Volume 58, pp. 22-42, 2023.

Asynchronous domain decomposition methods for nonlinear PDEs

Fayçal Chaouqui, Edmond Chow, and Daniel B. Szyld


One- and two-level parallel asynchronous methods for the numerical solution of nonlinear systems of equations, especially those arising from (nonlinear) partial differential equations, are studied. The proposed methods are based on domain decomposition techniques. Local convergence theorems are presented in several cases, with appropriate hypotheses. Computational results on a shared memory multiprocessor machine for various problems exhibiting nonlinearities are reported, illustrating the potential of these asynchronous methods, especially for heterogeneous clusters.

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Key words

asynchronous iterations, nonlinear problems, domain decomposition, partial differential equations, two-level methods

AMS subject classifications

65N22, 65M55, 65F10, 65F50,

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