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

2025-08-18

AI Summary

To address the low efficiency of multilevel elastic dynamics time-stepping, poor convergence under heterogeneous material distributions, and insufficient robustness at high resolutions in Incremental Potential Contact (IPC) simulation, this work proposes a geometry- and material-aware sparse multilevel basis function construction, integrated with a preconditioned conjugate gradient (PCG) solver to replace conventional sparse direct solvers. The method preserves robustness across complex geometries, heterogeneous material configurations, and high-resolution inputs while substantially improving computational efficiency. Experimental evaluation demonstrates that, achieving visually indistinguishable results from the gold-standard IPC reference (quantitative error ≈ 1%), the approach attains up to 13× speedup on identical hardware. This establishes an efficient and reliable numerical framework for high-fidelity, large-scale real-time deformable body simulation.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Hardware-aware ML

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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 $13 imes$ faster on identical hardware.

Problem

• Accelerates elastodynamic simulations with complex geometry
• Handles heterogeneous materials without convergence issues
• Maintains visual fidelity while improving computational speed

Innovation

• Multi-level elastodynamics timestep solver
• Sparse geometry-material-aware basis construction
• Fast preconditioned conjugate gradient solvers