Handling stiffness in simulating and calibrating physics-based soft object deformation
Motion simulation of soft objects such as cloth, plants, soft contacts and muscles is ubiquitous in computer graphics and robotics applications. Different approaches for physics-based modelling have been used, from mass- spring systems to spatial FEM semi-discretizations of the elastodynamic equations. This leads to a large, expensive to assemble, dynamic ODE in time, where the damped motion may mask highly oscillatory stiffness. The model described by the differential system must often be calibrated first to enable effective simulation, control and 3D-printing. Data-driven methods for this inverse problem are used for this purpose. Many expensive simulations of the motion in time are required for such calibrations. The choice of numerical method for discretizing the dynamical system depends on the purpose and context of the simulation. For more engineering- oriented applications that require quantitative accuracy, more careful and thus potentially much more expensive simulations are required. The level of need to respect the physics may strongly affect the choice of method. A semi-implicit time integration method using large time steps has been most popular in computer graphics until recently. This however introduces artificial damping, making the results dependent on the time step size. I will show a simple analysis of this effect and discuss its implications. I will then briefly discuss other approaches, including energy conserving methods, exponential methods, and methods that decouple fast and slow modes. There are different application environments where each of these approaches excel.
Uri Ascher has been a full professor of Computer Science at the University of British Columbia since 1986. He received his PhD from the University of Minnesota in 1975. His research interests are in scientific computing methods for differential equations with constraints, inverse problems, optimization, and various applications including computer graphics and image processing. He has co-authored four books and many scientific papers, and is currently an associate editor of three journals. He is a SIAM Fellow and recipient of the CAIMS Research Prize, and has given several conference plenary talks in recent years.