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

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

Research Staff

William Anderson: reduced order modeling, scientific machine learning, data-driven methods, numerical PDEs

Siu Wun (Tony) Cheung: finite element methods, reduced order modeling, multi-scale methods, and scientific machine learning

Youngsoo Choi: model order reduction, surrogate modeling, mathematical optimization, numerical linear algebra, numerical PDEs, machine learning, multidisciplinary design optimization, and quantum computing

Kevin Chung: reduced order modeling, scientific machine learning, optimization, optimal flow control, chaotic turbulent flow, uncertainty quantification, plasma physics

Rob Falgout: multilevel methods, parallel computing

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

Youngkyu Kim

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

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

Wayne Mitchell: multigrid algorithms, linear solvers, and algorithms for massively parallel high performance computing

Daniel Osei-Kuffuor: linear algebra and sparse matrix computations, numerical analysis and HPC, iterative solvers and preconditioners, variable precision computing, scalable algorithms for electronic structure calculations, performance portable scientific software design

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

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