Error analysis of a stochastic immersed boundary method incorporating thermal fluctuations

A stochastic numerical scheme for an extended immersed boundary method which incorporates thermal fluctuations for the simulation of microscopic biological systems consisting of fluid and immersed elastica was introduced in (1). The numerical scheme uses techniques from stochastic calculus to overcome stability and accuracy issues associated with standard finite difference methods. The numerical scheme handles a range of time steps in a unified manner, including time steps which are greater than the smallest time scales of the system. The time step regimes we shall investigate can be classified as small, intermediate, or large relative to the time scales of the fluid dynamics of the system. Small time steps resolve in a computationally explicit manner the dynamics of all the degrees of freedom of the system. Large time steps resolve in a computationally explicit manner only the degrees of freedom of the immersed elastica, with the contributions of the dynamics of the fluid degrees of f...

• Type: Journal
• Year: 2008
• Where: MCS
• Authors: Paul J. Atzberger, Peter R. Kramer
• Keywords: Explicit Manner, MCS 2008, Numerical Scheme, Pattern Recognition, Time Step