A Solution-Structure B-Spline-Based Framework for Hybrid Boundary Problems on Implicit Domains

Ammar Qarariyah, Tianhui Yang and Fang Deng ()
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Ammar Qarariyah: Computer Simulation in Sciences and Engineering, Bethlehem University, Bethlehem 92248, Palestine
Tianhui Yang: School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
Fang Deng: School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450045, China

Mathematics, 2024, vol. 12, issue 24, 1-19

Abstract: Solving partial differential equations (PDEs) on complex domains with hybrid boundary conditions presents significant challenges in numerical analysis. In this paper, we introduce a solution-structure-based framework that transforms non-homogeneous hybrid boundary problems into homogeneous ones, allowing exact conformity to the boundary conditions. By leveraging B-splines within the R-function method structure and adopting the stability principles of the WEB method, we construct a well-conditioned basis for numerical analysis. The framework is validated through a number of numerical examples of Poisson equations with hybrid boundary conditions on different implicit domains in two and three dimensions. The results reflect that the approach can achieve the optimal approximation order in solving hybrid problems.

Keywords: implicit domains; R-function method; hybrid boundary conditions; WEB method; solution structures (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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