Fast Nodal Hessian Computation for Peridynamic Fracture Simulation

Abstract Simulating dynamic fracture with physical realism and computational efficiency remains a formidable challenge in computer graphics. Non‐ordinary state‐based peridynamics (NOSB‐PD) offers a compelling framework for this task, but its non‐local nature makes the computation of second‐order derivatives (namely, the nodal Hessian blocks essential for implicit integration and advanced solvers) prohibitively expensive, preventing real‐time application. In this paper, we present a comprehensive framework that transforms this computational bottleneck into an efficient, practical operation. Our approach is built on two pillars: first, a novel analytical reformulation that exploits hidden mathematical symmetries and sparsity in NOSB‐PD, drastically reducing the complexity of Hessian block computation without approximation; second, a co‐designed ‘Warp‐Vertices‐Parallel’ GPU architecture that effectively manages irregular workloads and eliminates memory conflicts inherent in peridynamics. We demonstrate the versatility of our efficient computational core by seamlessly accelerating two distinct classes of algorithms: it enables a block‐diagonal preconditioner that outperforms traditional Jacobi preconditioning, and serves as the engine for a high‐performance Vertex Block Descent solver. Extensive experiments show that our method achieves substantial performance gains, enabling stable, interactive simulation of complex elastic and fracture phenomena while maintaining full physical accuracy. Our work establishes fast nodal Hessian computation as a fundamental primitive, bridging the gap between the strong physical capabilities of NOSB‐PD and its practical performance in graphics applications.