This paper introduces a new method for performing field transfer operations in black-box coupling, when source discretization information is not available. This approach uses a stochastic approximation of the Galerkin projection which leads to a method that asymptotically provides conservation. Error in the accuracy and conservation has been compared to the mesh intersection method and radial basis functions on a simple domain, as well as on meshes of the LTX fusion reactor. For all cases tested, our new method provides higher accuracy and less conservation error than radial basis functions and can be used for black-box coupling, unlike the mesh-intersection method. Additionally, we demonstrate the implementation and performance of our method on an NVIDIA GeForce RTX 4060 GPU, showing that the cost is competitive with the mesh intersection method.

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