GAMES Webinar 2021 – 213期(模拟专题) | Jingyu Chen (UCLA)，Kai Jia (MIT)
【GAMES Webinar 2021-213期】(模拟专题)
报告嘉宾1：Jingyu Chen (UCLA)
报告题目：A Momentum-Conserving Implicit Material Point Method for Surface Tension with Contact Angles and Spatial Gradients
We present a novel Material Point Method (MPM) discretization of surface tension forces that arise from spatially varying surface energies. These variations typically arise from surface energy dependence on temperature and/or concentration. Furthermore, since the surface energy is an interfacial property depending on the types of materials on either side of an interface, spatial variation is required for modeling the contact angle at the triple junction between a liquid, solid and surrounding air. Our discretization is based on the surface energy itself, rather than on the associated traction condition most commonly used for discretization with particle methods. Our energy based approach automatically captures surface gradients without the explicit need to resolve them as in traction condition based approaches. We include an implicit discretization of thermomechanical material coupling with a novel particle-based enforcement of Robin boundary conditions associated with convective heating. Lastly, we design a particle resampling approach needed to achieve perfect conservation of linear and angular momentum with Affine-Particle-In-Cell (APIC) [Jiang et al. 2015]. We show that our approach enables implicit time stepping for complex behaviors like the Marangoni effect and hydrophobicity/hydrophilicity. We demonstrate the robustness and utility of our method by simulating materials that exhibit highly diverse degrees of surface tension and thermomechanical effects, such as water, wine and wax.
Jingyu Chen is a Ph.D. student in mechanical engineering at UCLA, advised by Prof. Joseph Teran. Jingyu received his Bachelor’s degree in mechanical engineering from Rensselaer Polytechnic Institute in 2017. His current research focuses on various physics-based simulations of deformable solids, fluids, and thermomechanical effects.
报告题目：SANM: A Symbolic Asymptotic Numerical Solver with Applications in Mesh Deformation
Solving nonlinear systems is an important problem. Numerical continuation methods efficiently solve certain nonlinear systems. The Asymptotic Numerical Method (ANM) is a powerful continuation method that usually converges faster than Newtonian methods. ANM explores the landscape of the function by following a parameterized solution curve approximated with a high-order power series. Although ANM has successfully solved a few graphics and engineering problems, prior to our work, applying ANM to new problems required significant effort because the standard ANM assumes quadratic functions, while manually deriving the power series expansion for nonquadratic systems is a tedious and challenging task.
We present a novel solver, SANM, that applies ANM to solve symbolically represented nonlinear systems. SANM solves such systems in a fully automated manner. SANM also extends ANM to support many nonquadratic operators, including intricate ones such as singular value decomposition. Furthermore, SANM generalizes ANM to support the implicit homotopy form. Moreover, SANM achieves high computing performance via optimized system design and implementation.
We deploy SANM to solve forward and inverse elastic force equilibrium problems and controlled mesh deformation problems with a few constitutive models. Our results show that SANM converges faster than Newtonian solvers, requires little programming effort for new problems, and delivers comparable or better performance than a hand-coded, specialized ANM solver. While we demonstrate on mesh deformation problems, SANM is generic and potentially applicable to many tasks.
Kai Jia is a Ph.D. student at MIT EECS, advised by Martin Rinard. His major research interests lie in programming languages and artificial intelligence. He received a bachelor’s degree in Computer Science and Technology from Tsinghua University in 2015. Before starting his Ph.D., Kai worked in the industry, where he conducted computer vision research and led the development of an in-house deep learning framework.
许威威，现任浙江大学CAD&CG国家重点实验室百人计划研究员。曾任日本立命馆大学博士后，微软亚洲研究院网络图形组研究员, 杭州师范大学浙江省钱江学者特聘教授。主要研究方向为计算机图形学、三维重建、深度学习、物理仿真及3D打印。在国内外高水平学术会议和期刊发表论文80余篇，其中ACM Transactions on Graphics, IEEE TVCG, 及IEEE CVPR等CCF-A类论文20余篇。获中国和美国授权专利15项。所开发的三维注册和重建技术在高精度扫描仪及人体三维重建系统中得到应用。2014年受国家自然科学基金优秀青年基金资助，主持国家自然科学基金重点项目一项，获浙江省自然科学二等奖一项。
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