An exact Block-Newton algorithm for the solution of implicit time discretized coupled systems involved in fluid-structure interaction problems

Publisher Summary This chapter discusses a partitioned Newton based method for solving nonlinear and coupled systems arising in the numerical approximation of fluid-structure interaction problems. The partitioned procedures are particularly relevant while using efficient solvers for both the fluid and the solid subproblems. Using the Block–Newton-based methods for solving nonlinear coupled systems arising in the numerical approximation of the fluid-structure interaction problems with time implicit schemes requires the evaluation of Jacobians associated to each subsystems. Standard forms for solving the coupled nonlinear problem are—Block-Jacobi or Block-Gauss-Seidel iterations. However, these methods usually show poor convergence properties. To speed up the convergence, one can use the Newton–Raphson-based methods.