【GAMES Webinar 2024-347期】
模拟与动画专题
高性能物理仿真的设计与实践
· 1 ·
报告题目
Preconditioned Nonlinear Conjugate Gradient Method for Real-time Interior-point Hyperelasticity
报告嘉宾
沈星
网易伏羲实验室
报告时间
2024年11月7号 晚上8:00-8:30（北京时间）
报告方式
GAMES直播间: https://live.bilibili.com/h5/24617282
报告摘要
The linear conjugate gradient method is widely used in physical simulation, particularly for solving large-scale linear systems derived from Newton’s method. The nonlinear conjugate gradient method generalizes the conjugate gradient method to nonlinear optimization, which is extensively utilized in solving practical large-scale unconstrained optimization problems. However, it is rarely discussed in physical simulation due to the requirement of multiple vector-vector dot products. Fortunately, with the advancement of GPU-parallel acceleration techniques, it is no longer a bottleneck. In this paper, we propose a Jacobi preconditioned nonlinear conjugate gradient method for elastic deformation using interior-point methods. Our method is straightforward, GPU-parallelizable, and exhibits fast convergence and robustness against large time steps. The employment of the barrier function in interior-point methods necessitates continuous collision detection per iteration to obtain a penetration-free step size, which is computationally expensive and challenging to parallelize on GPUs. To address this issue, we introduce a line search strategy that deduces an appropriate step size in a single pass, eliminating the need for additional collision detection. Furthermore, we simplify and accelerate the computations of Jacobi preconditioning and Hessian-vector product for hyperelasticity and barrier function. Our method can accurately simulate objects comprising over 100,000 tetrahedra in complex self-collision scenarios at real-time speeds.
嘉宾简介
沈星，2022年博士毕业于浙江大学数学科学学院计算数学系。现工作于网易伏羲实验室。研究方向包括软体仿真，物理启发神经网络(PINNs), 图像分割等。
个人主页
https://xingbaji.github.io/
· 2 ·
报告题目
The Lightning-fast Method of Fundamental Solutions
报告嘉宾
陈炯
Inria
报告时间
2024年11月7号 晚上8:30-9:00（北京时间）
报告方式
GAMES直播间: https://live.bilibili.com/h5/24617282
报告摘要
The method of fundamental solutions (MFS) and its associated boundary element method (BEM) have gained popularity in computer graphics due to the reduced dimensionality they offer: for three-dimensional linear problems, they only require variables on the domain boundary to solve and evaluate the solution throughout space, making them a valuable tool in a wide variety of applications. However, MFS and BEM have poor computational scalability and huge memory requirements for large-scale problems, limiting their applicability and efficiency in practice. By leveraging connections with Gaussian Processes and exploiting the sparse structure of the inverses of boundary integral matrices, we introduce a variational preconditioner that can be computed via a sparse inverse-Cholesky factorization in a massively parallel manner. In this talk, I will show that applying our preconditioner to the Preconditioned Conjugate Gradient algorithm greatly improves the efficiency of MFS or BEM solves by orders of magnitude in our series of tests.
嘉宾简介
Jiong Chen is a researcher at Inria and a permanent member of the GeomeriX project-team. After earning his PhD from Zhejiang University in 2020, he spent one year each as a postdoctoral fellow at Télécom Paris and École Polytechnique before joining Inria Saclay. His research has been focusing on the numerical foundations of geometric modeling and physical simulation, covering topics such as multiscale analysis, numerical preconditioning and interactive techniques.
个人主页
https://jiongchen.github.io/
主持人简介
刘天添
太极图形
刘天添，太极图形首席研究科学家，在加入太极前曾任职微软亚洲研究院网络图形组研究员。于宾夕法尼亚大学大学获取博士学位。他的研究兴趣主要是高性能数值计算，实时物理仿真和几何处理，相关论文被ACM TOG收录十余篇。
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