This paper presents a novel approach for solving the {Poisson} equation on arbitrary domains using a direct Radial Basis Function (DRBF) partition of unity technique. The method involves dividing the primary domain into overlapping subdomains, calculating local approximations within each {subdomain}, and then combining these approximations through discontinuous weight functions to form a global solution. We also use polyharmonic spline (PHS) kernels, {with} scaling properties. This strategy improves stability, lowers computational costs, and replaces a single ill-conditioned linear system with several smaller, well-conditioned linear systems. Numerical experiments are performed to confirm the efficacy of the proposed method.
Fathi Dopolani, F. and Ahmadi Darani, M. (2025). RBF partition of unity methods for solving the Poison equation on irregular domains. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2025.65004.2967
MLA
Fathi Dopolani, F. , and Ahmadi Darani, M. . "RBF partition of unity methods for solving the Poison equation on irregular domains", Computational Methods for Differential Equations, , , 2025, -. doi: 10.22034/cmde.2025.65004.2967
HARVARD
Fathi Dopolani, F., Ahmadi Darani, M. (2025). 'RBF partition of unity methods for solving the Poison equation on irregular domains', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2025.65004.2967
CHICAGO
F. Fathi Dopolani and M. Ahmadi Darani, "RBF partition of unity methods for solving the Poison equation on irregular domains," Computational Methods for Differential Equations, (2025): -, doi: 10.22034/cmde.2025.65004.2967
VANCOUVER
Fathi Dopolani, F., Ahmadi Darani, M. RBF partition of unity methods for solving the Poison equation on irregular domains. Computational Methods for Differential Equations, 2025; (): -. doi: 10.22034/cmde.2025.65004.2967
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