ANALYSIS OF ACCURACY, CONVERGENCE, AND ROBUSTNESS OF INVERSE BOUNDARY RECONSTRUCTION ON VARIOUS COMPLEX DOMAIN GEOMETRIES AND KAWUNG BATIK MOTIFS THROUGH NUMERICAL SIMULATIONS

Abstract

Inverse boundary reconstruction is an important topic in inverse problem theory that aims to reconstruct an unknown boundary or interface from measurement data available on the exterior boundary of a domain. This study analyzes the accuracy, convergence, and robustness of a boundary reconstruction method for various complex domain geometries while also exploring the use of simulation-generated patterns as inspiration for batik motif development. Three numerical cases are investigated: a bean-shaped boundary within a circular domain, an apple-shaped boundary within a rounded-rectangle domain, and a complex kite/apple-like boundary within a kite-shaped domain. Simulations are performed using a parametric boundary representation under two data conditions, namely exact data and data contaminated with 3% perturbation. The reconstruction results demonstrate that the proposed method produces boundary approximations that closely match the exact boundaries for all tested geometric configurations. For exact data, the algorithm exhibits good convergence behavior and successfully captures the main geometric characteristics of the interior domain, even when the iterative process is initialized with a simple circular initial guess. Under 3% perturbed data, the reconstruction still preserves the principal shape of the exact boundary, although local oscillations appear due to the influence of noise. These results indicate that the method possesses good numerical stability and robustness against small to moderate levels of data perturbation. Furthermore, the geometric patterns generated from the reconstruction simulations were successfully adapted into a new batik motif named Kawung Laras Praba, illustrating the relationship between computational mathematics, geometric visualization, and cultural art development. This study contributes to the advancement of numerical methods for inverse problems while demonstrating the potential of mathematical simulation results as a source of inspiration for geometry-based batik motif design.