Hybrid Numerical Method (H-DRM) for Nonlinear Boundary Conditions

Abstract

This paper proposes an adaptive hybrid numerical method based on the Dual Reciprocity Method (DRM) to solve problems with large-scale nonlinear boundary conditions, naming it the Hybrid Adaptive Dual Reciprocity Method (H-DRM). The method uses a combination of the DRM to treat inhomogeneous terms, iterative techniques to deal with nonlinear boundary conditions, and an adaptive multiscale approach for large-scale problems. In addition, the H-DRM incorporates local finite elements in critical regions of the domain. This method aims to improve computational efficiency and accuracy for problems involving complex geometry and boundary nonlinearities, offering a robust solution for physical and engineering problems. Mathematical demonstrations and computational results are presented, validating the effectiveness of the method in comparison with other known methods, through an iterative process of 7 million iterations.