This paper describes a technique for incorporating real-time elastically deformable 3D organs in haptic surgical simulators. Our system is a physically based particle model utilizing a mass-springs-damper connectivity with an implicit predictor to speed up calculations during each time step. The solution involves repeated application of Newton's 2ndd Law of motion: F = ma using an implicit solv...

|Reaction-diiusion systems whose kinetics contain a stable limit cycle are an established class of models for a range of oscillatory biological and chemical phenomena. In this paper, the author compares two numerical methods for calculating the oscillatory wake solutions generated by spatially localized perturbations for one particular reaction-diiusion system, of-! type. The two methods are a ...

In this paper we present a novel, interactive shape modeling technique: Dynamic Implicit Solid Modeling, which unifies volumetric implicit functions and powerful physics-based modeling. Although implicit functions are extremely powerful in graphics, geometric design, and shape modeling, the full potential of implicit functions is yet to be fully realized due to the lack of flexible and interact...

Abstract—The solution of the nonlinear dynamic equilibrium equations of base-isolated structures adopting a conventional monolithic solution approach, i.e. an implicit single-step time integration method employed with an iteration procedure, and the use of existing nonlinear analytical models, such as differential equation models, to simulate the dynamic behavior of seismic isolators can requir...

In this paper we present a novel, interactive shape modeling technique: Dynamic Implicit Solid Modeling, which unifies volumetric implicit functions and powerful physics-based modeling. Although implicit functions are extremely powerful in graphics, geometric design, and shape modeling, the full potential of implicit functions is yet to be fully realized due to the lack of flexible and interact...

Systems driven by multiple physical processes are central to many areas of science and engineering. Time discretization multiphysics systems is challenging, since different have levels stiffness characteristic time scales. The multimethod approach discretizes each process with an appropriate numerical method; the methods coupled appropriately such that overall solution has desired accuracy stab...

Extrapolation methods for the solution of partial diierentialequations are commonly based on the existence of error expansions for the approximate solution. Implicit extrapolation, in the contrast, is based on applying extrapolation indirectly, by using it on quantities like the residual. In the context of multigrid methods, a special technique of this type is known as-extrapolation. For nite e...

Autonomous differential equations of fractional order and non-singular kernel are solved. While solutions can be obtained through numerical, graphical, or analytical solutions, we seek an implicit solution.