by strongly variable (e.g., stress-, temperature-, and pressure-dependent) viscosities with local contrasts spanning several orders of magnitude and demanding adaptivity in order to capture localized phenomena.

TerraNeo is an ambitious project to construct a next generation mantle circulation model. The time has come to leap forward and leverage the vast computing power that is becoming available with exascale computing to enable simulation based breakthrough results in our understanding of the solid Earth.

Publications

2023
2022
2020
2019
2018
2017
2016
2015
2014
2013

Theses

2020
2019
2018
2016
2013

Talks and presentations

2023
2022
  • N. Kohl, Performance of massively parallel multigrid on hybrid tetrahedral grids, 2022, ISC High Performance, Hamburg, Germany
  • N. Kohl, Massively parallel solvers for buoyancy-driven convection in Stokes flow , 2022, SIAM Conference on Parallel Processing for Scientific Computing, Seattle/Virtual, USA
2019
  • U. Rüde, Parallel algorithms for solving finite element systems with ten trillion unknowns, 2019, Modeling 2019, Olomouc, Czech Republic
  • U. Rüde, Extreme Scale Resilient Multigrid Solvers, 2019, Challenges in High Performance Computing, Canberra, Australia
  • M. Mohr, S. Bauer, D. Drzisga, S. Ghelichkhan, M. Huber, B. Keith, U. Rüde, B. Wohlmuth, Surrogate polynomials in matrix-free approaches for low-order FEM The Mathematics of Finite Elements and Applications (MAFELAP 2019), Brunel University London, 18 - 21 June 2019
  • N. Kohl, U. Rüde, Designing Finite Element Multigrid Solvers for Extreme-Scale Earth Mantle Convection Simulations, ISC High Performance 2019, Frankfurt, 16 - 20 June 2019
  • U. Rüde, Matrix-Free Multigrid on Hierarchical Hybrid Grids, 2019, 19th Copper Mountain Conference on Multigrid Methods, Copper Mountain, USA
  • U. Rüde, What is the largest finite element system that we can solve today?, 2019, Rencontres Mathématiques de Rouen 2019, Rouen, France
  • U. Rüde, Parallel multigrid for systems with a trillion unknowns and beyond, 2019, The 28th biennial Numerical Analysis Conference 2019, University of Strathclyde, Glasgow
  • D. Thönnes, N. Kohl, D. Drzisga, D. Bartuschat, U. Rüde, HyTeG: A High Performance Multigrid Framework on Hybrid Meshes, 2019, SIAM Conference on Computational Science and Engineering (CSE19), Spokane, Washington, USA, Feb. 25 - Mar. 01 2019
  • U. Rüde, TerraNeo - Towards an Efficient and Sustainable Extreme Scale Earth Mantle Convection Framework, 2019, SPPEXA Annual Plenary Meeting 2019
2018
  • U. Rüde, Extreme Performance for Computational Science, Second French-Japanese-German Workshop on Programming and Computing for Exascale and Beyond, October, 2018
  • U. Rüde, Performance Engineering for Computational Science, HPC-Status-Konferenz der Gauß-Allianz, October, 2018
  • N. Kohl, D. Thönnes, D. Drzisga, D. Bartuschat, U. Rüde, The HyTeG Finite-Element Framework for Scalable Geophysics Simulations International Symposium on Computational Science at Scale (Friedrich-Alexander-Universität Erlangen-Nürnberg, 09/05/18 - 09/07/18)
  • U. Rüde, Ultra scalable Algorithms for Complex Flows, VSC User Day 2018, May, 2018
  • D. Bartuschat, B. Gmeiner, D. Thönnes, N. Kohl, U. Rüde, D. Drzisga, M. Huber, L. John, C. Waluga, B. Wohlmuth, S. Bauer, M. Mohr, HP. Bunge, A Finite Element Multigrid Framework for Extreme-Scale Earth Mantle Convection Simulations SIAM Conference on Parallel Processing for Scientific Computing (SIAM PP 18) (Tokyo, 03/07/18 - 03/10/18)
