Hybrid Adaptive Dual Reciprocity Method for Efficient Solution of Large-Scale Non-Linear Boundary Conditions

TL;DR

This paper introduces a hybrid adaptive numerical method combining DRM, iterative techniques, and local finite elements to efficiently solve large-scale nonlinear boundary problems with improved accuracy.

Contribution

The paper presents the H-DRM, a novel hybrid adaptive approach that enhances computational efficiency and accuracy for complex, large-scale nonlinear boundary condition problems.

Findings

Validated effectiveness through computational experiments

Achieved high accuracy with fewer iterations

Demonstrated robustness for complex geometries

Abstract

This article proposes a hybrid adaptive numerical method based on the Dual Reciprocity Method (DRM) to solve problems with non-linear boundary conditions and large-scale problems, named Hybrid Adaptive Dual Reciprocity Method (H-DRM). The method uses a combination of DRM to handle non-homogeneous terms, iterative techniques to deal with non-linear boundary conditions, and an adaptive multiscale approach for large-scale problems. Additionally, 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 non-linearities at the boundary, offering a robust solution for physical and engineering problems. Demonstrations and computational results are presented, validating the effectiveness of the method compared to other known methods through an iterative process of 7 million iterations.