Eigenvalue problems are a cornerstone of modern applied mathematics, arising in diverse fields from quantum mechanics to structural engineering. At their heart, these problems seek scalar values and ...

Optical systems employ a rich array of physical effects which are described by well-understood equations. However, for all but the simplest devices these equations are typically too complex to permit ...

Analysis and application of numerical methods for solving large systems of linear equations, which often represent the bottleneck when computing solutions to equations arising in fluid mechanics, ...

In his doctoral thesis, Michael Roop develops numerical methods that allow finding physically reliable approximate solutions to nonlinear differential equations used to model turbulence.