TY - JOUR
T1 - Non-Iterative Parallel Schwarz Domain Decomposition Algorithms for a Two-Domain Parabolic Problem
AU - Shen , Minjie
AU - Yang , Danping
AU - Zheng , Haibiao
JO - Communications in Computational Physics
VL - 5
SP - 1552
EP - 1584
PY - 2025
DA - 2025/09
SN - 38
DO - http://doi.org/10.4208/cicp.OA-2024-0085
UR - https://global-sci.org/intro/article_detail/cicp/24466.html
KW - Domain decomposition, parallel Schwarz method, parabolic problems, error estimate.
AB - <p style="text-align: justify;">Based on overlapping domain decomposition, two parallel Schwarz finite
 element algorithms are presented for solving a two-domain parabolic problem. Our
 algorithms are based on two ideas. One is the observation that the influence of the
 non-homogeneous boundary data diminishes exponentially towards the interior of the
 subdomains. Another is to apply proper partitions of unity to distribute the residuals
 of the discretized systems reasonably into many subdomains so as to avoid repeated
 correction in the overlapping parts. The resulting algorithms are fully parallel in each
 subdomain. At each time step, only one iteration step is required to reach the optimal order of accuracy. The convergence rate depending on the mesh parameters are
 analyzed. Finally, numerical results are reported, which verify the theoretical analysis.</p>