A novel numerical method is proposed for the solution of transient multi-physics problems involving heat conduction, electrical current sharing and Joule heating. The innovation consists of a mesh-free Monte Carlo approach that eliminates or drastically reduces the particle scattering requirements typical of conventional Monte-Carlo methods. The proposed algorithm encapsulates a volume around each point that affects the solution at a given point in the domain; the volume includes other points that represent small perturbations along the path of energy transfer. The proposed method is highly parallelizable and amenable for GPU computing, and its computational performance was substantially increased by the elimination of scattered interpolation. The accuracy and simulation time of the proposed method are compared against a finite element solution and also against experimental results from existing literature. The proposed method provides accuracy comparable to that of finite element methods, achieving an order of magnitude reduction in simulation time.

中文翻译：

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有效浮动体积：一种高度并行化的无网格方法，用于解决具有非线性材料特性的多尺度几何中的瞬态多物理场问题

提出了一种新的数值方法来解决涉及热传导、电流共享和焦耳热的瞬态多物理场问题。该创新包括无网格蒙特卡罗方法，该方法消除或大大减少了传统蒙特卡罗方法典型的粒子散射要求。所提出的算法在每个点周围封装了一个体积，该体积会影响域中给定点的解；该体积包括代表能量传递路径上的小扰动的其他点。所提出的方法具有高度的并行性和适用于GPU计算的能力，并且由于消除了分散插值，其计算性能得到了显着提高。将所提出方法的精度和仿真时间与有限元解决方案以及现有文献的实验结果进行了比较。所提出的方法提供了与有限元方法相当的精度，实现了模拟时间的数量级减少。