PARALLEL CONTACT ANALYSIS ALGORITHM BASED ON DOMAIN DECOMPOSITION AND TWO-GRID METHOD

For most domain decomposition-based parallel analysis algorithms, a single computational grid cannot ensure real-time exchange of solution information between not directly neighboring subdomains, so the algorithms exhibit slow convergence rate. The two-grid method is an effective method to optimize the convergence rate of domain decomposition-based parallel analysis algorithms. Focusing on the elastic contact problem, it involves strongly nonlinear factors, such as unknown contact region, unknown contact state, inequality contact constraint, complicated frictional constitutive law, etc. If these contact nonlinear factors are not well assumed to become linear, it will be very difficult to construct global approximate solution on coarse mesh for the two-grid method; on the contrary, if the global approximate solution on coarse mesh is constructed under intentional assumption about contact state, then the iteration procedure will be easy to fall into intentionally assumed contact state and does not converge on condition that the iteration level is not increased. In view of this, this work constructs a global approximate solution on coarse mesh which does not rely on intentional assumption about contact state, then the two-grid method is adopted to optimize the convergence rate of domain decomposition-based parallel contact analysis algorithm. Firstly, the global computational domain is decomposed into non-overlapping subdomains along contact boundaries and division boundaries, the alternating direction method of multipliers is adopted to establish the one-grid based parallel contact analysis procedure. Next, similar to the multiscale strategy in LATIN method, the global problem which satisfies equilibrium between subdomains is constructed and restricted onto coarse mesh according to the geometric multigrid method, the approximate solution on coarse mesh is computed to correct the solution on computational mesh. Through comparison with dual mortar contact analysis algorithm, the effectiveness of the parallel contact analysis algorithm based on domain decomposition and two-grid method is verified for solving large-scale contact problems.