A Colloquium took place at West Point Academy organised by the Department of Mathematics of that Institution. The Meeting highlighted the applications of computer tools for the solution of a variety of problems and discussed their advantages and disadvantages.
The Colloquium was organised by Professor Ted Hromadka of West Point and supported by the members of his Department under the direction of Professor Colonel Steve Horton.
The invited keynote addresses were as follows:
“The Boundary Element Method from Conception to Reality” by Carlos A Brebbia, Director of Wessex Institute. Carlos discussed the origins of boundary elements and its emergence as a product of the research work on mixed formulations, integral equations and finite element approximations.
He stressed the importance of basic mixed formulations as a generalisation of the principle of virtual work. This allows for the satisfaction of different sets of equations and conditions, including those governing nonlinear and time dependent problems. Carlos then proceeded to introduce BEM using the Laplace equation as an example and explaining its unique characteristics and fundamental difference of boundary elements with finite difference or finite elements. He pointed out that the method is simple to use as it did not require internal discretisation and gives accurate results because of the properties of the fundamental solutions that it employs. It also allows for the easy handling of moving boundaries and is specially well suited to problems extending to infinity.
Following this, Carlos presented some case studies, including offshore structures and their cathodic protection design, as well as fracture mechanics and crack propagation.
The second presentation was entitled “The role of mathematics in structural dynamics” by JJ Connor. Jerry is Emeritus Professor at MIT and Adjunct Professor at WIT. He is currently in charge of research in the Boston Office of the Institute.
Jerry discussed a series of motion problems:
- Flexible structures
- Motion sensitive structures
- Material science achievements
- Damage limits and repair costs
- Motion based dumping
Jerry discussed the behaviour of flexible and rigid structures in terms of their response to external events, such as earthquakes and how the properties of these two types conflict with each other.
The best solution is to develop active control systems that respond to the excitation by altering the structures characteristics. They require a feedback loop which drives changes in the structure after each time step.
In conclusion, Jerry said that the key to motion control is the development of intelligent systems using control theory.
The next presentation was by Dr Paolo Zanetti, Director and founder of Envirocomp. The topic was on “Mathematical Methods in Air Pollution Studies”, starting by defining what constitutes air pollution and its different types.
Air drift of particles and industrial pollution cases are, in Paolo’s opinion, becoming more important.
Secondary pollution cases are difficult to define and to determine where they originate. They can be generated by a combination of primary pollutants. In these cases the use of computer models constitutes an essential tool.
Paolo then referred to the convenience in many cases of using single Guassian models although for complex cases the use of full Navier-Stokes models is the only way forward.
Air pollution studies require the use of accurate atmospheric models, which are of two types, ie Diagnostic and Prognostic.
He concentrated at the end of his presentation on the description of several important case studies, including industrial accidents, ammonia discharges, internal air pollution and a series of cases that went to litigation.
The final talk was by Professor Kapoor of Californian State University and Prof Ted Hromadka of West Point, who referred, through experimental and computational studies to the need to determine the range and applicability of computer models before accepting their validity.
They described the case of water in a channel which generated a hydraulic jump. Some computer models were unable to reproduce the phenomena, while others gave more accurate results.
A Panel Discussion took place at the end of the Colloquium. Colonel Doug McInvale who chaired the discussion, started by expressing the interest of the Academy in Computational Mathematics and the importance attached to the development of further capabilities in this area.
Following his remarks, a lively discussion took place at the end of which the speakers were congratulated for their presentations and thanked in the name of the Academy for having visited West Point.