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We discuss the numerical modeling of logging-while-drilling (LWD) tools for hydrocarbon exploration in arbitrary three-dimensional geometries using a new finite-difference time-domain (FDTD) scheme in cylindrical coordinates. Two locally conformal FDTD (LC-FDTD) schemes are employed to simulate eccentric LWD tools in realistic logging environments. An anisotropic perfectly matched layer absorbing boundary condition extended to cylindrical coordinates is incorporated in the FDTD method to simulate unbounded geophysical formations. Frequency-domain data are obtained from the time-domain results using a ramp-modulated sinusoidal source and an efficient early-time extraction algorithm. The FDTD simulations are validated against both numerical mode matching and pseudoanalytical approaches and show very good agreement.