Abstract
We are interested in solving the Helmholtz equation \( \left\{\begin{array}{llllllll}-\Delta u(x,y,z)\-k^2(x,y,z)u(x,y,z)\;=\;g(x,y,z),(x,y,z)\;\in\;\bf{\varOmega}, \\ \partial_n u(x,y,z)-{i}k(x,y,z)u(x,y,z)=\;0,\qquad (x,y,z)\;\in\partial{ \varOmega}, \end{array}\right.\) where \(k\;:=2 \pi f/c\) is the wavenumber with frequency \(f\;\in\;\mathbf{R}\;\;\mathrm{and}\;c\;:=\;c(x,y,z)\) is the velocity of the medium, which varies in space. The geophysical model SEG– SALT is used as a benchmark problem on which we will test some existing domain decomposition methods in this paper.
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Acknowledgements
The authors thank Paul Childs for providing the velocity data of the geophysical SEG–SALT model. This work was partially supported by the University of Geneva. The second author was also partially supported by the NSFC Tianyuan Mathematics Youth Fund 10926134.
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Gander, M.J., Zhang, H. (2013). Domain Decomposition Methods for the Helmholtz Equation: A Numerical Investigation. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_24
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DOI: https://doi.org/10.1007/978-3-642-35275-1_24
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