Abstract: This paper presents a fast and stable technique for simulating deformable objects. Unlike in previous physically based methods, our potential energy of deformation is purely geometrically based. It is defined as the L² norm of the change of the differential coordinates. A key feature of this energy formulation is that the corresponding stiffness matrix is approximately constant, which enables fast and stable implicit integration and large deformations. Our algorithm can simulate various effects including solid, thin shell and plasticity. We also adopt two schemes to accelerate the simulation process: dimensionality reduction in frequency domain and adaptive rotation computation in spatial domain.