José Antonio Fernández-Fernández, M.Sc.
Room 203
Phone: +49 241 80 24083
Email: fernandez@cs.rwth-aachen.de


Fast Corotated Elastic SPH Solids with Implicit Zero-Energy Mode Control

Tassilo Kugelstadt, Jan Bender, José Antonio Fernández-Fernández, Stefan Rhys Jeske, Fabian Löschner, Andreas Longva
Proceedings of the ACM on Computer Graphics and Interactive Techniques (Best Paper Award at SCA)

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. [KKB2018] 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 high-quality 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.

» Show Videos
» Show BibTeX

author = {Kugelstadt, Tassilo and Bender, Jan and Fern{\'{a}}ndez-Fern{\'{a}}ndez, Jos{\'{e}} Antonio and Jeske, Stefan Rhys and L{\"{o}}schner, Fabian and Longva, Andreas},
title = {Fast Corotated Elastic SPH Solids with Implicit Zero-Energy Mode Control},
year = {2021},
issue_date = {September 2021},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {4},
number = {3},
url = {https://doi.org/10.1145/3480142},
doi = {10.1145/3480142},
journal = {Proc. ACM Comput. Graph. Interact. Tech.},
month = sep,
articleno = {33},
numpages = {21},
keywords = {Smoothed Particle Hydrodynamics, fluid simulation, deformable solids, solid-fluid coupling}

Higher-Order Finite Elements for Embedded Simulation

Andreas Longva, Fabian Löschner, Tassilo Kugelstadt, José Antonio Fernández-Fernández, Jan Bender
ACM Transactions on Graphics (SIGGRAPH Asia 2020)

As demands for high-fidelity physics-based animations increase, the need for accurate methods for simulating deformable solids grows. While higher-order finite elements are commonplace in engineering due to their superior approximation properties for many problems, they have gained little traction in the computer graphics community. This may partially be explained by the need for finite element meshes to approximate the highly complex geometry of models used in graphics applications. Due to the additional per-element computational expense of higher-order elements, larger elements are needed, and the error incurred due to the geometry mismatch eradicates the benefits of higher-order discretizations. One solution to this problem is the embedding of the geometry into a coarser finite element mesh. However, to date there is no adequate, practical computational framework that permits the accurate embedding into higher-order elements.

We develop a novel, robust quadrature generation method that generates theoretically guaranteed high-quality sub-cell integration rules of arbitrary polynomial accuracy. The number of quadrature points generated is bounded only by the desired degree of the polynomial, independent of the embedded geometry. Additionally, we build on recent work in the Finite Cell Method (FCM) community so as to tackle the severe ill-conditioning caused by partially filled elements by adapting an Additive-Schwarz-based preconditioner so that it is suitable for use with state-of-the-art non-linear material models from the graphics literature. Together these two contributions constitute a general-purpose framework for embedded simulation with higher-order finite elements.

We finally demonstrate the benefits of our framework in several scenarios, in which second-order hexahedra and tetrahedra clearly outperform their first-order counterparts.

» Show Videos
» Show BibTeX

author= {Andreas Longva and Fabian L{\"{o}}schner and Tassilo Kugelstadt and Jos{\'{e}} Antonio Fern{\'{a}}ndez-Fern{\'{a}}ndez and Jan Bender },
title= {{Higher-Order Finite Elements for Embedded Simulation}},
year= {2020},
journal= {ACM Transactions on Graphics (SIGGRAPH Asia)},
publisher= {ACM},
volume = {39},
number = {6},
pages= {14}

Disclaimer Home Visual Computing institute RWTH Aachen University