Sparse, Geometry- and Material-Aware Bases for Multilevel Elastodynamic Simulation

TL;DR

This paper introduces a multi-level elastodynamics solver that uses a novel sparse basis construction to achieve faster simulations with high accuracy, handling complex geometries and materials efficiently.

Contribution

A new sparse, geometry- and material-aware basis construction method enables faster elastodynamic simulations without losing accuracy or robustness.

Findings

Achieves up to 13x speedup over standard IPC methods.

Maintains visual fidelity with approximately 1% relative displacement error.

Handles complex geometries and heterogeneous materials effectively.

Abstract

We present a multi-level elastodynamics timestep solver for accelerating incremental potential contact (IPC) simulations. Our method retains the robustness of gold standard IPC in the face of intricate geometry, complex heterogeneous material distributions and high resolution input data without sacrificing visual fidelity (per-timestep relative displacement error of $\approx1\%$). The success of our method is enabled by a novel, sparse, geometry- and material-aware basis construction method which allows for the use of fast preconditioned conjugate gradient solvers (in place of a sparse direct solver), but without suffering convergence issues due to stiff or heterogeneous materials. The end result is a solver that produces results visually indistinguishable and quantitatively very close to gold-standard IPC methods but up to $13\times$ faster on identical hardware.