Monte Carlo methods for solving Maxwell's equations?

AI Thread Summary
Maxwell's equations are often solved using deterministic methods like finite difference time domain (FDTD), which are computationally intensive. There is curiosity about the application of Monte Carlo methods for these equations, as they can be utilized in some contexts. The discussion highlights that the choice of numerical methods depends on the specific problem, suggesting that different methods may offer varying advantages. Additionally, a hybrid approach combining multiple numerical methods may be preferred for certain scenarios. Overall, the exploration of Monte Carlo methods in this context remains an interesting area for further investigation.
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Maxwell's equations are frequently solved numerically using deterministic methods such as finite difference time domain (FDTD) methods (https://en.wikipedia.org/wiki/Finite-difference_time-domain_method). The problem is that FDTD methods are known to be very computationally intensive. I'm wondering why aren't Monte Carlo methods (https://en.wikipedia.org/wiki/Monte_Carlo_method) ever applied to solve these equations? Is there a fundamental reason why not?
 
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