| An efficient computational scheme to simulate strongly-coupled multi-physics systems is studied in this thesis. Each problem domain, which may be modelled by a different physics principle, is solved by an existing Newton solver while the entire multi-domain system is also solved by Newton's method making this a multi-level Newton method. The inter-system coupling effects are incorporated by analytically evaluating the response sensitivity of each subsystem with respect to the responses of the other systems. The suggested method avoids the error prone finite difference based sensitivity analysis used in other multi-level Newton methods and, at the cost of minimal code modification, retains the advantage of rapid convergence over the conventional weakly coupled analyses by including all coupling terms. We analyze a fluid-structure interaction problem to demonstrate the method. Significant computational advantage is obtained over the finite difference based multi-level Newton approach and other conventional methods.; The suggested algorithm is extended to accommodate non-conforming interface meshes by accurately transferring the boundary data of one domain to another. The data transfer procedure satisfies the convergence and conservation requirements by employing the common refinement based discretization of the interface. |
