A Domain Decomposition Approach to Implementing Fault Slip in Finite-Element Models of Quasi-static and Dynamic Crustal Deformation

TL;DR

This paper introduces a domain decomposition method with Lagrange multipliers for implementing fault slip in finite-element models, enabling scalable simulations of crustal deformation in both static and dynamic contexts.

Contribution

The authors develop a novel domain decomposition approach with a custom preconditioner for fault slip modeling in finite-element codes, applicable to quasi-static and dynamic crustal deformation.

Findings

The method demonstrates excellent scalability with problem size.

Successful verification through benchmarks for viscoelastic deformation.

Effective simulation of dynamic rupture propagation.

Abstract

We employ a domain decomposition approach with Lagrange multipliers to implement fault slip in a finite-element code, PyLith, for use in both quasi-static and dynamic crustal deformation applications. This integrated approach to solving both quasi-static and dynamic simulations leverages common finite-element data structures and implementations of various boundary conditions, discretization schemes, and bulk and fault rheologies. We have developed a custom preconditioner for the Lagrange multiplier portion of the system of equations that provides excellent scalability with problem size compared to conventional additive Schwarz methods. We demonstrate application of this approach using benchmarks for both quasi-static viscoelastic deformation and dynamic spontaneous rupture propagation that verify the numerical implementation in PyLith.