The Mathematical Algorithms and Computing Group (MACG) conducts research and development of algorithms and software for solving linear and nonlinear systems, which are often obtained from approximations of partial differential equations and arise in numerous areas of science and engineering, including fluid dynamics, solid mechanics, combustion, elasticity, electromagnetics, large-scale data mining, and cybersecurity. Our customers are primarily scientists and engineers working in these fields. The algorithms we investigate include scalable algorithms, such as multigrid and multilevel methods. We also seek scalable spectral methods for extremely large graph matrices and rank-revealing decompositions of matrices in data mining applications. Our research includes the development of object-oriented code frameworks for the implementation of these algorithms on a wide range of serial and parallel architectures.

## Group Lead

Ulrike Meier Yang: iterative linear solvers, algebraic multigrid, parallel computing, scientific software, performance analysis

## Research Staff

Rob Falgout: multilevel methods, parallel computing

Alyson Fox: numerical linear algebra, graph Laplacian linear systems, algebraic multigrid solvers, error analysis of ZFP compression

Van Emden Henson: large scale graphs, dynamic graphs, hypergraphs, linear algebra and computational linear algebra applied to data analysis, eigenvalues and eigenvectors, spectral methods in data science, multigrid and algebraic multigrid methods

Christine Klymko: network analysis, numerical linear algebra, graph algorithms, data mining, scientific computing, numerical analysis, matrix analysis

Tim La Fond: network analysis, dynamic graph algorithms, data mining, anomaly detection

Ruipeng Li: sparse matrix computations, parallel computing, iterative methods for solving linear systems, preconditioning techniques, eigenvalue problems

Sarah Mackay: network science, combinatorial optimization, infrastructure simulations, group theory

Eisha Nathan: network analysis, graph algorithms, dynamic graphs, numerical linear algebra, data mining

Sarah Osborn: numerical linear algebra, numerical methods for partial differential equations, uncertainty quantification

Victor Paludetto Magri: preconditioning, multigrid methods, linear solvers, parallel computing

Colin Ponce: numerical linear algebra, algebraic multigrid, numerical methods for power grid analysis

Ben Priest: streaming and sketching algorithms, randomized linear algebra, massive graphs, distributed computing, scientific software

Geoffrey Sanders: algebraic multigrid, eigenspectra, multilinear (tensor) algebra, large-scale graphs

Bjorn Sjogreen: numerical methods for partial differential equations, wave propagation, computational seismology, compressible fluid flow, magnetohydrodynamics, high performance computing on GPUs, quantum computing

Panayot Vassilevski: numerical linear algebra, finite elements