Two approaches to three-dimensional structural topology optimization using level set parameterization with arbitrary finite-element meshes are presented. In both approaches the structural elasticity problem is solved on a fixed finite-element mesh. The shape sensitivities obtained from the solution of the structural problem are mapped to the orthogonal mesh in order to generate the corresponding advection velocities. The first approach superimposes a background Cartesian grid onto the finite element mesh. The level set function is defined on this Cartesian mesh with the advection velocities being taken as a weighted sum of the sensitivities at all nearby structural nodes within a prescribed radius. The second approach defines the level set function on a skewed structured mesh which is coincident with the finite element mesh. The Hamilton-Jacobi equation is then solved in this transformed mesh space and a Jacobian transformation is used create a one-to-one mapping between the structural elements and the nodes of the level set mesh. The two methods are evaluated and compared based upon the results of a benchmark problem involving three-dimensional topology optimization of an aircraft wing structure. The results indicate that the Jabobian mapping method offers a significant advantage over the superposition method, both in terms of convergence time as well as the objective value of the converged solution.