Our project addresses the general question of how to design effective
numerical integrators for interactive simulation, and the specific
challenges of two important and related topics: rigid body contact and
incompressible fluid mechanics.
Algorithms for Interactive Simulation
At the heart of all simulations is a numerical integrator for the
differential equations describing the dynamical system (which can
involve time and space derivatives). The problem is different from
usual because of the real time, interactive setting. The hard
requirement is to get an answer at a specified time. Our goal is to
design numerical methods to get this answer as accurately as possible
based on available computing resources. A related goal is to design
algorithms that can run in parallel on a network of interconnected
processing units.
Robust Contact Simulation
Most objects in our environment are quite rigid, and undergo only
small imperceptible deformations. For this reason, rigid body models
are widely used in interactive applications, for instance in robotics
and video games, since a freely moving rigid body can be efficiently
simulated. However, these models encounter serious difficulties when
contact is involved, especially in the presence of friction. Basic
mathematical requirements such as the existence and uniqueness of
solutions can no longer be guaranteed under the classical models, as
observed by Paul Painleve in 1895. We are investigating new frictional
contact simulation algorithms that retain much of the efficiency of
rigid body models, while significantly increasing the accuracy and
robustness of solutions.
Fast Simulation of Fluids
Fluids play a critical role in many environments, from ocean water to
fire, from the surrounding air to the fluids in our own
bodies. However, current approaches to modeling fluids in interactive
simulation either are very limited (e.g., Fourier synthesis of ocean
waves, overly simplified drag models for air resistance) or can't
effectively scale to the resolution desired (e.g., Smoothed Particle
Hydrodynamics models, which are limited in practice to a few thousand
particles to fill a volume). One part of this project is to develop
fast numerical fluid models to fill this gap.