  • D. Thönnes, N. Kohl, D. Bartuschat, U. Rüde: Sustainability and Efficiency for Simulation Software in the Exascale Era SIAM Conference on Parallel Processing for Scientific Computing (SIAM PP 18) (Tokyo, 03/07/18 - 03/10/18)
  • U. Rüde, Extreme Performance for Computational Science, 2018, Second French-Japanese-German Workshop on Programming and Computing for Exascale and Beyond
  • U. Rüde, TerraNeo: Towards a Sustainable Exascale Framework for Earth Mantle Convection, 2018, CoSaS 2018: International Symposium on Computational Science at Scale, Erlangen, Germany
  • U. Rüde, Fast scalable solvers for robust discretizations in CFD, 2018, ECCM-ECFD 2018: Minisymposium: Exascale algorithms and software techniques for computational fluid and solid mechanics (S. Turek, A. Klawonn, and U.Ruede), 11 - 15 June 2018, Glasgow, UK
2017
  • U. Rüde, Simulation mit Supercomputern: Die Grenzen der Vorhersagbarkeit sprengen, 2017, Conference: Collegium Alexandrinum der Universität Erlangen-Nürnberg
  • D. Bartuschat, U. Rüde, D. Thönnes, N. Kohl, D. Drzisga, M. Huber, L. John, C. Waluga, B. Wohlmuth, S. Bauer, M. Mohr, HP. Bunge: A parallel finite element multigrid framework for geodynamic simulations with more than ten trillion unknowns CSEConf2017 -- 2017 International Conference on Computational Science and Engineering - Software, Education, and Biomedical applications (Oslo, Norway, 10/23/17 - 10/25/17)
  • U. Rüde, Multiphysics simulation not yet at the extreme scale, 2017, LDAV 2017
  • M. Mohr, TerraNeo: Mantle Convection Modelling and the road to Exa-Scale, SIAM Conference on Mathematical and Computational Issues in the Geosciences 2017, Erlangen, Germany, Sep. 11 - 14, 2017.
  • U. Rüde, Supercomputing for Applications in the Material Sciences, 2017, MORE'17: Implicitly constituted materials: Modeling, Analysis and Computing
  • U. Rüde, M. Huber, B. Wohlmuth Resilience for Parallel Multigrid and Adaptive Mesh Refinement, 2017, SIAM Annual Meeting 2017
  • U. Rüde, Algorithmic Efficiency and the Energy Wall, 2017, PACO
  • U. Rüde, Numerical Simulation of Multiphase Flows at the Extreme Scale, 2017, EPSRC Fluid Dynamics Symposium: Fluid Dynamics Modelling for Real World Applications
  • U. Rüde, How to solve Finite element systems beyond a trillion degrees of freedom, 2017, PARNUM
  • S. Bauer, Terra-Neo, SPPEXA-Annual Meeting 2017, Garching, Germany, Mar. 20 - 21, 2017.
  • D. Bartuschat, Scaling Finite Element Multigrid Solvers to Ten Trillion (10^13) Unknowns, SIAM Conference on Computational Science and Engineering, Atlanta, USA, Feb. 27 - Mar. 3, 2017.
2016
  • U. Rüde, Parallel multigrid methods for Geodynamics, MMELSP 2016, Constanta, Romania, Oct. 12 - 16, 2016.
  • S. Bauer, M. Mohr, U. Rüde, M. Wittmann and B. Wohlmuth, A Novel Approach for Efficient Stencil Assembly in Curved Geometries, poster presentation, PASC 2016 conference, Lausanne, Switzerland, June 8 - 10, 2016.
  • D. Bartuschat, U. Rüde, Simulation of Earth Mantle Convection, ESCO 2016, Pilsen, Czech Republic, June 5 - 10, 2016.
  • U. Rüde, Parallel Textbook Multigrid Efficiency, 14th Copper Mountain Conference on Iterative Methods, Copper Mountain, USA, Mar. 20 - 25, 2016.
  • U. Rüde, Multigrid at the Extreme Scale, COSSE-Workshop 2016, Delft, Netherlands, Feb. 16, 2016.
