Carlos Quesada

Real-time simulation techniques for augmented learning in science and engineering

In this paper, we present the basics of a novel methodology for the development of simulation-based and augmented learning tools in the context of applied science and engineering. It is based on the extensive use of model order reduction, and particularly, of the so-called proper generalized decomposition method. This method provides a sort of meta-modeling tool without the need for prior computer experiments that allows the user to obtain real-time response in the solution of complex engineering or physical problems. This real-time capability also allows for its implementation in deployed, touch screen, handheld devices or even to be immersed into electronic textbooks. We explore here the basics of the proposed methodology and give examples on a few challenging applications never until now explored, up to our knowledge.

PGD-Based Model Reduction for Surgery Simulation: Solid Dynamics and Contact Detection

We present here an analysis of the possible advantages of using a priori model order reduction techniques for real-time simulation in computational surgery. Special attention will be paid to methods based upon Proper Generalized Decomposition techniques. These techniques allow for impressive savings in on-line computations by obtaining off-line a reduced-order approach to the problem at hand. This approach can be seen as a particular instance of meta-model, response surface or —as we have coined it— a sort of computational vademecum. In this work we detail the approach followed for the implementation of essential aspects in computational surgery, such as solid dynamics and contact detection.

Vademecums for Real-Time Computational Surgery

In this chapter the concept of computational vademecum is presented and analyzed in detail when applied for the real-time simulation in the field of computational surgery. In essence, a computational vademecum is an off-line computer simulation of a physical process in which different variables have been considered as parameters, thus giving rise to a high-dimensional problem. To avoid the numerical difficulties associated with meshing high-dimensional domains, and also their respective post-processing, proper generalized decomposition (PGD) methods have been employed. These allow to express the high-dimensional solution as a finite sum of separable functions, that can be post-processed on-line at tremendously high feedback rates, even on the order of kHz.