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- W2023338631 abstract "A finite element scheme is devised for the solution of nonlinear time-dependent exterior wave problems. The two-dimensional nonlinear scalar (Klein?Gordon) 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 in each time step. An artificial boundaryBis introduced, which bounds the computational domain ?, and a simple-iteration procedure is used to linearize the problem in the infinite domain outsideB. This enables the derivation of a Dirichlet-to-Neumann boundary condition onB. Finite element discretization and Newton iteration are finally employed to solve the problem in ?. The computational aspects of this method are discussed. Numerical results are presented for the nonlinear wave equation, whose solutions may blow up in a finite time under certain conditions, and it is shown that the behavior of the solution predicted by theory is captured by the scheme." @default.
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- W2023338631 date "1998-06-01" @default.
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- W2023338631 title "Finite-Element Solution of Nonlinear Time-Dependent Exterior Wave Problems" @default.
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- W2023338631 doi "https://doi.org/10.1006/jcph.1998.9999" @default.
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