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Accumulative Schwarz alternating method and equivalence to generalized complex variable method
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DOI：10.1016/j.compgeo.2025.107711.png)
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The recently proposed generalized complex variable method to eliminate iteration procedure of the conventional Schwarz alternating method has been successfully applied to several elasticity scenarios in tunnel engineering with satisfactory results. However, the reason to eliminate iteration still remains vague and ambiguous. To this end, this paper constructs a new accumulative Schwarz alternating method as an intermediate mathematical link to formally and explicitly prove the equivalence between the conventional Schwarz alternating method and the generalized complex variable method via a classic and elastic multi-cavity opening problem to elaborate the essence for iteration elimination. Numerical experiments suggest better numerical stability and efficiency of the non-iterative solution scheme shared by the accumulative Schwarz alternating method and the generalized complex variable method than the iterative solution scheme of the conventional Schwarz alternating method. The limitations and possible applications are also discussed.
Keyword:
Accumulative Schwarz alternating method
Generalized complex variable method
Mathematical equivalence
Accumulation order exchange
期刊
IF:
6.2
论文数:
7.2K
被引数:
2.9W
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