Geodesic
Domain decomposition for the numerical solution of the Cahn--Hilliard equation
Numerical methods and programming, Tome 26 (2025) no. 1, pp. 17-32.

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The article presents a parallel algorithm for the numerical solution of the Сahn–Hilliard equation in a three-dimensional formulation. The algorithm is based on an explicit finite difference scheme and a domain decomposition method. One MPI process is allocated for each subdomain, while the solution within the subdomain is calculated using CUDA technology for the GPU. The strong and weak scaling of the algorithm is investigated in application to the problem of phase separation for two different data exchange schemes between RAM and VRAM.
Keywords: phase-field method; domain decomposition; Cahn-Hilliard equation; heterogeneous computing. 
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     author = {D. I. Prokhorov},
     title = {Domain decomposition for the numerical solution of the {Cahn--Hilliard} equation},
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     publisher = {mathdoc},
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     number = {1},
     year = {2025},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2025_26_1_a3/}
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D. I. Prokhorov. Domain decomposition for the numerical solution of the Cahn--Hilliard equation. Numerical methods and programming, Tome 26 (2025) no. 1, pp. 17-32. http://geodesic.mathdoc.fr/item/VMP_2025_26_1_a3/