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.

中文翻译：

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用于多物理场问题强耦合建模的高效多线程 Newton-Raphson 算法

摘要 有限元高斯置信度传播（FGaBP）方法是一种迭代算法，具有丰富的并行性，可以替代传统的有限元方法（FEM），特别是对于大型多物理场问题。在本文中，我们扩展了 FGaBP 方法来解决肝肿瘤射频消融 (RFA) 建模中出现的电热耦合问题。耦合算法的最强形式，即 Newton-Raphson (NR) 方法，是使用 FGaBP 的局部计算并行实现的。通过计算每个元素的局部雅可比矩阵，然后在每次 NR 迭代中相应地更新电气和热问题的解决方案，所提出的算法中保留了 FGaBP 方法的并行可扩展性。