| Application | Key Mathematics Areas |
| Large scale shock wave physics code development | hyperbolic (and other) differential equations, difference schemes and assorted numerical techniques, and material modeling and the mathematics of implementing material models in computer programs (More recently, because of our focus on massively parallel computers, computer science is becoming a more important component of this work.) |
| Material constitutive modeling and equation of state | partial differential equations, continuum mechanics, and statistical mechanics |
| Reliability and uncertainty of large scale physical simulations | statistics and optimization (Statistics is one of the most widely needed and applied areas of mathematical science at Sandia.) |
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