Dataset and Source Code for " A Stabilized Generalized Jacobsthal-Lucas Polynomial Boundary Element Method for High-Order Boundary Approximation of Potential and Heat-Conduction Boundary Value Problems"
Year: 2026
Type: dataset
Abstract: The work presents a stabilized Boundary Element Method (BEM) formulation based on generalized Jacobsthal–Lucas polynomials (GJLPs) for high-order approximation of boundary value problems governed by potential theory and steady heat conduction. The method combines the boundary-only discretization advantage of BEM with a recurrence-generated two-parameter polynomial basis. To improve numerical robustness, the implementation uses QR-based stabilization of the GJLP basis and explicitly treats regular, near-singular, and singular boundary integral contributions.The repository provides the computational material required to reproduce the numerical experiments and figures reported in the manuscript. It includes MATLAB and Python scripts for generating the GJLP basis, applying QR stabilization, assembling the boundary integral system, solving the manufactured unit-circle benchmark problem, computing relative error and conditioning measures, and regenerating the publication figures and tables. Processed numerical data, figure files, documentation, and citation metadata are also included to support reproducibility and reuse.The package is intended for researchers working on boundary element methods, high-order numerical approximation, computational mechanics, applied mathematics, potential problems, heat-conduction analysis, and recurrence-based polynomial methods. It may also serve as a starting framework for future extensions to anisotropic heat conduction, thermoelasticity, fracture mechanics, and multiphysics boundary integral formulations.Main contents of the repository include:source code for the stabilized GJLP-BEM implementation;scripts for reproducing the benchmark results;processed numerical data for convergence and conditioning analysis;publication-quality figures;tables and supporting files used in the manuscript;documentation describing how to reproduce the results.
Source: Figshare
Author: Fahmy, Mohamed Abdelsabour
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7164756807