Physics-Based Animation

Mengfei Liu, Yue Chang, Zhecheng Wang, Peter Yichen Chen, Eitan Grinspun

We introduce a neural field construction that captures gradient discontinuities without baking their location into the network weights. By augmenting input coordinates with a smoothly clamped distance function in a lifting framework, we enable encoding of gradient jumps at evolving interfaces. This design supports discretization-agnostic simulation of parametrized shape families with heterogeneous materials and evolving creases, enabling new reduced-order capabilities such as shape morphing, interactive crease editing, and simulation of soft-rigid hybrid structures. We further demonstrate that our method can be combined with previous lifting techniques to jointly capture both gradient and value discontinuities, supporting simultaneous cuts and creases within a unified model.

Precise Gradient Discontinuities in Neural Fields for Subspace Physics

Jia-Ming Lu, Geng-Chen Cao, Chenfeng Li, Shi-Min Hu

This paper proposes a novel simulation approach that combines implicit integration with the Bonded Discrete Element Method (BDEM) to achieve faster, more stable and more accurate fracture simulation. The new method leverages the eiciency of implicit schemes in dynamic simulation and the versatility of BDEM in fracture modelling. Speciically, an optimization-based integrator for BDEM is introduced and combined with a manifold optimization approach to accelerate the solution process of the quaternion-constrained system. Our comparative experiments indicate that our method ofers better scale consistency and more realistic collision efects than FEM and MPM fragmentation approaches. Additionally, our method achieves a computational speedup of 2.1 ~ 9.8 times over explicit BDEM methods.

Implicit Bonded Discrete Element Method with Manifold Optimization

• Adaptive Optical Layers: Efficient Tall Cell Grids for Liquid Simulation
• A Semi-Analytical Energy Model for Particle-Based Fluid Simulation Involving Complex Moving Boundaries
• Dripping Thin Films for Real-time Digital Painting
• Fluid Composer: Fluid Detail Composition and Rendering Using Video Diffusion Models
• Designing inflatable shells using unstructured meshes
• Convex Primitive Decomposition for Collision Detection
• STAGED: Stress-Tensor Assisted Global-local-global solver for interactive Elastic shape Design
• Interpolated Adaptive Linear Reduced Order Modeling for Deformation Dynamics
• Progressively Projected Newton’s Method
• Affinification: A Fine Approximation of Deformations
• HeatMat: Simulation of City Material Impact on Urban Heat Island Effect

• Fast VEM Fluid Simulation
• Spatiotemporal FLIP for Fast Free-Surface and Two-Phase Simulation With Very Large Time Steps
• Fast Cutting of Cage Based Deformation with Walk on Spheres
• Buoyancy-driven Phase Separation in the Material Point Method
• Volume-Preserving LBM-MPM Coupling for Air-Water-Sand Mixtures
• A Nonlocal Monolithic Variational Framework for Free Surface Flows
• Stochastic geomorphological transport for terrain erosion simulation
• Mixwell: Sharp 2D Fluid Brushes for Progressive Physics-Based Mixing
• Curvature Space Editing of Highly-Coiled Hair
• M-ABD: Scalable, Efficient, and Robust Multi-Affine-Body Dynamics
• Heterogeneous Subspace Corrections for GPU Deformable Multibody Dynamics
• Distributed Affine Body Dynamics with Adaptive Consensus
• Better Bending: Analysis, Construction and Verification of Discrete Bending Models for Kirchhoff-Love Shells
• Efficient B-Spline Finite Elements for Cloth Simulation
• Interactive Yarn-level Knitwear with Nested Douglas-Rachford Splitting
• SymX: Energy-based Simulation from Symbolic Expressions
• MeshFEM: A Block-accelerated Solver for Nonlinear Finite Elements
• Fast Sparse Matrix Permutation for Mesh-Based Direct Solvers
• JGS2-GQ: Training-free 2nd Jacobi with Gaussian Quadrature
• Divide and Truncate: A Penetration and Inversion Free Framework for Coupled Multi-physics System
• Robust and Efficient Penetration-Free Elastodynamics without Barriers
• High-Order Continuous Geometrical Validity
• Floating-Point Robustness in Parametric Surface Continuous Collision Detection: From Algorithm to Benchmarking
• AGIPC: Adaptive In-Solve Algebraic Coarsening for GPU IPC
• YASPS: A Symbolic Framework for Extensible, High-Performance IPC Simulation
• Progressing Level-of-Detail Animation for Volumetric Elastodynamics
• Mixed Material Point Methods for Stiff Elastoplasticity
• MPM Lite: Linear Kernels and Integration without Particles
• Tube Maps: Fast SPH Boundary Handling with Tubular Coordinates
• Low-Rank Koopman Deformables with Log-Linear Time Integration
• Physics-Inspired Procedural Texturing of Extremely Deformable Surfaces
• Woodstock: Interactive Modeling of Fungal Wood Decay
• Untangling Surfaces via Shape and Mesh Repulsion
• Surface chamfering for robust tetrahedral meshing
• Boundary-aware Neural Model Reduction for PDEs
• Locality-Aware Automatic Differentiation on the GPU for Mesh-Based Computations

Jia-Ming Lu, Tailing Yuan, Zhe-Han Mo, Shi-Min Hu

This research presents an efficient multigrid solver for deformable body simulations on unstructured tetrahedral meshes. The method combines the Full Approximation Scheme with Galerkin formulation and introduces a matrix-free vertex block Jacobi smoother that eliminates the computational burden of dense coarse matrices. The approach supports both piecewise constant and linear Galerkin formulations and achieves up to 6.9x speedup over traditional methods. Comprehensive GPU optimization techniques address parallel architecture challenges through Morton sorting, grid reduction, and spatial hashing. Extensive experiments demonstrate robust convergence across varying mesh resolutions, material stiffness values, extreme deformations, and complex collision scenarios, enabling practical simulation of million-vertex meshes at interactive frame rates.

