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All Journal Rahmah
Gul Agha Jan Assar
Department of Applied Mathematics, Faculty of Mathematics, Kabul University
Humanities Economics, Econometrics & Finance Environmental Science Social Sciences Other

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A Variational Multigrid Framework for Multiscale Fault Systems with Rate- and State-Dependent Friction: Convergence Analysis and Adaptive Solution Strategies Gul Agha Jan Assar; Mohammad Khalid Storai
Rahmah : Jurnal Pengabdian Masyarakat Vol. 2 No. 1 (2026): Rahmah : Jurnal Pengabdian Masyarakat
Publisher : Jaanur ElBarik Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.65065/jvcdt034

Abstract

We present a comprehensive variational framework for the numerical simulation of multiscale geological fault systems governed by rate- and state-dependent friction laws. Extending the variational approach for subduction zones to layered fault networks with multiple non-intersecting interfaces, we derive a mathematical model that encompasses both Dieterich- and Ruina-type friction as special cases while accommodating large tangential displacements. Semi-discretization in time via an energy-conserving Newmark scheme yields a coupled system of nonsmooth convex minimization problems at each time step. Spatial discretization employs a dual-mortar finite element method with a piecewise-constant state approximation, enabling efficient decoupling via fixed-point iteration. For the resulting rate problems, we establish convergence of truncated nonsmooth Newton multigrid (TNNMG) methods and prove stability of the fully discrete scheme under standard regularity assumptions. Numerical experiments on spring-slider and layered five-body configurations demonstrate the robustness of the solver with respect to the number of faults, with adaptive time-stepping capturing slip events across multiple orders of magnitude in velocity variation
Co-Authors Mohammad Khalid Storai