Most approaches involve discrete algebraic analogs.
Some of our work is aimed at devising new iterative schemes, such as domain decomposition and multilevel techniques, for solving large linear or nonlinear systems. Other types of questions also arise. Because the work is so multifaceted, it requires broad training in numerical analysis, differential equations, classical analysis, and advanced linear algebra, as well as knowldege of continuum mechanics, stochastic processes, and large-scale computing.