Fast Galerkin Multigrid Method for Unstructured Meshes

Jia-Ming Lu, Shi-Min Hu

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.

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

Elie Diaz, Jerry Hsu, Eisen Montalvo-Ruiz, Chris Giles, Cem Yuksel

The efficient simulation of incompressible fluids remains a difficult and open problem. Prior works often make various tradeoffs between incompressibility, stability, and cost. Yet, it is rare to obtain all three. In this paper, we introduce a novel incompressible Smoothed Particle Hydrodynamics (SPH) scheme which uses a second-order implicit descent scheme to optimize a variational energy specially formulated to approach incompressibility. We demonstrate that our method is superior in both incompressibility and stability with a minimal cost to computational budget. Furthermore, we demonstrate that our method is unconditionally stable even under extreme time steps, making it suitable for interactive applications.

Implicit Position-Based Fluids

Lixin Ren, Xiaowei He, Shusen Liu, Yuzhong Guo, Enhua Wu

Prior research has demonstrated the efficacy of balanced trees as spatially adaptive grids for large-scale simulations. However, state-of-the-art methods for balanced tree construction are restricted by the iterative nature of the ripple effect, thus failing to fully leverage the massive parallelism offered by modern GPU architectures. We propose to reframe the construction of balanced trees as a process to merge N -balanced Minimum Spanning Trees (N -balanced MSTs) generated from a collection of seed points. To ensure optimal performance, we propose a stack-free parallel strategy for constructing all internal nodes of a specified N -balanced MST. This approach leverages two 32-bit integer registers as buffers rather than relying on an integer array as a stack during construction, which helps maintain balanced workloads across different GPU threads. We then propose a dynamic update algorithm utilizing refinement counters for all internal nodes to enable parallel insertion and deletion operations of N -balanced MSTs. This design achieves significant efficiency improvements compared to full reconstruction from scratch, thereby facilitating fluid simulations in handling dynamic moving boundaries. Our approach is fully compatible with GPU implementation and demonstrates up to an order-of-magnitude speedup compared to the state-of-the-art method [Wang et al. 2024]. The source code for the paper is publicly available at https://github.com/peridyno/peridyno.

A Stack-Free Parallel ℎ-Adaptation Algorithm for Dynamically Balanced Trees on GPUs

Cuncheng Zhu, Hang Yin, Albert Chern

We present a vorticity method for simulating incompressible viscous flows on curved surfaces governed by the Navier–Stokes equations. Unlike previous approaches, our formulation incorporates the often-overlooked Gaussian-curvature-dependent term in the viscous force, which influences both the vorticity equation and the evolution of harmonic components. We show that these curvature-related terms are crucial for reproducing physically correct fluid behavior. We introduce an implicit–explicit (IMEX) scheme for solving the resulting system on triangle meshes and demonstrate its effectiveness on surfaces with arbitrary topology, including non-orientable surfaces, and under a variety of boundary conditions. Our theoretical contributions include several explicit formulas: a vorticity jump condition across curvature sheets, a geometric correspondence between friction coefficients and boundary curvature adjustments, and the influence of boundary curvature on harmonic modes. These results not only simplify the algorithmic design but also offer geometric insight into curvature-driven fluid phenomena, such as the emergence of the Kutta condition under free-slip boundaries.

Viscous Vortex Dynamics on Surfaces

Daoming Liu, Jonathan Klein, Florian Rist, Wojtek Pałubicki, Sören Pirk, Dominik L. Michels

We propose a unified volumetric combustion simulator that supports general wooden structures capturing the multi-phase combustion of charring materials. Complex geometric structures can conveniently be represented in a voxel grid for the effective evaluation of volumetric effects. In addition, a signed distance field is introduced to efficiently query the surface information required to compute the insulating effect caused by the char layer. Non-charring materials such as acrylic glass or non-combustible materials such as stone can also be modeled in the simulator. Adaptive data structures are utilized to enable memory-efficient computations within our multiresolution approach. The simulator is qualitatively validated by showcasing the numerical simulation of a variety of scenes covering different kinds of structural configurations and materials. Two-way coupling of our combustion simulator and position-based dynamics is demonstrated capturing characteristic mechanical deformations caused by the combustion process. The volumetric combustion process of wooden structures is further quantitatively assessed by comparing our simulated results to sub-surface measurements of a real-world combustion experiment.

FLAMEFORGE: Combustion Simulation of Wooden Structures