Journal of Algorithms and Computation
Open Access

Comparative Analysis of Second-Order Unconstrainted Iterative Solvers for Non-Linear Inversion of Finite-Element Based DC Resistivity Simulation

Document Type : Research Paper

Authors

Amir Yazdanpanah 1
Maysam Abedi 2

1 Petroleum Engineering and Geophysics Laboratory, School of Mining Engineering, College of Engineering, University of Tehran, Iran

2 Petroleum Engineering and Geophysics Laboratory, School of Mining Engineering, College of Engineering University of Tehran, Iran

https://doi.org/10.22059/jac.2025.404126.1243
Abstract
Direct Current (DC) Electrical Resistivity Tomography (ERT) inversion is a non-linear, ill-posed problem requiring robust solvers for accurate subsurface resistivity reconstruction. This study systematically compares four second-order unconstrained iterative solvers which are Simple Newton, Newton-CG, Trust-Exact, and Trust-NCG, using synthetic dipole-dipole data with conductive and resistive anomalies in a homogeneous background. Inversion is performed within a finite-element framework with unstructured triangular meshes. Solver performance is assessed through reconstruction accuracy and computational efficiency using error metrics and data misfit. Results show Simple Newton fails due to instability and fixed step sizes. Newton-CG, Trust-Exact, and Trust-NCG converge reliably, with Trust-Exact and Trust-NCG markedly superior in resolving sharp resistivity contrasts, especially the conductive anomaly, owing to adaptive trust-region globalization. Newton-CG and Trust-NCG exhibit minor smoothing, reflecting a trade-off between speed and precision. These findings highlight the superiority of trust-region methods in weakly regularized non-linear geophysical inversion, emphasizing their ability to preserve sharp contrasts.

Keywords

Direct Current
Electrical Resistivity Tomography (ERT)
Non-Linear Inversion
Unconstrainted Iterative Solvers
Finite-Element
Journal of Algorithms and Computation
Volume 57, Issue 2
December 2025
Pages 112-128

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