We design and study Schwarz Waveform relaxation algorithms for the linear Schrödinger equation with a potential in one dimension. We show that the overlapping algorithm with Dirichlet exchanges of informations on the boundary is slowly convergent, and we introduce two new classes of algorithms: the optimized Robin algorithm and the quasi-optimal algorithm. Numerical results illustrate the great improvement of these methods over the classical algorithm.
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Halpern, L., Szeftel, J. (2008). Optimized and Quasi-optimal Schwarz Waveform Relaxation for the One Dimensional Schrödinger Equation. In: Langer, U., Discacciati, M., Keyes, D.E., Widlund, O.B., Zulehner, W. (eds) Domain Decomposition Methods in Science and Engineering XVII. Lecture Notes in Computational Science and Engineering, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75199-1_24
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DOI: https://doi.org/10.1007/978-3-540-75199-1_24
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