The DUNE-ALUGrid Module.

Martin Alkämper, Andreas Dedner, Robert Klöfkorn, Martin Nolte

Abstract


In this paper we present the new DUNE-ALUGrid module. This module
contains a major overhaul of the sources from the ALUGrid library and the
binding to the DUNE software framework. The main improvements concern the
parallel feature set of the library. The main changes include user-defined load
balancing, parallel grid construction, and an redesign of the 2d grid which can now
also be used for parallel computations. In addition many improvements
have been introduced into the code to increase the parallel efficiency and
to decrease the memory footprint. 

The original ALUGrid library is widely used within the DUNE community due to its good parallel performance for problems requiring local adaptivity and dynamic load balancing. Therefore, this new model will benefit a number of DUNE users. In addition we have
added features to increase the range of problems for which the grid manager can
be used, for example, introducing a 3d tetrahedral grid using a parallel newest vertex bisection algorithm for conforming grid refinement. In this paper we will discuss the new features, extensions to the DUNE interface,  and explain for various examples how the code is used in parallel environments.




Keywords


Numerical software, Adaptive-parallel grid, Load Balancing, DUNE

Full Text:

PDF

References


T. Albrecht, A. Dedner, M. Lüthi, and T. Vetter. Finite Element Surface Registration Incorporating Curvature, Volume Preservation, and Statistical Model Information. Comp. Math. Methods in

Medicine, 2013, 2013.

M. Bader. Space-Filling Curves - An Introduction with Applications in Scientific Computing, volume 9 of Texts in Computational Science and Engineering. Springer-Verlag, 2013. URL http://link.springer.com/book/10.1007/978-3-642-31046-1/page/1.

W. Bangerth, T. Heister, L. Heltai, G. Kanschat, M. Kronbichler, M. Maier, B. Turcksin, and T. D. Young. The deal.ii library, version 8.1. arXiv preprint http://arxiv.org/abs/1312.2266v4,

P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, R. Kornhuber, M. Ohlberger, and O. Sander. A Generic Grid Interface for Parallel and Adaptive Scientific Computing. Part II: Implementation and Tests in DUNE. Computing, 82(2–3):121–138, 2008a. URL http://www.springerlink.com/content/gn177r643q2168g7/.

P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, M. Ohlberger, and O. Sander. A Generic Grid Interface for Parallel and Adaptive Scientific Computing. Part I: Abstract Framework. Computing, 82(2–3):103–119, 2008b. URL http://www.springerlink.com/content/

v77662363u41534/.

E. G. Boman, U. V. Catalyurek, C. Chevalier, and K. D. Devine. The Zoltan and Isorropia parallel toolkits for combinatorial scientific computing: Partitioning, ordering, and coloring. Scientific Programming, 20(2), 2012. URL http://www.cs.sandia.gov/zoltan/.

S. Brdar, M. Baldauf, A. Dedner, and R. Klöfkorn. Comparison of dynamical cores for NWP models: comparison of COSMO and DUNE. Theoretical and Computational Fluid Dynamics, 27 (3-4):453–472, 2013. URL http://dx.doi.org/10.1007/s00162-012-0264-z.

A. Burri, A. Dedner, R. Klöfkorn, and M. Ohlberger. An ecient implementation of an adaptive and parallel grid in dune. In E. K. et al., editor, Computational Science and High Performance Computing II, volume 91, pages 67–82. Springer, 2006. URL http://dx.doi.org/10.1007/3-540-31768-6_7.

C. Burstedde, L. Wilcox, and O. Ghattas. p4est: Scalable algorithms for parallel adaptive mesh refinement on forests of octrees. SIAM Journal on Scientific Computing, 33(3):1103–1133, 2011.URL http://dx.doi.org/10.1137/100791634

A. Dedner and R. Klöfkorn. A Generic Stabilization Approach for Higher Order Discontinuous Galerkin Methods for Convection Dominated Problems. J. Sci. Comput., 47(3):365–388, 2011.URL http://dx.doi.org/10.1007/s10915-010-9448-0.

A. Dedner, C. Rohde, B. Schupp, and M. Wesenberg. A parallel, load balanced MHD code on locally adapted, unstructured grids in 3D. Comput. Vis. Sci., 7(2):79–96, 2004. B. Faigle. Adaptive modelling of compositional multi-phase flow with capillary pressure. PhD thesis, Universität Stuttgart, 2014. URL http://elib.uni-stuttgart.de/opus/volltexte/2014/

/.

A. Fallahi and B. Oswald. The element level time domain (eltd) method for the analysis of nano-optical systems: Ii. dispersive media. Photonics and Nanostructures - Fundamentals and Applications, 10(2):223 – 235, 2012. URL http://www.sciencedirect.com/science/article/

pii/S156944101200017X.

W. Frings, F.Wolf, and V. Petkov. Scalable massively parallel I/O to task-local files. In Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis, SC ’09, pages 17:1–17:11, New York, NY, USA, 2009. ACM. URL http://doi.acm.org/10.1145/1654059.

J.-L. Gailly and M. Adler. zlib – A Massively SpiùYet Delicately Unobtrusive Compression Library. URL http://www.zlib.net/.

T. Geßner and D. Kröner. Dynamic mesh adaption for supersonic reactive flow. In H. Freistühler and G. Warnecke, editors, Hyperbolic Problems: Theory, Numerics, Applications, volume 140 of International Series of Numerical Mathematics, pages 415–424. Birkhäuser Basel, 2001. URL

http://dx.doi.org/10.1007/978-3-0348-8370-2_44.

