Professor Borggaard's research interests are in the general areas of numerical analysis and computational science/scientific computation.
In particular, he looks at optimization and control problems for systems described by partial differential equations. This includes numerical methods for approximating PDEs such as boundary element, finite difference and finite element methods; gradient-based optimization algorithms including efficient gradient computation (sensitivity analysis, automatic differentiation, etc.); and the interplay between these two processes. Sensitivity analysis has a number of practical applications, for instance, one can use it to propagate uncertainty through PDE simulations.
He is currently looking at modeling/sensitivity analysis for large-eddy simulation, using optimization to address optimal sensor/actuator placement in control problems, efficient computation of feedback control laws, optimization under noise and uncertainty, and reduced-order modeling.