This paper uses the fictitious boundary method described in Ref.[1]
for the solution of incompressible flow with moving rigid bodies
in complex geometries. The method is based on a special treatment 
of Dirichlet boundary conditions inside of a FEM approach 
in the context of a hierarchical multigrid scheme such that the flow 
can be efficiently computed on a fixed computational mesh while the 
solid boundaries are allowed to move freely through the given mesh. 
In this paper, we focus on the calculations of the drag and lift forces 
acting on the moving solid bodies which are not captured by the mesh. 
The comparison between the present 
and benchmark results for the flow around a circular cylinder with 
different Reynolds numbers is first presented, and then the result for
a circular cylinder oscillating in a channel is given.
The simulation results compared with corresponding reference results
are found to be very reasonable and satisfactory.