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Interaction of Waves with Frictional Interfaces Using Summation-by-Parts Difference Operators: Weak Enforcement of Nonlinear Boundary Conditions
Department of Geophysics, Stanford University.
Department of Geophysics, Stanford University.
Linköping University, Department of Mathematics, Scientific Computing. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7972-6183
2012 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 50, no 2, 341-367 p.Article in journal (Refereed) Published
Abstract [en]

We present a high-order difference method for problems in elastodynamics involving

the interaction of waves with highly nonlinear frictional interfaces. We restrict our

attention to two-dimensional antiplane problems involving deformation in only one direction.

Jump conditions that relate tractions on the interface, or fault, to the relative sliding velocity

across it are of a form closely related to those used in earthquake rupture models and

other frictional sliding problems. By using summation-by-parts (SBP) finite difference operators

and weak enforcement of boundary and interface conditions, a strictly stable method

is developed. Furthermore, it is shown that unless the nonlinear interface conditions are formulated

in terms of characteristic variables, as opposed to the physical variables in terms of

which they are more naturally stated, the semi-discretized system of equations can become

extremely stiff, preventing efficient solution using explicit time integrators.

The use of SBP operators also provides a rigorously defined energy balance for the discretized

problem that, as the mesh is refined, approaches the exact energy balance in the

continuous problem. This enables one to investigate earthquake energetics, for example the

efficiency with which elastic strain energy released during rupture is converted to radiated

energy carried by seismic waves, rather than dissipated by frictional sliding of the fault.

These theoretical results are confirmed by several numerical tests in both one and two dimensions

demonstrating the computational efficiency, the high-order convergence rate of

the method, the benefits of using strictly stable numerical methods for long time integration,

and the accuracy of the energy balance.

Place, publisher, year, edition, pages
Springer , 2012. Vol. 50, no 2, 341-367 p.
Keyword [en]
High order finite difference · Nonlinear boundary conditions · Simultaneous
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-67938DOI: 10.1007/s10915-011-9485-3ISI: 000299001800005OAI: oai:DiVA.org:liu-67938DiVA: diva2:414352
Note
funding agencies|NSF| EAR-0910574 EAR-0529922 |Southern California Earthquake Center (SCEC)||USGS| 07HQAG0008 1417 |Available from: 2011-05-09 Created: 2011-05-03 Last updated: 2013-08-30Bibliographically approved

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Nordström, Jan
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