  • M. Huber, Resilience for Multigrid Software at the Extreme Scale, SPPEXA-Annual Meeting 2016, Munich, Germany, Jan. 25 - 27, 2016.
  • M. Huber, Resilience for Multigrid Software at the Extreme Scale, SIAM Parallel Processing 2016, Paris, France, Apr. 12 - 15, 2016.
  • M. Huber, Towards controlling errors in faulty computing environments, Seminar of the Department of Numerical Mathematics, Charles University, Prague, Czech Republic, June 8, 2016.
  • B. Wohlmuth, The role of mathematics in high performance computing for geophysical problems, Magne S. Espedal Lecture, University of Bergen, Norway, Sept. 26, 2016.
  • B. Wohlmuth, Hybrid hierarchical concepts for large scale flow simulations, CCOMAS 2016, Crete, Greece, June 7, 2016.
  • B. Wohlmuth, Reduction techniques in PDE simulation, 7th European Congress of Mathematics, Berlin, Germany, July 19, 2016.
  • B. Wohlmuth, The role of numerical analysis in multi-physics applications, Heidelberg, Germany, Nov. 9, 2016.
  • B. Wohlmuth, Model reduction techniques in vibro-acoustics, MAFELAP, Brunel University, UK, June 16, 2016.
  • B. Wohlmuth, Large scale flow simulations, MOX, Milano, Italy, Mar. 3, 2016.
  • B. Wohlmuth, Reduction techniques in PDE simulation, WCCM XII $\&$ APCOM VI, Seoul, Korea, July 26, 2016.
  • J. Weismüller, Fast asthenosphere motion in high-resolution global mantle flow models, EGU 2016, Vienna, Austria, Apr. 17 - 22, 2016
  • S. Bauer, Efficient stencil assembly in global geodynamic models, EGU 2016, Vienna, Austria, Apr. 17 - 22, 2016.
2015
  • J. Weismüller, B. Gmeiner, M. Huber, L. John, M. Mohr, U. Rüde, B. Wohlmuth and H.-P. Bunge, Mantle Convection on Modern Supercomputers, poster presentation, AGU Fall Meeting 2015, San Francisco, USA, Dec. 14 - 18, 2015.
  • L. John, Robust hybrid parallel multigrid methods for incompressible fluids, Workshop on advanced numerical techniques in biomedical computing, Simula Oslo, Norway, Dec. 3, 2015.
  • L. John, Robust parallel multigrid methods for the Stokes equations, Enumath Conference, Ankara, Turkey, Sept. 14 - 18, 2015.
  • J. Weismüller, B. Gmeiner, M. Mohr, C. Waluga, B. Wohlmuth, U. Rüde and H.-P. Bunge. Mantle convection on modern supercomputers, European Geosciences Union General Assembly 2015, Vienna, Austria, Apr. 12 - 17, 2015.
  • S. Baumann and M. Mohr, Aspects of Multigrid for Mantle Convection, 17th Copper Mountain Conference on Multigrid Methods, USA, Mar. 22 - 27, 2015.
  • M. Huber, Resilience for Exascale Enabled Multigrid Methods, 17th Copper Mountain Conference on Multigrid Methods, USA, Mar. 22 - 27, 2015.
  • L. John, Robust parallel hierarchical hybrid multigrid methods for the Stokes equations, 17th Copper Mountain Conference on Multigrid Methods, USA, Mar. 22 - 27, 2015.
  • U. Rüde. Visiting professor at the National University of Singapore, High Performance and Parallel Computing for Materials Defects and Multiphase Flows, Jan. 1 - Mar. 31, 2015.
  • B. Wohlmuth. Local modifications – global effects, MFO Workshop, Jan. 15, 2015.
  • U. Rüde. Parallel multigrid solvers for geophysical flow, Workshop on Recent Advances in Parallel and High Performance Computing Techniques and Applications, NUS, Singapur, Jan. 14, 2015.
  • U. Rüde. Coupled Physical Models for Exa-Scale Computing, 9th International Conference on Computational Physics, NUS, Singapur, Jan. 10, 2015.
