Real-time simulation of dynamically deformable finite element models using modal analysis and spectral Lanczos decomposition methods.

Real-time simulation of deformable objects using finite element models is a challenge in medical simulation. We present two efficient methods for simulating real-time behavior of a dynamically deformable 3D object modeled by finite element equations. The first method is based on modal analysis, which utilizes the most significant vibration modes of the object to compute the deformation field in real-time for applied forces. The second method uses the spectral Lanczos decomposition to obtain the explicit solutions of the finite element equations that govern the dynamics of deformations. Both methods rely on modeling approximations, but generate solutions that are computationally faster than the ones obtained through direct numerical integration techniques. In both methods, the errors introduced through approximations were insignificant compare to the computational advantage gained for achieving real-time update rates.