We present a numerical method for solving Weyls embedding problem which consists in finding a global isometric embedding of a positively curved and positive-definite spherical 2-metric into the Euclidean 3-space. The method is based on a construction introduced by Weingarten and was used in Nirenbergs proof of Weyls conjecture. The target embedding results as the endpoint of an embedding flow in R ~3 beginning at the unit spheres embedding. We employ spectral methods to handle functions on the surface and to solve various (non)linear elliptic PDEs. The code requires no additional input or steering from the operator and its convergence is guaranteed by the Nirenberg arguments. Possible applications in 3 + 1 numerical relativity range from quasi-local mass and momentum measures to coarse-graining in inhomogeneous cosmological models.
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