For contributions to the finite element method.

For contributions in high-performance algorithms and streaming analytics, and for leadership in the field of computational science.

For contributions to numerical linear algebra, especially eigenvalue computation, and applications to computational science and engineering.

For contributions to robotics, the control of mechanical systems, and mathematical systems theory.

For fundamental contributions to applied mathematics algorithms in geometric modeling, imaging science, bioinformatics, and data visualization.

For pioneering contributions to integer programming.

For contributions to molecular photonics.

For contributions to multilevel iterative methods and adaptive numerical methods for partial differential equations.

For contributions to control and inverse problems for partial differential equations.

For significant and lasting contributions to inverse problems in wave phenomena and electromagnetics applied to optics.

For contributions to systems theory, stochastic control, and communication networks.

For contributions to mathematical physics.

For contributions to the cross-fertilization between industrial problems and advanced theory of partial differential equations.

For innovative combinations of analysis and computation to obtain fundamental insights into complex dynamics of spatially extended systems.

For contributions to dynamic game theory and application to robust control of systems with uncertainty.

For contributions to numerical methods for the partial differential equations of computational science.

For contributions to continuous optimization, both theory and applications, including the field of robust optimization.

For contributions to applied harmonic analysis, especially sampling theory and frames theory.

For contributions to numerical methods for optimal control and model reduction.

For contributions to stochastics and control.

For contributions to numerical linear algebra and its applications, especially sparse linear systems and preconditioning.

For the development of adaptive algorithms and software for partial differential equations.

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

For contributions to computational methods in optimal control and nonlinear programming with industrial applications.

For the design and creation of fast numerical algorithms and seminal theory for linearized inverse problems.

For contributions to mathematical aspects of materials science, especially the modeling of martensitic transformation and its consequences.

For contributions to mathematical statistics.

For contributions in large-scale nonlinear optimization theory and algorithms, particularly IPOPT, and their novel application to flowsheet optimization, process control, data reconciliation, and complex process applications.

For contributions to chemistry and engineering.

For contributions to numerical linear algebra, especially numerical methods for least squares problems.

For contributions to the dynamics and control of mechanical systems.

For contributions to establishing the fields of industrial and applied mathematics and for his service to those fields.

For contributions to analysis and algorithms for graphs and networks and computational complexity analysis of control problems.

For contributions to numerical partial differential equations, especially least-squares finite element methods, stabilized finite element methods, and software.

For fundamental contributions to nonlinear waves.

For contributions to the theory of splines and other problems related to the approximation of functions.

For the mathematical and computational study of wave propagation and imaging in random media.

For fundamental contributions to the development, teaching, and practice of optimization in engineering.

For multigrid theory and algorithms.

For contributions to differential equations, predator-prey systems and harvesting, mathematical epidemiology of infectious diseases, and applied mathematics education.

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

For contributions to algorithms, numerical analysis, and computational number theory.

For contributions to mathematical neuroscience and cell biology, with a particular focus on stochastic processes.

For fundamental contributions to the theory, development, and practice of finite element methods, including mixed, hybrid, discontinuous, and virtual element Galerkin methods.

For contributions to dynamics and control.

For contributions to linear algebra and combinatorics.

For contributions to signal processing, image analysis, and ant robotics.

For contributions to the theory of composite materials and the numerical simulation of wave phenomena.

For contributions to geometric control, distributed control, and network systems with application to robotic coordination, power grids, and social networks.

For contributions in numerical linear algebra, control theory, and model reduction.

For advances in martingale transforms and applications of probabilistic methods in analysis.

For contributions to control and approximation of partial differential equations.

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

For contributions to systems and control.