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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. 

Strand-based hair simulations have recently become increasingly popular for a range of real-time applications. However, accurately simulating the full number of hair strands remains challenging. A commonly employed technique involves simulating a subset of guide hairs to capture the overall behavior of the hairstyle. Details are then enriched by interpolation using linear skinning. Hair interpolation enables fast real-time simulations but frequently leads to various artifacts during runtime. As the skinning weights are often pre-computed, substantial variations between the initial and deformed shapes of the hair can cause severe deviations in fine hair geometry. Straight hairs may become kinked, and curly hairs may become zigzags. This work introduces a novel physical-driven hair interpolation scheme that utilizes existing simulated guide hair data. Instead of directly operating on positions, we interpolate the internal forces from the guide hairs before efficiently reconstructing the rendered hairs based on their material model. We formulate our problem as a constraint satisfaction problem for which we present an efficient solution. Further practical considerations are addressed using regularization terms that regulate penetration avoidance and drift correction. We have tested various hairstyles to illustrate that our approach can generate visually plausible rendered hairs with only a few guide hairs and minimal computational overhead, amounting to only about 20% of conventional linear hair interpolation. This efficiency underscores the practical viability of our method for real-time applications. 

We propose a height-field-based real-time simulation method for sand and water mixtures. Inspired by the shallow-water assumption, our approach extends the governing equations to handle two-phase flows of sand and water using height fields. Our depth-integrated governing equations can model the elastoplastic behavior of sand, as well as sand-water-mixing phenomena such as friction, diffusion, saturation, and momentum exchange. We further propose an operator-splitting time integrator that is both GPU-friendly and stable under moderate time step sizes. We have evaluated our method on a set of benchmark scenarios involving large bodies of heterogeneous materials, where our GPU-based algorithm runs at real-time frame rates. Our method achieves a desirable trade-off between fidelity and performance, bringing an unprecedentedly immersive experience for real-time applications. 

Lagrangian/Eulerian hybrid strand-based hair simulation techniques have quickly become a popular approach in VFX and real-time graphics applications. With Lagrangian hair dynamics, the inter-hair contacts are resolved in the Eulerian grid using the continuum method, i.e., the MPM scheme with the granular Drucker-Prager rheology, to avoid expensive collision detection and handling. This fuzzy collision handling makes the authoring process significantly easier. However, although current hair grooming tools provide a wide range of strand-based modeling tools for this simulation approach, the crucial sag-free initialization functionality remains often ignored. Thus, when the simulation starts, gravity would cause any artistic hairstyle to sag and deform into unintended and undesirable shapes. This paper proposes a novel four-stage sag-free initialization framework to solve stable quasistatic configurations for hybrid strand-based hair dynamic systems. These four stages are split into two global-local pairs. The first one ensures static equilibrium at every Eulerian grid node with additional inequality constraints to prevent stress from exiting the yielding surface. We then derive several associated closed-form solutions in the local stage to compute segment rest lengths, orientations, and particle deformation gradients in parallel. The second global-local step solves along each hair strand to ensure all the bend and twist constraints produce zero net torque on every hair segment, followed by a local step to adjust the rest Darboux vectors to a unit quaternion. We also introduce an essential modification for the Darboux vector to eliminate the ambiguity of the Cosserat rod rest pose in both initialization and simulation. We evaluate our method on a wide range of hairstyles, and our approach can only take a few seconds to minutes to get the rest quasistatic configurations for hundreds of hair strands. Our results show that our method successfully prevents sagging and has minimal impact on the hair motion during simulation. 

Noncentrosymmetric (NCS) silicon phosphides have recently shown promise as nonlinear optical materials due to the balance of strong second harmonic generation (SHG) activity and large laser damage threshold (LDT) values. While arsenides of electropositive metals, such as Ba, Mg, Zn, and Cd were explored, no NLO properties for transition metal tetrel arsenides have yet been reported. IrSi 3 As 3 is a novel compound, isostructural to IrSi 3 P 3 , which allows a direct investigation on the impact of the heavier pnictogen on structural and optical properties. The direct bandgap is reduced from 1.8 eV for IrSi 3 P 3 to 1.55 eV for IrSi 3 As 3 . Unlike many NLO chalcogenides, IrSi 3 As 3 has a small bandgap without compromising the balance between SHG signal and high LDT values. IrSi 3 As 3 was found to outperform both its phosphide analogue IrSi 3 P 3 , as well as the state-of-the-art infrared SHG standard AgGaS 2 (AGS) in SHG activity and the LDT. 

Initializing simulations of deformable objects involves setting the rest state of all internal forces at the rest shape of the object. However, often times the rest shape is not explicitly provided. In its absence, it is common to initialize by treating the given initial shape as the rest shape. This leads to sagging, the undesirable deformation under gravity as soon as the simulation begins. Prior solutions to sagging are limited to specific simulation systems and material models, most of them cannot handle frictional contact, and they require solving expensive global nonlinear optimization problems. We introduce a novel solution to the sagging problem that can be applied to a variety of simulation systems and materials. The key feature of our approach is that we avoid solving a global nonlinear optimization problem by performing the initialization in two stages. First, we use a global linear optimization for static equilibrium. Any nonlinearity of the material definition is handled in the local stage, which solves many small local problems efficiently and in parallel. Notably, our method can properly handle frictional contact orders of magnitude faster than prior work. We show that our approach can be applied to various simulation systems by presenting examples with mass-spring systems, cloth simulations, the finite element method, the material point method, and position-based dynamics. 

Fluidic devices are crucial components in many industrial applications involving fluid mechanics. Computational design of a high-performance fluidic system faces multifaceted challenges regarding its geometric representation and physical accuracy. We present a novel topology optimization method to design fluidic devices in a Stokes flow context. Our approach is featured by its capability in accommodating a broad spectrum of boundary conditions at the solid-fluid interface. Our key contribution is an anisotropic and differentiable constitutive model that unifies the representation of different phases and boundary conditions in a Stokes model, enabling a topology optimization method that can synthesize novel structures with accurate boundary conditions from a background grid discretization. We demonstrate the efficacy of our approach by conducting several fluidic system design tasks with over four million design parameters.