Many computer simulations require repetitive core computations that are not specific to the actual application. Efficient simulations require the design of numerical algorithms for these core computations that not only compute the desired quantities but also exploit the capabilities of the computers being used in the simulations.
A computer simulation is only as good as the mathematical models used for the computer description of the problem and the numerical algorithms used in the computations. Models involve variables, parameters, and relationships that may be fuzzy, deterministic, probabilistic, discrete, or continuous. Models must retain the significant behavior of the system but be simple enough to be used computationally. They must mimic the behavior of the given system within the context of the use of the model. Typically there is no theory to tell us whether or not a given model is adequate. Mathematical analysis and physical intuition play key roles in the reduction of complex models to feasible models which preserve the behavior necessary to answer whatever questions we want to ask.
In many cases, these models involve very large matrices, and the associated simulations require computations on these large matrices. Variants of eigenvalue algorithms which she developed together with colleagues at IBM and at the Max-Planck Institute at Garching, Germany, have been used inside of simulation codes in magnetohydrodynamics, molecular dynamics, genetics, electronic structures, and structural analysis, and in basic science studies in physics and chemistry.