We present a numerical investigation of nonlinear cluster lens reconstruction using weak lensing mass mapping. Recent advances in imaging and shear estimation have pushed reliable reduced shear measurements closer to cluster cores, making mass reconstruction accessible in the nonlinear regime. However, the Kaiser-Squires based algorithm becomes unstable in cluster cores, where convergence $\kappa$ significantly deviates from zero and the linear approximation breaks down. To address this limitation, we develop a reconstruction framework with two key modifications: applying smooth masks in these regions and using a model-derived analytical solution as the initial guess, rather than assuming $\kappa =0$. We validate our framework using simulated cluster lensing data with known mass distributions, incorporating realistic masks that arise from limitations in reduced shear measurements. We show that in the absence of shape noise, our framework yields high-fidelity mass reconstruction in regions with large reduced shear, with the best-performing method achieving residuals below $0.02\sigma$ in the unmasked regions. We further discover that iterative reconstruction methods can diverge beyond an optimal iteration count. Our modifications effectively suppress this instability, pushing mass reconstruction to higher accuracy and stability in the nonlinear regime.

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• Gravitational lenses
• Galaxy clusters
• Astronomical masses & mass distributions