First presenter Co-presenter(s)
Name :  Ekaterina Auer * Name:   
E-mail: E-mail:  
Affiliation: University of Duisburg-Essen Name:   
Department: Faculty of Engineering, INKO  E-mail:    
City: Duisburg Name:   
State/Province:   E-mail:    
Country: Germany Name:   
02-01  E-mail:    
Session: 2- Interaction Between Computer Algebra and Interval Computations Schedule:
Thursday, 15:00
Related website:  
Title of
Applications of Verified Methods in Biomechanics

In the recent years, verified methods have been applied in engineering to propagate uncertainty, for example, measurement uncertainty, through a given system and to compute its parameter sensitivities. The measurement uncertainty becomes especially problematic in biomechanics where the presence of living subjects prohibits frequent use of some more precise methods that have adverse health effects. One of the drawbacks of verified solutions to this problem from the point of view of mechanics is that they use derivatives which are in general not available inside numerical modeling and simulation software.

The problem of obtaining derivatives can be solved, for example, by using algorithmic differentiation implemented through overloading. However, this presupposes that the code we use does not contain conditional expressions that depend on their argument, that is, directives of the form {\tt IF x<0 THEN f(x)=f1(x)}. Generally, this too rigid restriction obstructs the applicability of verified methods. Recently, algorithmic differentiation tools have been developed that can handle conditional expressions for floating-point- based codes (e.g. {\sc CppAD} \url{}). The task now is to adjust them to interval-based data types.

However, this task is not as straightforward as it might seem. An interval comparison operator might have a number of semantically different definitions. The one most suitable in our situation can take not only true or false as its value. There is also a third case to consider where we cannot tell how one interval compares to another, the so-called `maybe case'. In this talk, we will discuss possible solutions to the problem of differentiating piecewise functions in interval-based implementations. Moreover, we will give an idea of how computer algebra methods can be applied in a general biomechanical context.