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Efficient modeling and computation of the nonlinear interaction of fluid with a solid undergoing nonlinear deformation has remained a challenging problem in computational science and engineering. Direct numerical simulation of the non-linear equations, governing even the most simplified fluid-structure interaction model depends on the convergence of iterative solvers which in turn relies heavily on the properties of the coupled system. The purpose of this work is to model and simulate multi-physics applications that involve fluid-structure interaction using a distributed multilevel algorithm with finite elements. The proposed algorithm is tested using COMSOL which offers the flexibility and efficiency to study coupled problems involving fluid-structure interaction. Numerical results for some benchmark fluid-structure interactions are presented that validate the proposed computational methodology for solving coupled problems involving fluid-structure interaction is reliable and robust.