# Survey of Finite Element Method-Based Real-Time Simulations
## 6 Full Extent FE Models in Real-Time Applications  
Though keeping FE models in their full extent (all nodal DOFs kept, which means no reduction performed) offers great fidelity in modeling, it is, on the other hand, a rather challenging task to perform real-time simulations based on such models. Even with a relatively moderate number of DOFs, the resulting systems of equations are usually prohibitively large for a successful real-time simulation based on rigorous FE formulations and using conventional hardware components. This is particularly valid if nonlinearities are involved in the simulation. Hence, various ideas on how to simplify the way of formulating the problem and finding the solution and thus perform a reasonable trade-off between accuracy and numerical efficiency were proposed in order to meet the objective of real-time simulation. The solutions depend on the specific field of application. In the early days of the FEM-based virtual reality and augmented reality (AR) concept, the hardware components could offer significantly less computational power compared to what is available at present. Therefore, at that time, if the full extent FE models were to be used, it was necessary to restrict their use to linear regimes as the assumption of linearity allows for significant savings in numerical effort. However, this approach remained until the present days in applications in which linear models do meet the simulation requirements. [PERSON] et al. [45] aimed at enhancements in structural analysis by means of AR technologies. For this purpose, they developed a system that integrates sensor measurement and real-time FEA simulation into an AR-based environment. A network of wireless sensors acquired spatially distributed loads, while FEA generated fast solutions for the sensed loads. The speed of computation was enabled by introducing the assumption of linear and quasi-static behavior, which allowed to pre-compute the inverse of the stiffness matrix. Finally, the obtained FEA results were superimposed directly onto real-world objects for enhanced data exploration. A rather similar approach was seen in the work by [PERSON] et al. [46]. Additionally, in this work the general idea was to visualize the FE results by overlaying them over the real model. The user may interactively define the boundary conditions on the observed model and based on the FE results assess the stress/strain distribution. A cantilever test was used for demonstration. [PERSON] et al. [47] used the linear inverse FEM to perform real time full-field reconstruction of displacements based on limited set of discrete strain data. To obtain the strain data, in situ strain measurements of the deformed structural shape were done. They demonstrated the approach on a composite stiffened structures for static, dynamic and thermal loadings. Linear FE models were also seen as a trade-off between numerical efficiency and biomechanical realism in the field of surgery simulators that demand modeling soft tissues. In one of the pioneer works in 90's, [PERSON] and [PERSON] [48] used linear elasticity combined with simple tetrahedral elements. They further reduced the numerical effort by performing condensation so that only the surface nodes remained during the simulation available for interaction. In addition, the condensed stiffness matrix was inverted before the simulation. [PERSON] et al. [49] proposed physical models based on FEM and linear elasticity, in which precomputed deformations were combined to enable real-time simulations. [PERSON] et al. [50] developed several biomechanical models based on linear elasticity and FEM with anisotropic mechanical behavior included. They implemented transversely isotropic properties and added external elastic membrane to the models to represent relatively stiff skin of internal organs (\"surface anisotropy\"). Furthermore, their development addressed the problem of contact with an instrument and determination of reaction forces for the need of force-feedback devices and haptic rendering.