# Survey of Finite Element Method-Based Real-Time Simulations
## 6 Full Extent FE Models in Real-Time Applications
The attractiveness of this field of application in this period is reflected in the fact that survey papers presenting developments in real-time simulation for surgery simulation were already published at the end of 1990s [51] and the beginning of 2000s [52; 53]. Inclusion of nonlinear effects in real-time simulations is actually of crucial importance in many applications, but it also implies considerably larger numerical effort, in particular when full extent FE models are used. Commercially available FEA programs mostly implement the total or updated Lagrangian formulations [24] as standard solutions with the basic difference between them in the choice of the reference configuration. Those formulations are characterized by high accuracy, but also by significant numerical effort and convergence issues. [PERSON] et al. [54] applied total Lagrangian formulation in combination with material nonlinearities in modeling soft tissue deformations for laparoscopic surgery simulation. They addressed the high computational demand of the approach by using a \"brute force\" method (i.e., by parallelizing the computation on a large, three-dimensional network of high-performance processor units). Despite of the fact that they report on a not highly realistic simulation of uterus tissue deformation. On the other hand, various ideas were implemented to keep the numerical effort in acceptable limits despite the use of rigorous FE formulations. For instance, [PERSON] et al. [55] proposed an approach denoted as a hybrid condensed FE model. The idea is to partition the model into two regions--a part of the model that is being interacted with and the rest of the model. Hence, a complex nonlinear FE model that can also deal with topological change was used to model a small-scale FE model that represents the operational region, while a linear and topology-fixed FE model was used to model the large-scale nonoperational region. The development was done for a virtual training system for knee arthroscopic surgery. In another field of application, [PERSON] et al. [56] focused their work on development of real-time interaction between a designer and a virtual prototype as a promising way to perform optimization of parts design. In the first step, which they refer to as the \"training phase,\" they performed a set of nonlinear FE computations. Over the course of simulation, deformations for a current load case is determined by interpolating between the results obtained in the \"training phase.\" One may actually notice here a certain parallel with the approach based on neural networks. The complexity of simulations based on rigorous nonlinear FE computations drove the researchers to propose innovative formulations for nonlinear FE computations but also to consider different options for solvers. The consideration of solvers is closely related to time integration schemes. A number of authors emphasize the low computational effort needed to resolve a time-step (decoupled equations, provided a lumped mass matrix is used) and no need for iterations due to nonlinearities as major advantages of an explicit time-integration scheme [57; 58]. However, those advantages come together with the disadvantage of a limited and typically rather short time-step due to the conditional stability of the method. Soft materials, such as tissues often involved in real-time simulations, would allow for somewhat larger time-steps as a consequence of their low stiffness. On the other hand, high internal damping is also intrinsic for such materials and this is a parameter that further decreases the time-step. Since real-time simulations are of primary interest for processes that are observable to human perception (i.e., relatively slow dynamics is observed), an adequate time-step of numerical integration could easily be in the order of magnitude of \(10^{-2}\) s. Such a large time-step calls for implicit time integration schemes that are unconditionally stable [59; 60].