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 cyber security. 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
Min 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