M. Jehl, A. Dedner, T. Betcke, K. Aristovich, R. Klöfkorn, and D. Holder. A Fast Parallel Solver for the Forward Problem in Electrical Impedance Tomography. Biomedical Engineering, IEEE Transactions on, 62(1):126–137, Jan 2015. URL http://dx.doi.org/10.1109/TBME.2014.2342280.

G. Karypis and V. Kumar. A fast and highly quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput., 20(1):359–392, 1999. URL http://glaros.dtc.umn.edu/gkhome/metis/metis/overview.

B. Kirk, J. Peterson, R. Stogne, and G. Carey. libMesh: A C++ Library for Parallel Adaptive Mesh Refinement/Coarsening Simulations. Engineering with Computers, 22(3–4):237–254, 2006. URL http://dx.doi.org/10.1007/s00366-006-0049-3.

R. Klöfkorn. Numerics for Evolution Equations — A General Interface Based Design Concept. PhD thesis, Albert-Ludwigs-Universität Freiburg, 2009. URL http://www.freidok.uni-freiburg.de/volltexte/7175/.

R. Klöfkorn. Elementcient Matrix-Free Implementation of Discontinuous Galerkin Methods for Compressible Flow Problems. In A. H. et al., editor, Proceedings of the ALGORITMY 2012, pages 11–21,

URL http://www.iam.fmph.uniba.sk/algoritmy2012/zbornik/2Kloefkornf.pdf.

R. Klöfkorn and M. Nolte. Performance Pitfalls in the Dune Grid Interface. In A. Dedner, B. Flemisch, and R. Klöfkorn, editors, Advances in Dune, pages 45–58. Springer Berlin Heidelberg, 2012. URL http://dx.doi.org/10.1007/978-3-642-28589-9_4.

R. Klöfkorn and M. Nolte. Solving the Reactive Compressible Navier-Stokes Equations in a Moving Domain. In K. Binder, G. Münster, and M. Kremer, editors, NIC Symposium 2014 - Proceedings, volume 47. John von Neumann Institute for Computing Jülich, 2014.

S. Lang, C. Wieners, and G. Wittum. The Application of Adaptive Parallel Multigrid Methods to Problems in Nonlinear Solid Mechanics. In E. e. a. Stein, editor, Error-controlled adaptive finite elements in solid mechanics, pages 346–379.Wiley, 2003.

D. Lea. A memory allocator. Unix/Mail, 1996. URL http://gee.cs.oswego.edu/dl/html/malloc.html.

C. May. Realistic simulation of semiconductor nanostructures. PhD thesis, Eidgenössische Technische Hochschule ETH Zürich, 2009. URL http://dx.doi.org/10.3929/ethz-a-006092601.

E. Müller and R. Scheichl. Massively parallel solvers for elliptic partial differtential equations in numerical weather and climate prediction. Q.J.R. Meteorol. Soc., 2014. URL http://dx.doi.org/10.1002/qj.2327.

S. Müthing and P. Bastian. Dune-Multidomaingrid: A Metagrid Approach to Subdomain Modeling. In A. Dedner, B. Flemisch, and R. Klöfkorn, editors, Advances in DUNE, pages 59–73.

Springer Berlin Heidelberg, 2012. URL http://dx.doi.org/10.1007/978-3-642-28589-9_5.

NCAR/CISL. Computational and Information Systems Laboratory. Yellowstone: IBM iDataPlex System (Climate Simulation Laboratory). Boulder, CO: National Center for Atmospheric Research., 2012. URL http://n2t.net/ark:/85065/d7wd3xhc.

K. Schloegel, G. Karypis, and V. Kumar. Parallel static and dynamic multi-constraint graph partitioning. Concurrency and Computation: Practice and Experience, 14(3):219 – 240, 2002. URL

http://glaros.dtc.umn.edu/gkhome/metis/parmetis/overview.

A. Schmidt and K. Siebert. Design of Adaptive Finite Element Software – The Finite Elemet Toolbox ALBERTA. Springer, 2005.

B. Schupp. Entwicklung eines ecientzienten Verfahrens zur Simulation kompressibler Strömungen in 3D auf Parallelrechnern. Doctoral Dissertation (in German), Albert-Ludwigs-Universität Freiburg, 1999. URL http://www.freidok.uni-freiburg.de/volltexte/68/.

E. Toro. Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer, 2009.

S. Vey and A. Voigt. Amdis: adaptive multidimensional simulations. Comput.Visual. Sci., 10(1): 57–67, 2007. ISSN 1432-9360. doi: 10.1007/s00791-006-0048-3. URL http://dx.doi.org/10.1007,s00791-006-0048-3.

T. Witkowski, S. Ling, S. Praetorius, and A. Voigt. Software concepts and numerical algorithms for a scalable adaptive parallel finite element method. Advances in Computational Mathematics,

pages 1–33, 2015. ISSN 1019-7168. doi: 10.1007/s10444-015-9405-4. URL http://dx.doi.org/10.1007/s10444-015-9405-4.

T. Xie, S. Seol, and M. Shephard. Generic components for petascale adaptive unstructured meshbased simulations. Engineering with Computers, 30(1):79–95, 2014. URL http://dx.doi.org/

1007/s00366-012-0288-4. Archive





DOI: https://doi.org/10.11588/ans.2016.1.23252

URN (PDF): http://nbn-resolving.de/urn:nbn:de:bsz:16-ans-232527