For contributions to numerical solution of differential equations and numerical software.

For contributions to the application of mathematics in incompressible flow, thin films, image processing, and swarming.

For advances in finite element and multigrid methods for the numerical solution of partial differential equations.

For developing the foundations of the modern theory of Runge-Kutta methods.

For contributions to analysis and algorithms for differential algebraic equations.

For contributions to numerical analysis and image processing, and for service to the mathematical community.

For contributions to the mathematical analysis of nonlinear partial differential equations, fluid dynamics, and turbulence.

For contributions to the theory and applications of nonlinear optimization.

For contributions to sparse matrix computations.

For contributions to stochastics and control.

For contributions to numerical analysis and multiscale modeling.

For contributions to the development and analysis of algorithms for sparse matrix problems.

For contributions in computational science and engineering, especially parallel computing.

For contributions to network flows, integer programming, and combinatorial algorithms.

For contributions to stochastic modeling, spectral elements, and fluid mechanics.

For contributions to wave propagation, nonlinear dynamics, optical fibers and waveguides, and computational neuroscience.

For research contributions in chemical engineering, applied mathematics, and the computational sciences.

For advances in hyperbolic conservation laws and the study of shock waves.

For contribution to numerical analysis and scientific computing, particularly for conservation laws.

For contributions to systems and control.

For contributions to numerical partial differential equations, especially multigrid and first-order system least-squares methods.

For contributions to theory and applications of linear algebra.

For contributions to the theory and practice of continuous optimization.

For contributions in numerical linear algebra and its applications.

For contributions to the mathematics of inverse problems and for advancing the application of mathematics in industry.

For contributions to parallel and high performance computing, and algorithms for matrix computations.

For the development of new methods in computational combustion and their application to problems involving hydrocarbon chemistry.

For contributions to numerical linear algebra, optimization, and model reduction.

For contributions to the analysis of inverse problems and partial differential equations.

For contributions to the theory of elasticity and to developmental biology, and for outstanding service to the mathematical sciences.

For contributions to the analysis and applications of nonlinear waves.

For contributions to the theory of domain decomposition methods.

*Deceased