Reliable Iterative Dynamics: A Versatile Method for Fast and Robust Simulation

Abstract

Simulating stiff materials has long posed formidable challenges for traditional physics-based solvers. Explicit time integration schemes demand prohibitively small time steps, while implicit methods necessitate an excessive number of iterations to converge, often yielding visually objectionable transient configurations in the early iterations, severely limiting their real-time applicability. Position-based dynamics techniques can efficiently simulate stiff constraints but are inherently restricted to constraint-based formulations, curtailing their versatility. We present ”Reliable Iterative Dynamics” (RID), a novel iterative solver that introduces a dual descent framework with theoretical guarantees for visual reliability at each iteration, while maintaining fast and stable convergence even for extremely stiff systems. Our core innovation is an iterative method that circumvents the need for numerous iterations or small time steps to handle stiff materials robustly. Experimental evaluations demonstrate our method’s ability to handle a wide range of materials, from soft to infinitely rigid, while producing visually reliable results even with large time steps and minimal iterations. The versatile formulation allows seamless integration with diverse simulation paradigms like the finite element method, material point method, smoothed particle hydrodynamics, and incremental potential contact for applications ranging from elastic body simulations to fluids and collision handling.