Asynchronous implicit backward Euler integration

In standard deformable object simulation in computer animation, all the mesh elements or vertices are timestepped synchronously, i.e., under the same timestep. Previous asynchronous methods have been largely limited to explicit integration. We demonstrate how to perform spatially-varying timesteps for the widely popular implicit backward Euler integrator. Spatially-varying timesteps are useful when the object exhibits spatially-varying material properties such as Young's modulus or mass density. In synchronous simulation, a region with a high stiffness (or low mass density) will force a small timestep for the entire mesh, at a great computational cost, or else, the motion in the stiff (or low mass density) region will be artificially damped and inaccurate. Our method can assign smaller timesteps to stiffer (or lighter) regions, which makes it possible to properly resolve (sample) the high-frequency deformable dynamics arising from the stiff (or light) materials, resulting in greater accuracy and less artificial damping. Because soft (or heavy) regions can continue using a large timestep, our method provides a significantly higher accuracy under a fixed computational budget.