Monte Carlo methods for modeling magnetostatic NDE phenomena: a feasibility study

Abstract

Magnetostatic methods that are used for the nondestructive evaluation (NDE) of ferromagnetic materials can be modeled by partial differential equations. Conventional numerical methods such as finite difference, finite elements or boundary integral methods for large problems typically require an iterative matrix inversion scheme to solve the system of equations. Parallel implementation of such schemes is extremely difficult due to the data dependencies in the matrices. Monte Carlo methods offer an alternative approach by reducing the differential equation to simple, independent, random processes that are inherently amenable to parallel implementation. This paper investigates the use of Monte Carlo methods for modeling magnetostatic flux leakage NDE phenomena. The model is validated by comparing the results with those obtained with finite element models. The approach offers significant reduction in computational burden especially for 3-D problems.