In principle, all materials science problems are easy to solve. One describes the system using quantum mechanical wave functions, solves the Schrödinger equation using the appropriate boundary conditions, and converts the result into the microscopic and/or macroscopic observables of interest. Unfortunately, carrying out this program is usually many orders of magnitude too difficult. As a result, various approximations and simplifications are introduced to obtain descriptions having the minimum complexity to describe a given class of phenomena. (A simple example is the treatment of lattice vibrations in solids using a ball-and-spring description.) Such a simplified description is called a model.
Due to the complexity of virtually all problems concerning materials, it is fair to say that the use of models is ubiquitous in materials science. In many situations, however, models sufficiently complex to describe the phenomena of interest are too difficult to be solved analytically. The computer has played an essential role in obtaining descriptions of material behavior based on such complex models. Traditionally, the amount of computer power available has restricted such models to idealized problems, which are then used as prototypes for the actual problems. Recently, however, the role of modeling has expanded to include treatment of specific and realistic materials problems. Development of these new classes of applications has been driven by the tremendous increase in computer power which has become available to the average researcher. The increase in computer capacity has catalyzed implementation of more realistic descriptions of material response.