DSpace Repository :: Browsing by Author "Bender, Jan"

Browsing by Author "Bender, Jan"

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A comparison of linear consistent correction methods for first-order SPH derivatives
(ACM Association for Computing Machinery, 2023) Westhofen, Lukas; Jeske, Stefan; Bender, Jan; Wang, Huamin; Ye, Yuting; Victor Zordan
Awell-known issue with the widely used Smoothed Particle Hydrodynamics (SPH) method is the neighborhood deficiency. Near the surface, the SPH interpolant fails to accurately capture the underlying fields due to a lack of neighboring particles. These errors may introduce ghost forces or other visual artifacts into the simulation. In this work we investigate three different popular methods to correct the first-order spatial derivative SPH operators up to linear accuracy, namely the Kernel Gradient Correction (KGC), Moving Least Squares (MLS) and Reproducing Kernel Particle Method (RKPM). We provide a thorough, theoretical comparison in which we remark strong resemblance between the aforementioned methods. We support this by an analysis using synthetic test scenarios. Additionally, we apply the correction methods in simulations with boundary handling, viscosity, surface tension, vorticity and elastic solids to showcase the reduction or elimination of common numerical artifacts like ghost forces. Lastly, we show that incorporating the correction algorithms in a state-of-the-art SPH solver only incurs a negligible reduction in computational performance.
Consistent SPH Rigid-Fluid Coupling
(The Eurographics Association, 2023) Bender, Jan; Westhofen, Lukas; Rhys Jeske, Stefan; Guthe, Michael; Grosch, Thorsten
A common way to handle boundaries in SPH fluid simulations is to sample the surface of the boundary geometry using particles. These boundary particles are assigned the same properties as the fluid particles and are considered in the pressure force computation to avoid a penetration of the boundary. However, the pressure solver requires a pressure value for each particle. These are typically not computed for the boundary particles due to the computational overhead. Therefore, several strategies have been investigated in previous works to obtain boundary pressure values. A popular, simple technique is pressure mirroring, which mirrors the values from the fluid particles. This method is efficient, but may cause visual artifacts. More complex approaches like pressure extrapolation aim to avoid these artifacts at the cost of computation time. We introduce a constraint-based derivation of Divergence-Free SPH (DFSPH) - a common state-of-the-art pressure solver. This derivation gives us new insights on how to integrate boundary particles in the pressure solve without the need of explicitly computing boundary pressure values. This yields a more elegant formulation of the pressure solver that avoids the aforementioned problems.
Direct Position‐Based Solver for Stiff Rods
(© 2018 The Eurographics Association and John Wiley & Sons Ltd., 2018) Deul, Crispin; Kugelstadt, Tassilo; Weiler, Marcel; Bender, Jan; Chen, Min and Benes, Bedrich
In this paper, we present a novel direct solver for the efficient simulation of stiff, inextensible elastic rods within the position‐based dynamics (PBD) framework. It is based on the XPBD algorithm, which extends PBD to simulate elastic objects with physically meaningful material parameters. XPBD approximates an implicit Euler integration and solves the system of non‐linear equations using a non‐linear Gauss–Seidel solver. However, this solver requires many iterations to converge for complex models and if convergence is not reached, the material becomes too soft. In contrast, we use Newton iterations in combination with our direct solver to solve the non‐linear equations which significantly improves convergence by solving all constraints of an acyclic structure (tree), simultaneously. Our solver only requires a few Newton iterations to achieve high stiffness and inextensibility. We model inextensible rods and trees using rigid segments connected by constraints. Bending and twisting constraints are derived from the well‐established Cosserat model. The high performance of our solver is demonstrated in highly realistic simulations of rods consisting of multiple 10 000 segments. In summary, our method allows the efficient simulation of stiff rods in the PBD framework with a speedup of two orders of magnitude compared to the original XPBD approach.We present a novel direct solver for the efficient simulation of stiff, inextensible elastic rods. It is based on the XPBD algorithm, which extends Position‐Based Dynamics to simulate elastic objects with physically meaningful material parameters. However, the non‐linear Gauss‐Seidel solver of XPBD requires many iterations to converge for complex models and if convergence is not reached, the material becomes too soft. In contrast, we use Newton iterations in combination with our direct solver which significantly improves convergence by solving all constraints of an acyclic structure simultaneously. We model rods using rigid segments connected by constraints. Bending and twisting constraints are derived from the Cosserat model. The high performance of our solver allows the simulation of rods consisting of multiple 10 000 segments with a speedup of two orders of magnitude compared to the original XPBD approach.
