Computational materials science and engineering uses modeling, simulation, theory, and informatics to understand materials. The main goals include discovering new materials, determining material behavior and mechanisms, explaining experiments, and exploring materials theories. It is analogous to computational chemistry and computational biology as an increasingly important subfield of materials science.

Just as materials science spans all length scales, from electrons to components, so do its computational sub-disciplines. While many methods and variations have been and continue to be developed, seven main simulation techniques, or motifs, have emerged.

These computer simulation methods use underlying models and approximations to understand material behavior in more complex scenarios than pure theory generally allows and with more detail and precision than is often possible from experiments. Each method can be used independently to predict materials properties and mechanisms, to feed information to other simulation methods run separately or concurrently, or to directly compare or contrast with experimental results.

One notable sub-field of computational materials science is integrated computational materials engineering (ICME), which seeks to use computational results and methods in conjunction with experiments, with a focus on industrial and commercial application. Major current themes in the field include uncertainty quantification and propagation throughout simulations for eventual decision making, data infrastructure for sharing simulation inputs and results, high-throughput materials design and discovery, and new approaches given significant increases in computing power and the continuing history of supercomputing.

Electronic structure methods solve the Schrödinger equation to calculate the energy of a system of electrons and atoms, the fundamental units of condensed matter. Many variations of electronic structure methods exist of varying computational complexity, with a range of trade-offs between speed and accuracy.

Due to its balance of computational cost and predictive capability density functional theory (DFT) has the most significant use in materials science. DFT most often refers to the calculation of the lowest energy state of the system; however, molecular dynamics (atomic motion through time) can be run with DFT computing forces between atoms.

While DFT and many other electronic structures methods are described as ab initio, there are still approximations and inputs. Within DFT there are increasingly complex, accurate, and slow approximations underlying the simulation because the exact exchange-correlation functional is not known. The simplest model is the Local-density approximation (LDA), becoming more complex with the generalized-gradient approximation (GGA) and beyond. An additional common approximation is to use a pseudopotential in place of core electrons, significantly speeding up simulations.

This section discusses the two major atomic simulation methods in materials science. Other particle-based methods include material point method and particle-in-cell, most often used for solid mechanics and plasma physics, respectively.