In this talk we discuss a class of problems in optimal design of subsurface remediation and flow control systems. The objective functions and constraints are constructed from PDE solvers for the flow and species transport equations. We show how to realize the problems with well-known production codes, how these codes and the underlying physics present obstacles to the optimization algorithms, and how sampling methods, in particular implicit filtering, can overcome these problems.
The objective functions and constraints in these problems are typically non-smooth in all the design parameters and discontinuous in some of them. We will discuss the physical reasons for these properties and how optimization methods can deal with them.