High accuracy mantle convection simulation through modern numerical methods

Martin Kronbichler, Timo Heister, Wolfgang Bangerth

Research output: Contribution to journalArticlepeer-review

236 Scopus citations


Numerical simulation of the processes in the Earth's mantle is a key piece in understanding its dynamics, composition, history and interaction with the lithosphere and the Earth's core. However, doing so presents many practical difficulties related to the numerical methods that can accurately represent these processes at relevant scales. This paper presents an overview of the state of the art in algorithms for high-Rayleigh number flows such as those in the Earth's mantle, and discusses their implementation in the Open Source code Aspect (Advanced Solver for Problems in Earth's ConvecTion). Specifically, we show how an interconnected set of methods for adaptive mesh refinement (AMR), higher order spatial and temporal discretizations, advection stabilization and efficient linear solvers can provide high accuracy at a numerical cost unachievable with traditional methods, and how these methods can be designed in a way so that they scale to large numbers of processors on compute clusters. Aspect relies on the numerical software packages deal.II and Trilinos, enabling us to focus on high level code and keeping our implementation compact. We present results from validation tests using widely used benchmarks for our code, as well as scaling results from parallel runs. © 2012 The Authors Geophysical Journal International © 2012 RAS.
Original languageEnglish (US)
Pages (from-to)12-29
Number of pages18
JournalGeophysical Journal International
Issue number1
StatePublished - Aug 21 2012
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The first author was supported by the Graduate School in Mathematics and Computing (FMB) at Uppsala University, Sweden. The second and third authors are supported in part through the Computational Infrastructure in Geodynamics initiative (CIG), through the National Science Foundation under Award No. EAR-0949446 and The University of California-Davis. This publication is based in part on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The third author is also supported in part by an Alfred P. Sloan Research Fellowship.Some computations for this paper were performed on the 'Ranger' and 'Lonestar' clusters at the Texas Advanced Computing Center (TACC), and the 'Brazos' and 'Hurr' clusters at the Institute for Applied Mathematics and Computational Science (IAMCS) at Texas A&M University. Ranger was funded by NSF award OCI-0622780, and we used an allocation obtained under NSF award TG-MCA04N026. The authors acknowledge the Texas A&M Supercomputing Facility for providing computing resources on 'Lonestar' useful in conducting the research reported in this paper. Part of Brazos was supported by NSF award DMS-0922866. Hurr is supported by Award No. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST). Some computations were performed on resources provided by SNIC through Uppsala Multidisciplinary Center for Advanced Computational Science (UPPMAX) under project p2010002.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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