Fast Corotated Elastic SPH Solids with Implicit Zero-Energy Mode Control
(ACM, 2021) Kugelstadt, Tassilo; Bender, Jan; Fernández-Fernández, José Antonio; Jeske, Stefan Rhys; Löschner, Fabian; Longva, Andreas; Narain, Rahul and Neff, Michael and Zordan, Victor
We develop a new operator splitting formulation for the simulation of corotated linearly elastic solids with Smoothed Particle Hydrodynamics (SPH). Based on the technique of Kugelstadt et al. [2018] originally developed for the Finite Element Method (FEM), we split the elastic energy into two separate terms corresponding to stretching and volume conservation, and based on this principle, we design a splitting scheme compatible with SPH. The operator splitting scheme enables us to treat the two terms separately, and because the stretching forces lead to a stiffness matrix that is constant in time, we are able to prefactor the system matrix for the implicit integration step. Solid-solid contact and fluid-solid interaction is achieved through a unified pressure solve. We demonstrate more than an order of magnitude improvement in computation time compared to a state-of-the-art SPH simulator for elastic solids. We further improve the stability and reliability of the simulation through several additional contributions. We introduce a new implicit penalty mechanism that suppresses zero-energy modes inherent in the SPH formulation for elastic solids, and present a new, physics-inspired sampling algorithm for generating highquality particle distributions for the rest shape of an elastic solid. We finally also devise an efficient method for interpolating vertex positions of a high-resolution surface mesh based on the SPH particle positions for use in high-fidelity visualization.
Higher-Order Time Integration for Deformable Solids
(The Eurographics Association and John Wiley & Sons Ltd., 2020) Löschner, Fabian; Longva, Andreas; Jeske, Stefan; Kugelstadt, Tassilo; Bender, Jan; Bender, Jan and Popa, Tiberiu
Visually appealing and vivid simulations of deformable solids represent an important aspect of physically based computer animation. For the temporal discretization, it is customary in computer animation to use first-order accurate integration methods, such as Backward Euler, due to their simplicity and robustness. Although there is notable research on second-order methods, their use is not widespread. Many of these well-known methods have significant drawbacks such as severe numerical damping or scene-dependent time step restrictions to ensure stability. In this paper, we discuss the most relevant requirements on such methods in computer animation and motivate the interest beyond first-order accuracy. Keeping these requirements in mind, we investigate several promising methods from the families of diagonally implicit Runge-Kutta (DIRK) and Rosenbrock methods which currently do not appear to have considerable popularity in this field. We show that the usage of such methods improves the visual quality of physical animations. In addition, we demonstrate that they allow distinctly more control over damping at lower computational cost than classical methods. As part of our theoretical contribution, we review aspects of simulations that are often considered more intricate with higher-order methods, such as contact handling. To this end, we derive an implicit linearized contact model based on a predictor-corrector approach that leads to consistent behavior with higher-order integrators as predictors. Our contact model is well suited for the simulation of stiff, nonlinear materials with the integration methods presented in this paper and more common methods such as Backward Euler alike.
Micropolar Elasticity in Physically-Based Animation
(ACM Association for Computing Machinery, 2023) Löschner, Fabian; Fernández-Fernández, José Antonio; Jeske, Stefan Rhys; Longva, Andreas; Bender, Jan; Wang, Huamin; Ye, Yuting; Victor Zordan
We explore micropolar materials for the simulation of volumetric deformable solids. In graphics, micropolar models have only been used in the form of one-dimensional Cosserat rods, where a rotating frame is attached to each material point on the one-dimensional centerline. By carrying this idea over to volumetric solids, every material point is associated with a microrotation, an independent degree of freedom that can be coupled to the displacement through a material’s strain energy density. The additional degrees of freedom give us more control over bending and torsion modes of a material. We propose a new orthotropic micropolar curvature energy that allows us to make materials stiff to bending in specific directions. For the simulation of dynamic micropolar deformables we propose a novel incremental potential formulation with a consistent FEM discretization that is well suited for the use in physically-based animation. This allows us to easily couple micropolar deformables with dynamic collisions through a contact model inspired from the Incremental Potential Contact (IPC) approach. For the spatial discretization with FEM we discuss the challenges related to the rotational degrees of freedom and propose a scheme based on the interpolation of angular velocities followed by quaternion time integration at the quadrature points. In our evaluation we validate the consistency and accuracy of our discretization approach and demonstrate several compelling use cases for micropolar materials. This includes explicit control over bending and torsion stiffness, deformation through prescription of a volumetric curvature field and robust interaction of micropolar deformables with dynamic collisions.