  • B. Wohlmuth. From reduced complexity to large scale computation, AfriComp 2015, Marrakesh, Jan. 8, 2015.
2014
  • U. Rüde. The Emergence of Predictive Science - Computational Science and Engineering, Indo-European Winter Academy, IIT Kanpur, Kanpur, Indien, Dec. 4, 2014.
  • C. Waluga. Achieving local mass-conservation in coupled flow/transport problems using continuous pressure spaces. Talk at IGPM Oberseminar, RWTH Aachen, Germany, Dec. 4, 2014.
  • B. Wohlmuth. Energy- and mass-corrections for optimal control problems, IGDK Annual Colloquium, Herrsching, Dec. 3-5, 2014.
  • C. Waluga. Physics-aware solver concepts for geophysical applications on massively parallel architectures. Numerical Methods on High-Performance Computers, Heidelberg, Germany, Dec. 1-3, 2014.
  • U. Rüde. Combining Granular Dynamics and Lattice Boltzmann Methods, Gastvorlesung, IIT Delhi, Delhi, Indien, Dec. 1, 2014.
  • H.-P. Bunge. Observations and Geodynamic Interpretation of Rapid Plate Motion Variations. Invited talk in Structure and dynamics of Earth-like Planets, workshop, College de France, Nov. 21, 2014.
  • U. Rüde. Parallel Multigrid Solvers for Geophysical Flow Problems, Gastvorlesung, Australien National University, Canberra, AUS, Nov. 17, 2014.
  • U. Rüde. Towards Exa-Scale Simulation Technology, Gastvorlesung, Universidade Federal do Parana, Curitiba, Brasilien, Oct. 30, 2014.
  • U. Rüde. Introduction to Multigrid Methods, Gastvorlesung, Universidade Federal do Paran\'{a, Curitiba, Brasilien, Oct. 29, 2014.
  • B. Wohlmuth. Singularities and pollution in case of re-entrant corners, IMA Workshop on Structure-Preserving Discretizations of Partial Differential Equations, Minneapolis, Oct. 22, 2014.
  • B. Wohlmuth. From reduced complexity to large scale computation, Chicago, Oct. 19, 2014.
  • U. Rüde. Optimal Algorithms for Elliptic PDE in the Presence of Singularities, 10th Workshop on Mathematical Modelling of Environmental and Life Sciences Problems, Constanta, Romania, Oct. 16, 2014.
  • U. Rüde. Challenges and Opportunities of Extreme Scale Numerical Simulation, Seminarul Stiintific de Matematica Aplicata, Ovidius-Universitatea, Constanta, Romania, Oct. 15, 2014.
  • U. Rüde. Towards Exascale Simulation Technology, Ringvorlesung "Simulationswissenschaften", TU Clausthal, Göttingen, Oct. 1, 2014.
  • U. Rüde. Perspectives of Granular Dynamics and Lattice Boltzmann Methods in Porous Media Applications, Workshop "Reactive Flows in Deformable, Complex Media", Oberwolfach, Sept. 23, 2014.
  • B. Wohlmuth. From reduced complexity to large scale computation, PTM-DMV 2014, Pozna, Sept. 19, 2014.
  • U. Rüde. Challenges and Opportunities of Extreme Scale Numerical Simulation, Lectures on Numerical Mathematics and Applications, Uni Würzburg, Würzburg, Aug. 27, 2014.
  • U. Rüde. Is 2.44 trillion unknowns the largest finite element system that can be solved today?, 4th European Seminar on Computing (ESCO 2014), Pilsen, Jun 16, 2014.
  • U. Rüde. Is 2.44 trillion unknowns the largest finite element system that can be solved today, Einladung, Charles University, Prag, Jun 09, 2014.
  • B. Wohlmuth. Consistent modelling of interface conditions for multi-physics applications, Charles University Prague, Jun 9, 2014.
  • B. Wohlmuth. Dual and hybrid hierarchical grids for fast Stokes solvers, Schnelle iterative Löser, MFO, May 11-16, 2014.
