A High-precision Stochastic Solver for Steady-state Thermal Analysis with Fourier Heat Transfer Robin Boundary Conditions

In this work, we propose a path integral random walk (PIRW) solver, the first accurate stochastic method for steady-state thermal analysis with mixed boundary conditions, especially involving Fourier heat transfer Robin boundary conditions. We innovatively adopt the strictly correct calculation of the local time and the Feynman-Kac functional eˆc (t) to handle Neumann and Robin boundary conditions with high precision. Compared with ANSYS, experimental results show that PIRW achieves over 121× speedup and over 83× storage space reduction with a negligible error within 0.8°C at a single point. An application combining PIRW with low-accuracy ANSYS for the temperature calculation at hot-spots is provided as a more accurate and faster solution than only ANSYS used.