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Earth System Modelling - Volume 2 pp 35–49Cite as

Efficiency for Adaptive Triangular Meshes: Key Issues of Future Approaches

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Part of the book series: SpringerBriefs in Earth System Sciences ((BRIEFSEARTHSYST,volume 1))

Abstract

In recent years, adaptive mesh refinement applications entered the field of ESM. These methods reveal their strength, wherever there are large (spatial) scale differences interacting locally. If a localized small scale feature needs to be resolved in order to simulate its influence on the large scale accurately, then adaptive mesh refinement comes to play.

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References

  • Bader M, Schraufstetter S, Vigh CA, Behrens J (2008) Memory efficient adaptive mesh generation and implementation of multigrid algorithms using sierpinski curves. Int J Comput Sci Eng 4(1):12–21

    Google Scholar 

  • Bader M, C B, Schwaiger J, Vigh CA (2010) Dynamically adaptive simulations with minimal memory requirement–solving the shallow water equations using Sierpinski curves. SIAM J Sci Comput 32(1):212–228

    Google Scholar 

  • Bänsch E (1991) Local mesh refinement in 2 and 3 dimensions. Impact Comput Sci Eng 3:181–191

    Google Scholar 

  • Behrens J (2005) Multilevel optimization by space-filling curves in adaptive atmospheric modeling. In: Hülsemann F, Kowarschik M, Rüde U (eds) Frontiers in simulation—18th symposium on simulation techniques. SCS Publishing House, Erlangen, pp 186–196

    Google Scholar 

  • Behrens J (2006) Adaptive atmospheric modeling—key techniques in grid generation, data structures, and numerical operations with applications, LNCSE, vol 54. Springer, Berlin

    Google Scholar 

  • Behrens J, Zimmermann J (2000) Parallelizing an unstructured grid generator with a space-filling curve approach. In: Bode A, Ludwig T, Karl W, Wismüller R (eds) Euro-Par 2000 parallel processing–6th international Euro-Par conference, Munich, Germany, August/Sptember 2000 proceedings, Springer Verlag, Berlin, Lecture Notes in Computer Science, vol 1900, pp 815–823

    Google Scholar 

  • Behrens J, Dethloff K, Hiller W, Rinke A (2000) Evolution of small-scale filaments in an adaptive advection model for idealized tracer transport. Mon Weather Rev 128:2976–2982

    Article  Google Scholar 

  • Behrens J, Rakowsky N, Hiller W, Handorf D, Läuter M, Päpke J, Dethloff K (2005) Amatos: parallel adaptive mesh generator for atmospheric and oceanic simulation. Ocean Modell 10(1–2):171–183

    Article  Google Scholar 

  • Carstensen C (2004) All first-order averaging techniques for a posteriori finite element error control on unstructured grids are efficient and reliable. Math Computat 73(247):1153–1165

    Article  Google Scholar 

  • Causon DM, Ingram DM, Mingham CG, Yang G, Pearson RV (2000) Calculation of shallow water flows using a Cartesian cut cell approach. Adv Water Res 23(5):545–562

    Article  Google Scholar 

  • Danilov S, Kivman G, Schröter J (2004) A finite element ocean model: principles and evaluation. Ocean Modell 6:125–150

    Article  Google Scholar 

  • de Berg M, van Kreveld M, Overmars M, Schwarzkopf O (2000) Computational geometry: Algorithms and applications. 2nd edn. Springer, Berlin

    Google Scholar 

  • Dörfler W (1996) A convergent adaptive algorithm for Poisson’s equation. SIAM J Numer Anal 33(3):1106–1134

    Article  Google Scholar 

  • Hanert E, Legat V, Deleersnijder E (2002) A comparison of three finite elements to solve the linear shallow water equations. Ocean Modell 5:17–35

    Article  Google Scholar 

  • Harig S, Chaeroni C, Pranowo WS, Behrens J (2008) Tsunami simulations on several scales: Comparison of approaches with unstructured meshes and nested grids. Ocean Dyn 58:429–440

    Google Scholar 

  • Läuter M, Handorf D, Rakowsky N, Behrens J, Frickenhaus S, Best M, Dethloff K, Hiller W (2007) A parallel adaptive barotropic model of the atmosphere. J Comput Phys 223(2):609–628

    Google Scholar 

  • Piggott MD, Pain CC, Gorman GJ, Power PW, Goddard AHJ (2005) h, r, and hr adaptivity with applications in numerical ocean modelling. Ocean Modell 10:95–113

    Article  Google Scholar 

  • Power PW, Piggott MD, Fang F, Gorman GJ, Pain CC, Marshall DP, Goddard AJH, Navon IM (2006) Adjoint goal-based error norms for adaptive mesh ocean modelling. Ocean Modell 15:3–38

    Article  Google Scholar 

  • Tanemura M, Ogawa T, Ogita N (1983) A new algorithm for three-dimensional Voronoi tesselation. J Comput Phys 51(2):191–207

    Article  Google Scholar 

  • Zienkiewicz OC, Zhu JZ (1987) A simple error estimator and adaptive procedure for practical engineering analysis. Int J Numer Meth Eng 24:337–357

    Article  Google Scholar 

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Authors and Affiliations

  1. KlimaCampus, Universität Hamburg, Grindelberg 5, 20144, Hamburg, Germany

    Jörn Behrens

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  1. Jörn Behrens
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Correspondence to Jörn Behrens .

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Behrens, J. (2012). Efficiency for Adaptive Triangular Meshes: Key Issues of Future Approaches. In: Earth System Modelling - Volume 2. SpringerBriefs in Earth System Sciences, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23831-4_5

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