  • J. Weismüller, B. Gmeiner, M. Mohr, C. Waluga, H.-P. Bunge, Developing an exascale model for mantle convection, European Geosciences Union General Assembly 2014, Vienna, Austria, Apr. 27 - May 02, 2014.
  • U. Rüde. Is 2,44 trillion unknowns the largest finite element system that can be solved today?, Workshop "Advances in Numerical Algorithms and High Performance Computing", London, Apr. 14, 2014.
  • C. Waluga. Discretization Concepts for Terra-Neo. ExaStencils workshop 2014, University of Dresden, Germany, Mar. 31 - Apr. 1, 2014.
  • B. Wohlmuth. Duality and hierarchy in modern finite element analysis, Department of Mathematics, The University of Texas at Austin, Mar. 21, 2014.
  • U. Rüde. The waLBerla Framework: Multi-physics Simulations on Heterogeneous Platforms, 16th SIAM Conference on Parallel Processing for Scientific Computing (PP 14), SIAM, Portland, USA, Feb. 20, 2014.
  • B. Wohlmuth. Numerical schemes for variational inequalities in PDE based contact problems, BIRS, Banff, Feb. 19, 2014.
  • U. Rüde, Towards an Integrated Performance Oriented Co-Design Methodology, Dagstuhl Seminar "Connecting Performance Analysis and Visualization to Advance Extreme Scale Computing", Jan. 09, 2014.
2013
  • B. Gmeiner, C. Waluga, U. Rüde, B. Wohlmuth, Performance and Scalability of Hierarchical Hybrid Multigrid Solvers for Stokes Systems, New Algorithms for Exascale Computing, University of Cologne, Germany, Dec. 5, 2013.
  • U. Rüde, Towards Exa-Scale Simulation for Science and Engineering, Invitation, EDF, Paris, Nov. 29, 2013.
  • B. Gmeiner, U. Rüde, C. Waluga, and B. Wohlmuth, Mathematics meets high performance computation in geo-physics applications: Highly scalable multigrid Stokes solver for buoyancy driven non-isothermal Stokes simulation, 2014 DFG Math Calendar, p.20 (October)
  • U. Rüde, New Math for Exascale Computational Science?, DOE Workshop on Applied Mathematics Research for Exascale Computing, Washington Aug. 22, 2013.
  • H.-P. Bunge. Data Assimilation in Global Mantle Flow Models: Theory, Modelling and Uncertainties to Reconstruct Earth Structure Back in Time, invited lecture, SIAM GS13, Jun 17-20, Padua, Italy, 2013.
  • B. Gmeiner, U. Rüde, B. Wohlmuth, Peta-Scale Multigrid for the Stokes System with Finite Elements, 9th International Conference on Large-Scale Scientific Computations, Sozopol, Bulgaria, Jun. 06, 2013.
  • U. Rüde, Introduction to Parallel Scientific Computing, Workshop "Lecture on Numerical Mathematics and Applications", Zaragoza, Spain, Jun. 03, 2013.
  • J. Weismüller, M. Mohr, H.-P. Bunge, Convective patterns in a 2d mantle convection simulation, European Geosciences Union General Assembly 2013, Vienna, Austria, Apr. 07-12, 2013.
  • U. Rüde, Textbook parallel efficiency for multigrid, Weizmann Workshop 2013 on Multilevel computational methods and optimization, Israel, Apr. 04, 2013.
  • B. Gmeiner, U. Rüde, PetaScale Finite Element Methods for Hierarchical Hybrid Grids using Hybrid Parallelization, 16th Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado, USA, Mar. 19, 2013.
  • B. Wohlmuth, Consistent Modeling of Interface Conditions for Multi-Physics Applications, SIAM Conference on Computational Science and Engineering, Boston, USA, Mar. 01, 2013.
  • U. Rüde, Towards Exascale Computing: Multilevel Methods and Flow Solvers for Millions of Cores, Invitation, IWR - Institutskolloquium, Interdisciplinary Center for Scientific Computing, Heidelberg, Jan. 25, 2013.
2012