A highly parallel algorithm has been developed and exploited to compute the planetary normal modes of the elastic-gravitational system, which is approximated via the mixed finite element method on unstructured tetrahedral meshes. The eigenmodes of the relevant generalized eigenvalue problem were extracted by a Lanczos approach combined with polynomial filtering. In contrast with the standard shift-and-invert and the full-mode coupling algorithms, the polynomial filtering technique is ideally suited for solving large-scale 3-D interior eigenvalue problems since it significantly enhances the memory and computational efficiency without loss of accuracy. The parallel efficiency and scalability of this approach are demonstrated on Stampede2 at the Texas Advanced Computing Center. To our knowledge, this is the first time that the direct calculation of the normal modes of 3-D strongly heterogeneous planets, in particular, Earth and Mars, is made feasible via a combination of multiple matrix-free methods and a separation of the essential spectra.
|Original language||English (US)|
|Title of host publication||Proceedings - International Conference for High Performance Computing, Networking, Storage, and Analysis, SC 2018|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||13|
|State||Published - Mar 11 2019|
|Event||2018 International Conference for High Performance Computing, Networking, Storage, and Analysis, SC 2018 - Dallas, United States|
Duration: Nov 11 2018 → Nov 16 2018
|Name||Proceedings - International Conference for High Performance Computing, Networking, Storage, and Analysis, SC 2018|
|Conference||2018 International Conference for High Performance Computing, Networking, Storage, and Analysis, SC 2018|
|Period||11/11/18 → 11/16/18|
Bibliographical noteFunding Information:
ACKNOWLEDGMENT J.S and M.dH were supported by the Simons foundation and XSEDE TG-EAR170019. The work of R.L was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 (LLNL-CONF-753896). Y.X and Y.S were supported by NSF grants CCF-1318597, DMS-1521573, CCF-1505970.
© 2018 IEEE.
- Eigenvalues and Eigenfunctions