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arXiv · 2410.21567

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

Rômulo Damasclin Chaves dos Santos·Jorge Henrique de Oliveira Sales
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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.

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Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales. 2024-10-28. Hybrid Adaptive Dual Reciprocity Method for Efficient Solution of Large-Scale Non-Linear Boundary Conditions. https://arxiv.org/abs/2410.21567

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