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In parallel simulation, convergence and parallelism are often seen as inherently conflicting objectives. Improved parallelism typically entails lighter local computation and weaker coupling, which unavoidably slow the global convergence. This paper presents a novel GPU algorithm that achieves convergence rates comparable to fullspace Newton's method while maintaining good parallelizability just like the Jacobi method. Our approach is built on a key insight into the phenomenon ofovershoot.Overshoot occurs when a local solver aggressively minimizes its local energy without accounting for the global context, resulting in a local update that undermines global convergence. To address this, we derive a theoretically second-order optimal solution to mitigate overshoot. Furthermore, we adapt this solution into a pre-computable form. Leveraging Cubature sampling, our runtime cost is only marginally higher than the Jacobi method, yet our algorithm converges nearly quadratically as Newton's method. We also introduce a novel full-coordinate formulation for more efficient pre-computation. Our method integrates seamlessly with the incremental potential contact method and achieves second-order convergence for both stiff and soft materials. Experimental results demonstrate that our approach delivers high-quality simulations and outperforms state-of-the-art GPU methods with 50× to 100× better convergence. 

Whenever the concept of high-performance cloth simulation is brought up, GPU acceleration is almost always the first that comes to mind. Leveraging immense parallelization, GPU algorithms have demonstrated significant success recently, whereas CPU methods are somewhat overlooked. Indeed, the need for an efficient CPU simulator is evident and pressing. In many scenarios, high-end GPUs may be unavailable or are already allocated to other tasks, such as rendering and shading. A high-performance CPU alternative can greatly boost the overall system capability and user experience. Inspired by this demand, this paper proposes a CPU algorithm for high-resolution cloth simulation. By partitioning the garment model into multiple (but not massive) sub-meshes or domains, we assign per-domain computations to individual CPU processors. Borrowing the idea of projective dynamics that breaks the computation into global and local steps, our key contribution is a new parallelization paradigm at domains for both global and local steps so that domain-level calculations are sequential and lightweight. The CPU has much fewer processing units than a GPU. Our algorithm mitigates this disadvantage by wisely balancing the scale of the parallelization and convergence. We validate our method in a wide range of simulation problems involving high-resolution garment models. Performance-wise, our method is at least one order faster than existing CPU methods, and it delivers a similar performance compared with the state-of-the-art GPU algorithms in many examples, but without using a GPU. 

Recent advances in large models have significantly advanced image-to-3D reconstruction. However, the generated models are often fused into a single piece, limiting their applicability in downstream tasks. This paper focuses on 3D garment generation, a key area for applications like virtual try-on with dynamic garment animations, which require garments to be separable and simulation-ready. We introduce Dress-1-to-3, a novel pipeline that reconstructs physics-plausible, simulation-ready separated garments with sewing patterns and humans from an in-the-wild image. Starting with the image, our approach combines a pre-trained image-to-sewing pattern generation model for creating coarse sewing patterns with a pre-trained multi-view diffusion model to produce multi-view images. The sewing pattern is further refined using a differentiable garment simulator based on the generated multi-view images. Versatile experiments demonstrate that our optimization approach substantially enhances the geometric alignment of the reconstructed 3D garments and humans with the input image. Furthermore, by integrating a texture generation module and a human motion generation module, we produce customized physics-plausible and realistic dynamic garment demonstrations. Our project page is https://dress-1-to-3.github.io/. 

We introduce PhysGaussian a new method that seamlessly integrates physically grounded Newtonian dynamics within 3D Gaussians to achieve high-quality novel motion synthesis. Employing a customized Material Point Method (MPM) our approach enriches 3D Gaussian kernels with physically meaningful kinematic deformation and mechanical stress attributes all evolved in line with continuum mechanics principles. A defining characteristic of our method is the seamless integration between physical simulation and visual rendering: both components utilize the same 3D Gaussian kernels as their discrete representations. This negates the necessity for triangle/tetrahedron meshing marching cubes cage meshes or any other geometry embedding highlighting the principle of "what you see is what you simulate (WS^2)". Our method demonstrates exceptional versatility across a wide variety of materials--including elastic entities plastic metals non-Newtonian fluids and granular materials--showcasing its strong capabilities in creating diverse visual content with novel viewpoints and movements. 

In this paper, we present a GPU algorithm for finite element hyperelastic simulation. We show that the interior-point method, known to be effective for robust collision resolution, can be coupled with non-Newton procedures and be massively sped up on the GPU. Newton's method has been widely chosen for the interior-point family, which fully solves a linear system at each step. After that, the active set associated with collision/contact constraints is updated. Mimicking this routine using a non-Newton optimization (like gradient descent or ADMM) unfortunately does not deliver expected accelerations. This is because the barrier functions employed in an interior-point method need to be updated at every iteration to strictly confine the search to the feasible region. The associated cost (e.g., per-iteration CCD) quickly overweights the benefit brought by the GPU, and a new parallelism modality is needed. Our algorithm is inspired by the domain decomposition method and designed to move interior-point-related computations to local domains as much as possible. We minimize the size of each domain (i.e., a stencil) by restricting it to a single element, so as to fully exploit the capacity of modern GPUs. The stencil-level results are integrated into a global update using a novel hybrid sweep scheme. Our algorithm is locally second-order offering better convergence. It enables simulation acceleration of up to two orders over its CPU counterpart. We demonstrate the scalability, robustness, efficiency, and quality of our algorithm in a variety of simulation scenarios with complex and detailed collision geometries. 

We present a robust and efficient method for simulating Lagrangian solid-fluid coupling based on a new operator splitting strategy. We use variational formulations to approximate fluid properties and solid-fluid interactions, and introduce a unified two-way coupling formulation for SPH fluids and FEM solids using interior point barrier-based frictional contact. We split the resulting optimization problem into a fluid phase and a solid-coupling phase using a novel time-splitting approach with augmentedcontact proxies, and propose efficient custom linear solvers. Our technique accounts for fluids interaction with nonlinear hyperelastic objects of different geometries and codimensions, while maintaining an algorithmically guaranteed non-penetrating criterion. Comprehensive benchmarks and experiments demonstrate the efficacy of our method.