Preconditioned Nonlinear Conjugate Gradient Method for Real-time Interior-point Hyperelasticity

TL;DR

This paper introduces a GPU-parallelizable, preconditioned nonlinear conjugate gradient method for real-time hyperelasticity simulation, improving efficiency and robustness in large-scale, complex collision scenarios.

Contribution

It proposes a novel Jacobi preconditioned nonlinear conjugate gradient approach with a line search strategy, optimized for GPU acceleration in real-time hyperelasticity simulations.

Findings

Simulates over 100,000 tetrahedra in real-time

Achieves fast convergence and robustness with large time steps

Eliminates costly collision detection through line search

Abstract

The linear conjugate gradient method is widely used in physical simulation, particularly for solving large-scale linear systems derived from Newton's method. The nonlinear conjugate gradient method generalizes the conjugate gradient method to nonlinear optimization, which is extensively utilized in solving practical large-scale unconstrained optimization problems. However, it is rarely discussed in physical simulation due to the requirement of multiple vector-vector dot products. Fortunately, with the advancement of GPU-parallel acceleration techniques, it is no longer a bottleneck. In this paper, we propose a Jacobi preconditioned nonlinear conjugate gradient method for elastic deformation using interior-point methods. Our method is straightforward, GPU-parallelizable, and exhibits fast convergence and robustness against large time steps. The employment of the barrier function in interior-point methods necessitates continuous collision detection per iteration to obtain a penetration-free step size, which is computationally expensive and challenging to parallelize on GPUs. To address this issue, we introduce a line search strategy that deduces an appropriate step size in a single pass, eliminating the need for additional collision detection. Furthermore, we simplify and accelerate the computations of Jacobi preconditioning and Hessian-vector product for hyperelasticity and barrier function. Our method can accurately simulate objects comprising over 100,000 tetrahedra in complex self-collision scenarios at real-time speeds.