A domain decomposition method based on natural boundary reduction for nonlinear time-dependent exterior wave problems
A new domain decomposition method based on natural boundary reduction is devised for the solution of nonlinear time-dependent exterior wave problems. The two-dimensional nonlinear scalar wave equation is taken as a model to illustrate the method. The governing equation is first discretized in time, leading to a time-stepping scheme, where a nonlinear exterior elliptic problem has to be solved at each time step. Two artificial boundaries are introduced. The Schwarz alternating method is proposed. The convergence of this algorithm is given. The contraction factor for exterior circular domain is also discussed. Numerical results are presented for the nonlinear wave equation to demonstrate the performance of the method.
nonlinear wave equations natural boundary reduction (nbr) domain decomposition method (ddm) exterior problems