Abstract
The Finite Element Gaussian Belief Propagation (FGaBP) method is an iterative algorithm with abundant parallelism making it an alternative for the traditional Finite Element Method (FEM), especially for large multi-physics problems. In this paper, we extend the FGaBP method to solve the coupled electrical–thermal problem that emerges in the modeling of radiofrequency ablation (RFA) of hepatic tumors. The strongest form of coupling algorithms, which is the Newton–Raphson (NR) method, is implemented in parallel using the localized computations of FGaBP. The parallel scalability of the FGaBP method is retained in the proposed algorithm by calculating local Jacobian matrices for each element and then updating the solutions for both electrical and thermal problems accordingly at each NR iteration.
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