How much complexity is too much you should

How much complexity is too much? “you should try to make things as simple as possible, but not too simple” A. Einstein “All modeling is a gross simplification of the real system. ” G. Whelan “Don’t work any harder than you have to. ” K. Castleton

Talking Points • Who is Karl Castleton and “What does he do? ” • The ADVECTIVE, DISPERSIVE, and DECAY equation. • Intuition about the system • Intuition about the equation • Semi-Analytical techniques • Numerical techniques • Conclusions

Who is Karl Castleton • Mesa State Graduate: A. A. S. 1987, B. S. 1992 Computer Science and Mathematics • Washington State University: M. S. Computer Science 1997 • Works at Pacific Northwest National Laboratory • Master Project solved the advective, dispersive, decay equation by three different methods

The “Equation” • Used in Civil Engineering, Environmental, Pharmaceutical, System Biological modeling • Is a partial differential equation • A number of analytical solutions for simplified cases • Flow, spreading, and degrading

Intuition about the system Dz Uy Ux Dx C Ux Uy Dx Dz

Intuition about the equation • • Plug flow Spreading in three dimensions Degradation, decay within the cell Simplification can yield analytical results

Semi-Analytical Techniques • Take the mathematics as far as it can go and then use a computer to put you over the top. • Reduce the model to a system that has an analytical result for instantaneous release. • Convolute the instantaneous release with input forcing function.

Numerical Techniques • • • Just implement the equation “Easy” to implement Code can be very close to equation Can consume a lot of computer resources Does allow for a variety of values

Conclusion • There are many ways to solve a modeling question • Use no more or less than you need • Do not always use the same tool/technique • Do not work any harder than you have to.