  In this paper, we propose a numerical algorithm based on a cell-centered
finite volume method to compute a distance from given objects on a
three-dimensional computational domain discretized by polyhedral cells.
Inspired by the vanishing viscosity method, a Laplacian regularized eikonal
equation is solved and the Soner boundary condition is applied to the boundary
of the domain to avoid a non-viscosity solution. As the regularization
parameter depending on a characteristic length of the discretized domain is
reduced, a corresponding numerical solution is calculated. A convergence to the
viscosity solution is verified numerically as the characteristic length becomes
smaller and the regularization parameter accordingly becomes smaller. From the
numerical experiments, the second experimental order of convergence in the
$L^1$ norm error is confirmed for smooth solutions. Compared to solve a
time-dependent form of eikonal equation, the Laplacian regularized eikonal
equation has the advantage of reducing computational cost dramatically when a
more significant number of cells is used or a region of interest is far away
from the given objects. Moreover, the implementation of parallel computing
using domain decomposition with $1$-ring face neighborhood structure can be
done straightforwardly by a standard cell-centered finite volume code.
