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| Titel |
Advances in three-dimensional, finite-element based marker-in-cell methods applied to geodynamics |
| VerfasserIn |
D. A. May |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250069553
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| Zusammenfassung |
| The use of a mixed finite element formulation to discretise Stokes equations, coupled with a particle based Lagrangian representation of the material lithology, is a common numerical technique employed within the Earth sciences to study geodynamic processes. The extension of this methodology to study high-resolution, three-dimensional problems, even in 2012, still represents a number of significant computational challenges. Of paramount concern are the high computational memory requirements, and the development of efficient and robust linear and non-linear solvers, which are performant on massively parallel supercomputers.
In this presentation, I describe a flexible methodology, which aims to rectify both of these issues. The key to the approach is to 1) always pose the discrete problem in defect-correction form and 2) utilise a mixture of assembled and matrix-free operations to evaluate the non-linear residual, and the operators required to define the multilevel preconditioner for the Jacobian.
The performance characteristics of the hybrid matrix-free, partially assembled multilevel preconditioning strategy is demonstrated by considering several variable viscosity Stokes problems employing the mixed element types Q2-P1 and Q1-Q1 (Bochev stabilisation). The robustness of the preconditioner with respect to the viscosity contrast and the topology of the viscosity field, together with the parallel scalability will be discussed. |
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