SCA 2020 CGF 39-8: Frontmatter
(The Eurographics Association and John Wiley & Sons Ltd., 2020) Bender, Jan; Popa, Tiberiu; Bender, Jan and Popa, Tiberiu
Smoothed Particle Hydrodynamics Techniques for the Physics Based Simulation of Fluids and Solids
(The Eurographics Association, 2019) Koschier, Dan; Bender, Jan; Solenthaler, Barbara; Teschner, Matthias; Jakob, Wenzel and Puppo, Enrico
Graphics research on Smoothed Particle Hydrodynamics (SPH) has produced fantastic visual results that are unique across the board of research communities concerned with SPH simulations. Generally, the SPH formalism serves as a spatial discretization technique, commonly used for the numerical simulation of continuum mechanical problems such as the simulation of fluids, highly viscous materials, and deformable solids. Recent advances in the field have made it possible to efficiently simulate massive scenes with highly complex boundary geometries on a single PC [Com16b, Com16a]. Moreover, novel techniques allow to robustly handle interactions among various materials [Com18,Com17]. As of today, graphics-inspired pressure solvers, neighborhood search algorithms, boundary formulations, and other contributions often serve as core components in commercial software for animation purposes [Nex17] as well as in computer-aided engineering software [FIF16]. This tutorial covers various aspects of SPH simulations. Governing equations for mechanical phenomena and their SPH discretizations are discussed. Concepts and implementations of core components such as neighborhood search algorithms, pressure solvers, and boundary handling techniques are presented. Implementation hints for the realization of SPH solvers for fluids, elastic solids, and rigid bodies are given. The tutorial combines the introduction of theoretical concepts with the presentation of actual implementations.
A Survey on SPH Methods in Computer Graphics
(The Eurographics Association and John Wiley & Sons Ltd., 2022) Koschier, Dan; Bender, Jan; Solenthaler, Barbara; Teschner, Matthias; Meneveaux, Daniel; Patanè, Giuseppe
Throughout the past decades, the graphics community has spent major resources on the research and development of physics simulators on the mission to computer-generate behaviors achieving outstanding visual effects or to make the virtual world indistinguishable from reality. The variety and impact of recent research based on Smoothed Particle Hydrodynamics (SPH) demonstrates the concept's importance as one of the most versatile tools for the simulation of fluids and solids. With this survey, we offer an overview of the developments and still-active research on physics simulation methodologies based on SPH that has not been addressed in previous SPH surveys. Following an introduction about typical SPH discretization techniques, we provide an overview over the most used incompressibility solvers and present novel insights regarding their relation and conditional equivalence. The survey further covers recent advances in implicit and particle-based boundary handling and sampling techniques. While SPH is best known in the context of fluid simulation we discuss modern concepts to augment the range of simulatable physical characteristics including turbulence, highly viscous matter, deformable solids, as well as rigid body contact handling. Besides the purely numerical approaches, simulation techniques aided by machine learning are on the rise. Thus, the survey discusses recent data-driven approaches and the impact of differentiable solvers on artist control. Finally, we provide context for discussion by outlining existing problems and opportunities to open up new research directions.
VMV 2022: Frontmatter
(The Eurographics Association, 2022) Bender, Jan; Botsch, Mario; Keim, Daniel A.; Bender, Jan; Botsch, Mario; Keim, Daniel A.
Weighted Laplacian Smoothing for Surface Reconstruction of Particle-based Fluids
(The Eurographics Association, 2023) Löschner, Fabian; Böttcher, Timna; Rhys Jeske, Stefan; Bender, Jan; Guthe, Michael; Grosch, Thorsten
In physically-based animation, producing detailed and realistic surface reconstructions for rendering is an important part of a simulation pipeline for particle-based fluids. In this paper we propose a post-processing approach to obtain smooth surfaces from ''blobby'' marching cubes triangulations without visual volume loss or shrinkage of drops and splashes. In contrast to other state-of-the-art methods that often require changes to the entire reconstruction pipeline our approach is easy to implement and less computationally expensive. The main component is Laplacian mesh smoothing with our proposed feature weights that dampen the smoothing in regions of the mesh with splashes and isolated particles without reducing effectiveness in regions that are supposed to be flat. In addition, we suggest a specialized decimation procedure to avoid artifacts due to low-quality triangle configurations generated by marching cubes and a normal smoothing pass to further increase quality when visualizing the mesh with physically-based rendering. For improved computational efficiency of the method, we outline the option of integrating computation of our weights into an existing reconstruction pipeline as most involved quantities are already known during reconstruction. Finally, we evaluate our post-processing implementation on high-resolution smoothed particle hydrodynamics (SPH) simulations.

Browsing by Author "Bender, Jan"

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