Numerical Methods include a vast toolbox of mathematical methods for solving complex multidisciplinary problems of modeling and analysis. Numerical methods are usually applied to problems where closed form solutions are either impossible or highly inconvenient to obtain. Many numerical techniques such as the finite element method, boundary element method, discrete element method and others can be used to simulate prostheses and other biomedical devices, etc. These advanced numerical tools are able to produce sophisticated models in bioengineering, incorporating non linear material behaviour, fatigue effects, contact problems between bone and metals, dynamic behaviour of fluids in arteries, boundaries identification for medical images treatment, and so on.

The course will review some of the most powerful tools mentioned above, and go further to cover advanced algorithms and parallel applications. Some of the algorithms described will include nonlinear stress analysis and fluid flow.

The course will assume no more than an introductory knowledge of these tools on the part of the participants, but will move quickly to include software demonstrations and “hands on” experience of the codes that will be provided during the workshop.

While numerical methods is an inherently generic discipline that has applications in all branches of science and engineering, the second half of the workshop will focus on bioengineering applications reflecting the experience of the instructors.

Implementation of Courses

The organization of this PASI proposal has two distinct parts. During the first week of the course, the topics covered are interdisciplinary subjects of numerical methods and computational mechanics. In the second week, the focus of the seminar will be on using the tools learned in week 1 in applications more focused on bioengineering. In particular, case histories will be presented related to prostheses, valves and modeling.

The schedule of the seminar, because of its advanced technological nature, is designed in a way that lecturers and participating students interact. Thus, sessions will consist of the professor's presentation, followed by Q&A and discussion periods.

Participation and interaction Interaction between lecturers and student participants is one of the main goals of the seminar. Besides the method of courses, in order to encourage further interaction, several events are planned.