解算器
离散化
可微函数
颂歌
计算机科学
积分器
数学优化
有限元法
非线性系统
最优化问题
应用数学
数学
算法
数学分析
物理
热力学
量子力学
计算机网络
带宽(计算)
作者
Zizhou Huang,Davi Colli Tozoni,Arvi Gjoka,Zachary Ferguson,Teseo Schneider,Daniele Panozzo,Denis Zorin
摘要
We introduce a general differentiable solver for time-dependent deformation problems with contact and friction. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed incremental potential contact method for handling contact and friction forces to solve ODE- and PDE-constrained optimization problems on scenes with complex geometry. It supports static and dynamic problems and differentiation with respect to all physical parameters involved in the physical problem description, which include shape, material parameters, friction parameters, and initial conditions. Our analytically derived adjoint formulation is efficient, with a small overhead (typically less than 10% for nonlinear problems) over the forward simulation, and shares many similarities with the forward problem, allowing the reuse of large parts of existing forward simulator code. We implement our approach on top of the open-source PolyFEM library and demonstrate the applicability of our solver to shape design, initial condition optimization, and material estimation on both simulated results and physical validations.
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