Narrow Results

We study an iteration for the solution of two-body contact problems without friction based on one-sided contact problems for one body and Neumann problems for the other one. The convergence of this iteration is proved in the continuous setting by reformulating it as a fixed point iteration for a contractive operator. In addition, the application of the method with mortar finite elements is discussed, and the convergence of the corresponding discrete iteration is verified.

We couple a time-dependent poroelastic model in a region with an elastic model in adjacent regions. We discretize each model independently on non-matching grids and we realize a domain decomposition on the interface between the regions by introducing DG jumps and mortars. The unknowns are condensed on the interface, so that at each time step, the computation in each subdomain can be performed in parallel. In addition, by extrapolating the displacement, we present an algorithm where the computations of the pressure and displacement are decoupled. We show that the matrix of the interface problem is positive definite and establish error estimates for this scheme.

This paper describes a generic algorithm for concurrently solving multiple sub-domains that are selectively discretized in space and time. The mathematical background for this approach is largely based upon the fundamental principles of domain decomposition methods (DDM) and Lagrange multipliers. A proof of stability is provided using energy method and overall efficiency, accuracy and stability of multiple sub-domain coupling is evaluated using a series of numerical examples. Numerical stability is verified by ensuring energy balance at global as well as component sub-domain level. Discussed examples highlight the greatest advantage of MGMT method; which is high simulation speedups (at the cost of reasonably small errors).