Prof. Dr. Carsten Burstedde

E-mail: burstedde(at)
Phone: +49 228 73 3165
Room: 4.009
Location: Wegelerstr. 6
Institute: Institute for Numerical Simulation
Research Area: Research Area J
Mathscinet-Number: 790099

Academic Career

1995 - 2001

Undergraduate studies, University of Cologne


Vordiplom (intermediate diploma) in both Mathematics and Physics

1997 -1998

Exchange year (physics), University of Edinburgh, Scotland, UK


Diploma of physics (with distinction); Master's equivalent

2001 - 2006

Graduate studies, University of Bonn


Dr. rer. nat. (magna cum laude)


Postdoc, RWTH Aachen

2006 - 2008

Postdoc, ICES, University of Texas, Austin, TX, USA

2008 - 2010

Research Associate, ICES, TX, USA

2010 - 2011

Research Scientist, ICES, TX, USA

Since 2011

Professor (W2), University of Bonn

Research Profile

My research over the past years has been centered around developing fast and scalable algorithms to work with adaptive meshes on large parallel computers. A computational mesh is a collection of elements of primitive shapes, in this case (smoothly mapped) quadrilaterals (2D) or hexahedra (3D), together with a definition of the connectivity between neighboring elements. There are various constructions that allow for adaptivity, that is, non-uniform size- and spatial distribution of elements. The approach that has been most successful in our work is the synthesis of a coarse conforming mesh, where neighboring elements fully match along their boundary faces and edges, with a non-conforming recursive subdivision of each of these coarse mesh elements that is mathematically a tree. This scheme may conveniently be called a forest of elements. The key to efficient algorithms for refining, coarsening, partitioning, and traversing such a mesh, and identifying and numbering its faces, edges, and nodes, lies in exploiting the tree structure in favorable ways while respecting the reality of parallel hardware and its networking stack.
This research has led to new algorithms and their implementation in the publicly available software ''p4est''. In various collaborations over the past decade, these algorithms have been integrated with scientific applications. In addition to the simulation of earth's mantle convection and the propagation of elastic and acoustic waves using Galerkin discretizations, we have enabled finite volume methods for simulating atmospheric flow, semi-Lagrangian methods for the research of crystal growth, and Lattice-Boltzmann methods to simulate general fluid flow.
These applications benefit significantly from the flexibility offered by adaptive mesh refinement (AMR) and the speed and scalability of mesh-related operations.

In collaboration with PhD student Johannes Holke, we have recently proposed an extension of the so-called Morton- or Z-curve to triangular and tetrahedral elements and implemented basic algorithms for non-conforming simplicial AMR.
Especially the 3D case is less obvious and more complex than the existing hexahedral logic.
Encouraged by our initial results, we are working towards the long-term goal of non-conforming hybrid AMR, that is, allowing to mix shapes of many kinds in the same mesh, ideally offering a speed comparable to hex-only algorithms.

In collaboration with PhD student Alberto Fonseca, we are working to introduce parallel adaptivity into a community code for the simulation of subsurface flow, such as that of groundwater through the earth. Our hope is that extending the scalability of existing codes, even in the case of standard uniform meshes, will allow for more highly resolved simulations and thus more accurate research in computational hydrology.
With respect to future applications, we are targeting the simulation of the transport of volcanic ash. In addition, we have begun collaborating on parallel GPU-based techniques for fluid flow.

Research Projects and Activities

Johannes Holke's work on tetrahedral AMR is sponsored by the Bonn International Graduate School as part of the Hausdorff Center for Mathematics.

Alberto Fonseca is supported by the Collaborative Research Center SFB/TR 32. Both centers are funded by the German Research Foundation (DFG).

We have been awarded close to 9 million compute hours on the “Juqueen” supercomputer at the Jülich Supercomputing Centre in 2013 - 2017.

Selected Publications

[1] Carsten Burstedde, Johannes Holke
A tetrahedral space-filling curve for nonconforming adaptive meshes
SIAM J. Sci. Comput. , 38: (5): C471--C503
DOI: 10.1137/15M1040049
[2] Mohammad Mirzadeh, Arthur Guittet, Carsten Burstedde, Frederic Gibou
Parallel level-set methods on adaptive tree-based grids
J. Comput. Phys. , 322: : 345--364
DOI: 10.1016/
[3] Tobin Isaac, Carsten Burstedde, Lucas C. Wilcox, Omar Ghattas
Recursive algorithms for distributed forests of octrees
SIAM J. Sci. Comput. , 37: (5): C497--C531
DOI: 10.1137/140970963
[4] Carsten Burstedde, Georg Stadler, Laura Alisic, Lucas C. Wilcox, Eh Tan, Michael Gurnis, Omar Ghattas
Large-scale adaptive mantle convection simulation
Geophysical Journal International , 192: (3): 889-906
DOI: 10.1093/gji/ggs070
[5] Hari Sundar, George Biros, Carsten Burstedde, Johann Rudi, Omar Ghattas, Georg Stadler
Parallel Geometric-Algebraic Multigrid on Unstructured Forests of Octrees
SC12: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis
Publisher: ACM/IEEE
[6] James Martin, Lucas C. Wilcox, Carsten Burstedde, Omar Ghattas
A stochastic Newton MCMC method for large-scale statistical inverse problems with application to seismic inversion
SIAM J. Sci. Comput. , 34: (3): A1460--A1487
DOI: 10.1137/110845598
[7] Wolfgang Bangerth, Carsten Burstedde, Timo Heister, Martin Kronbichler
Algorithms and data structures for massively parallel generic adaptive finite element codes
ACM Trans. Math. Software , 38: (2): Art. 14, 28
DOI: 10.1145/2049673.2049678
[8] Carsten Burstedde, Lucas C. Wilcox, Omar Ghattas
p4est: scalable algorithms for parallel adaptive mesh refinement on forests of octrees
SIAM J. Sci. Comput. , 33: (3): 1103--1133
DOI: 10.1137/100791634
[9] Carsten Burstedde, Omar Ghattas, Michael Gurnis, Tobin Isaac, Georg Stadler, Tim Warburton, Lucas C. Wilcox
Extreme-Scale AMR
SC10: Proceedings of the International Conference for High Performance Computing, Networking, Storage, and Analysis
Publisher: ACM/IEEE
[10] Carsten Burstedde, Omar Ghattas, Michael Gurnis, Eh Tan, Tiankai Tu, Georg Stadler, Lucas C. Wilcox, Shijie Zhong
Scalable adaptive mantle convection simulation on petascale supercomputers
SC08: Proceedings of the International Conference for High Performance Computing, Networking, Storage, and Analysis
Publisher: ACM/IEEE
ISBN: 978-1-4244-2835-9

Publication List


• Simula Research Laboratory (Scientific Advisory Board, 2014 – 2016)
• Archive of Numerical Software



NSF TeraGrid Capability Computing Challenge Award


Best Poster Award at the ACM/IEEE SC Conference


Springer CSE Prize

Selected Invited Lectures


Parallel adaptive mesh refinement for element based flow simulation. Invited presentation at the ICMS workshop on Galerkin methods with applications in weather and climate forecasting, Edinburgh, Scotland, UK


Parallel Tree Algorithms for Adaptive Mesh Refinement. Plenary lecture at the Tetrahedron V Workshop on Grid Generation for Numerical Computations, Liège, Belgium

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