On the Schwarz alternating method with more than two subdomains for nonlinear monotone problems
SIAM Journal on Numerical Analysis
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Some Nonoverlapping Domain Decomposition Methods
SIAM Review
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
A New Family of Mixed Finite Elements for the Linear Elastodynamic Problem
SIAM Journal on Numerical Analysis
Slip-dependent friction in dynamic elasticity
Nonlinear Analysis: Theory, Methods & Applications
Convergence Rate Analysis of a Multiplicative Schwarz Method for Variational Inequalities
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Schwarz method for earthquake source dynamics
Journal of Computational Physics
| Hi-index | 31.46 |
The anti-plane shearing problem on a system of finite faults under a slip-dependent friction in a linear elastic domain is considered. Using a Newmark method for the time discretization of the problem, we have obtained an elliptic variational inequality at each time step. An upper bound for the time step size, which is not a CFL condition, is deduced from the solution uniqueness criterion using the first eigenvalue of the tangent problem. Finite element form of the variational inequality is solved by a Schwarz method assuming that the inner nodes of the domain lie in one subdomain and the nodes on the fault lie in other subdomains. Two decompositions of the domain are analyzed, one made up of two subdomains and another one with three subdomains. Numerical experiments are performed to illustrate convergence for a single time step (convergence of the Schwarz algorithm, influence of the mesh size, influence of the time step), convergence in time (instability capturing, energy dissipation, optimal time step) and an application to a relevant physical problem (interacting parallel fault segments).