Abstract
It is very natural to solve time dependent problems with Domain Decomposition Methods by using an implicit scheme for the time variable and then applying a classical iterative domain decomposition method at each time step. This is however not what the Schwarz Waveform Relaxation (SWR) methods do. The SWR methods are a combination of the Schwarz Domain Decomposition methods, see [10], and the Waveform Relaxation algorithm, see [7]. Combined, one obtains a new method which decomposes the domain into subdomains on which time dependent problems are solved. Iterations are then introduced, where communication between subdomains is done at artificial interfaces along the whole time window.
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Courvoisier, Y., Gander, M.J. (2013). Time Domain Maxwell Equations Solved with Schwarz Waveform Relaxation Methods. 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_30
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DOI: https://doi.org/10.1007/978-3-642-35275-1_30
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