A multigrid solver for modeling complex interseismic stress fields

  • Authors:

  • Seoleun Shin;Gert Zöller;Matthias Holschneider;Sebastian Reich

  • Affiliations:

  • Universität Potsdam, Institut für Mathematik, Am Neuen Palais 10, D-14469 Potsdam, Germany;Universität Potsdam, Institut für Mathematik, Am Neuen Palais 10, D-14469 Potsdam, Germany;Universität Potsdam, Institut für Mathematik, Am Neuen Palais 10, D-14469 Potsdam, Germany;Universität Potsdam, Institut für Mathematik, Am Neuen Palais 10, D-14469 Potsdam, Germany

  • Venue:
  • Computers & Geosciences
  • Year:
  • 2011

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Abstract

We develop a multigrid, multiple time stepping scheme to reduce computational efforts for calculating complex stress interactions in a strike-slip 2D planar fault for the simulation of seismicity. The key elements of the multilevel solver are separation of length scale, grid-coarsening, and hierarchy. In this study the complex stress interactions are split into two parts: the first with a small contribution is computed on a coarse level, and the rest for strong interactions is on a fine level. This partition leads to a significant reduction of the number of computations. The reduction of complexity is even enhanced by combining the multigrid with multiple time stepping. Computational efficiency is enhanced by a factor of 10 while retaining a reasonable accuracy, compared to the original full matrix-vortex multiplication. The accuracy of solution and computational efficiency depend on a given cut-off radius that splits multiplications into the two parts. The multigrid scheme is constructed in such a way that it conserves stress in the entire half-space.