We propose an efficient numerical algorithm for computing deformations of “very” soft tissues (such as the brain, liver, kidney etc.), with applications to real time surgical simulation. The algorithm is based on the finite element method using the Total Lagrangian formulation, where stresses and strains are measured with respect to the original configuration. This choice allows for pre-computi...

Grid staggering for wave equations is a validated approach for many applications, as it generally enhances stability and accuracy. This paper is about time staggering. Our aim is to assess a fourth-order, explicit, time-staggered integration method from the literature, through a comparison with two alternative fourth-order, explicit methods. These are the classical Runge-Kutta method and a symm...

Realistic animation of soft objects such as cloth is essential for plausible character animation. Many techniques have been proposed for the simulation of soft objects, and most of them are based on numerical integration. Among the techniques, the implicit integration method is the most likely technique for realtime environments, since it allows large time steps for cloth simulation by ensuring...

Explicit Runge–Kutta schemes with large stable step sizes are developed for integration of high order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge–Kutta schemes available in literature. Furthermore, they have a small principal error n...

Time fractional PDEs have been used in many applications for modeling and simulations. Many of these are multiscale contain high contrast variations the media properties. It requires very small time step size to perform detailed computations. On other hand, presence spatial grids, is required explicit methods. Explicit methods advantages as we discuss paper. In this paper, propose a partial met...

In this paper we present an explicit fourth-order method for the integration of Hamilton’s Equations. This method preserves the property that the time evolution of such a system yields a canonical transformation from the initial conditions to the final state. That is, the integration step is an explicit symplectic map. Although the result is first derived for a specific type of Hamiltonian, it ...