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Accurate Calculation of Fault-Rupture Models Using the High-Order Discontinuous Galerkin Method on Tetrahedral Meshes

Käser, Martin, Paul Martin Mai, and Michael Dumbser (2007), Accurate Calculation of Fault-Rupture Models Using the High-Order Discontinuous Galerkin Method on Tetrahedral Meshes, Bull. Seis. Soc. Am., 97(5), 1570-1586, doi:10.1785/0120060253.

Abstract
We present a new method for near-source ground-motion calculations due to earthquake
rupture on potentially geometrically complex faults. Following the recently introduced Discontinuous Galerkin approach with local time stepping on tetrahedral meshes, we use piecewise polynomial approximations of the unknown variables inside each element and achieve the same approximation order in time and space due to the new ADER time integration scheme that uses Arbitrary high-order DERivatives. We show how an external source term and its heterogeneous properties in space and time, given by a fine discretization of an extended rupture surface, can be included in much coarser tetrahedral meshes due to the subcell resolution of the high-order polynomial representation. Hereby, the rupture surface is represented very generally as a point cloud of the center locations of individual subfaults at which each polynomial test function is evaluated exactly inside an element and the space-time integration of the source term is accurately computed at each time step. Besides the incorporation of complex source kinematics we also present the effects of model boundaries that can degrade the accuracy of seismograms due to weak artificial reflections. We propose an extended computational domain of a coarsely meshed buffer region and show, that our scheme using the local time stepping completely avoids such boundary problems with only slightly increasing the computational cost. We validate the new approach against different test cases, comparing our results with analytic, quasi-analytic and a series of reference solutions. Our work shows that adding the functionality of accurately treating finite source rupture models into the general framework of the ADER-Discontinuous Galerkin approach is an important contribution to model realistic earthquake scenarios, allowing to efficiently include heterogeneous source kinematics and complex rupture surface geometries into near-source ground-motion simulations.
BibTeX
@article{id871,
  author = {Martin K{\"a}ser and Paul Martin Mai and Michael Dumbser},
  journal = {Bull. Seis. Soc. Am.},
  month = {oct},
  number = {5},
  pages = {1570-1586},
  title = {{Accurate Calculation of Fault-Rupture Models Using the High-Order Discontinuous Galerkin Method on Tetrahedral Meshes}},
  volume = {97},
  year = {2007},
  doi = {10.1785/0120060253},
}
EndNote
%0 Journal Article
%A Käser, Martin
%A Mai, Paul Martin
%A Dumbser, Michael
%D 2007
%N 5
%V 97
%J Bull. Seis. Soc. Am.
%P 1570-1586
%T Accurate Calculation of Fault-Rupture Models Using the High-Order Discontinuous Galerkin Method on Tetrahedral Meshes
%8 oct
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Printed 15. Dec 2019 22:26