# Survey of Finite Element Method-Based Real-Time Simulations
## 7 Conclusions  
FEM-based real-time simulation has entered numerous fields ranging from entertainment to engineering. Although we are witnessing the early days of its development, an immense amount of work has already been done to respond to the challenges of performing real-time simulations using currently available computer hardware technology. This paper aimed at a not exhaustive but representative survey of the development in the field. It would certainly take a prohibitively large space to mention all or most of the work done and, hence, the objective was to represent different directions and ideas on how to balance between conflicting objectives of high numerical efficiency and acceptable accuracy required for real-time simulations. The solution in the form of mass-spring systems obviously offers attractive simplicity and efficiency, which come at the price of rather problematic accuracy and ambiguity of model building. Though considered obsolete today, the approach still represents an option in the fields where the accuracy is not a critical demand and can also be used for a rough approximation of deformable environment of the objects the focus of interaction is put on. Model order reduction techniques have already proven to be extremely useful in the field of MBS dynamics for engineering tasks, but also found their applications in various interactive simulations in the field of computer graphics. Different attempts have been made to tackle the most serious shortage of the approach, namely its intrinsic limitation to linear deformations. Implementation of the geometric stiffness and modal warping were mentioned as moderate remedies, but interestingly, so far, no report could be found that combines both approaches, which should offer a new quality due to their complementariness. FEM-based training of neural networks was addressed as a sort of indirect approach to model reduction. It is a promising approach that may address nonlinearities in structural behavior as well, but its success strongly depends on the \"density\" of the deformation set used in training the neural networks. Finally, the most daring solutions keep the FE models in their full extent and, additionally, involve nonlinear deformational behavior. The hardware developments in the past two decades encouraged the researchers to explore new ideas in order to address this particular challenge. Currently, the approach based on the simplified co-rotational FE formulation, or \"warped stiffness\" as denoted by some authors, in combination with the coupled mesh technique appears to be rather promising for applications on conventional hardware components. The formulation implements simplifications that allow to use the precomputed linear stiffness matrices of each element, while the coupled mesh technique enables the use of relatively coarse FE meshes for complex geometries. Figure 5: Dog model: (**a**) Geometry, FE mesh, and texture; (**b**) screenshots from an interactive simulation [7]. With the hindsight on development done, it is reasonable to expect that new brilliant ideas are probably just around the corner. In addition, having in mind the Moore's law of hardware development and the already existing new strategies of hardware usage that bring significant increase in computational power, it is certain that the field of FEM-based real-time simulations has a very promising future in the field of structural analysis. In addition, it should be emphasized that related fields, such as computational fluid dynamic (CFD) and particle physics, encounter similar challenges and the interest in real-time simulations by means of conventional and state-of-the-art hardware components in those fields is equally large. The developments in all those fields already began to merge in order to enable real-time simulation of coupled-field effects, which represents a quantum leap toward high-fidelity simulation. Conceptualization, data curation D.M. and M.Z. ; writing--original draft preparation, D.M. ; writing--review and editing, M.Z.