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| Titel |
Implementing a matrix-free Newton-Krylov method in NorESM |
| VerfasserIn |
Ingjald Pilskog, Samar Khatiwala, Jerry Tjiputra |
| Konferenz |
EGU General Assembly 2017
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| Medientyp |
Artikel
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| Sprache |
en
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 19 (2017) |
| Datensatznummer |
250150545
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| Publikation (Nr.) |
 EGU/EGU2017-15017.pdf |
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| Zusammenfassung |
| Quasi-equilibrium ocean biogeochemistry states in Earth system models require prohibitively
demanding computational time, especially for when large number of tracers are involved.
This so-called spin-up typically is measured in the order of thousands of model years
integration. In this study, we implement a matrix-free Newton-Krylov method (Khatiwala,
2008) in the Norwegian Earth system model (NorESM) so the spin-up time can be reduced.
The idea is to construct the function F(u) = Φ(u(0),T) −u(0) = 0, which can be expressed
as a matrix in which we can apply Newton-Krylov methods to find the quasi-equilibrium
states. Unfortunately the interconnectivity and complexity of the processes leads to a dense
matrix, making it expensive and impractical to calculate the necessary Jacobian,
J = ∂F∕∂u.
The Newton-Krylov method remedies this issue through solving the matrix-vector
product Jδu, that can be approximated by (F (un + σδun)− F (un− 1))∕σ. The
differencing parameterσ is typical chosen dynamically, and n is the iteration index.
Matrix-free Newton-Krylov method requires a good preconditioner to improve the
convergence rate. By exploiting the inherent locality of the advection-diffusion operator, and
that in most biogeochemical models, the source/sink term at a grid point depends only on
tracer concentrations in the same vertical column, we obtain a good, sparse preconditioner.
The performance of this preconditioner can be improved again by applying both outer
Broyden updates during the Newton steps and inner Broyden updates during the Krylov
steps.
Khatiwala, S., 2008. Fast spin up of ocean biogeochemical models using matrix-free
Newton-Krylov. Ocean Model. 23 (3-4), 121-129. |
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