Publications in VIVO

Co-author Network

McCormick, Steve

Professor Emerita/Emeritus

Positions

Professor Emerita/Emeritus, Applied Mathematics

Research Areas

Applied Mathematics

Research

keywords

Multilevel methods, partial differential equations, integral equations, computational fluid dynamics, adaptive mesh refinement methods, iterative schemes in general, least squares problems, eigenvalue problems, image reconstruction, human organ simulation, math software, vector and parallel supercomputing, inverse problems, particle transport, structural analysis, plasma physics, combustion, quantum chromdynamics

Publications

selected publications

book
- A Multigrid Tutorial 2000
- A Multigrid Tutorial, Second Edition 2000
- Optimization in solving elliptic problems 1996
- Multilevel Projection Methods for Partial Differential Equations 1992
- Multilevel Adaptive Methods for Partial Differential Equations 1989
- Multigrid methods. Ed. 110. 1988
- Multigrid Methods 1987
chapter
- Adaptive Smoothed Aggregation in Lattice QCD. 505-512. 2007
- Spectral Element Agglomerate AMGe. 513-521. 2007
- Parallel Multigrid Methods. Icase Larc Interdisciplinary Series in Science and Engineering. 203-224. 1997
- Multilevel projection methods for partial differential equations. 287-292. 1993
- Finite volume element and multilevel adaptive methods. 539-553. 1992
- Multilevel adaptive methods for Eagle code. 687-701. 1991
- Multilevel adaptive methods for the Eagle code 1991
- Iterative solution of elliptic equations with refinement: the model multi-level case. 93-102. 1989
- Iterative solution of elliptic equations with refinement: the two-level case. 81-92. 1989
- Multigrid, the rotated hybrid scheme and the fast adaptive composite grid method for planar cavity flow. 125-132. 1989
- Applications of the fast adaptive composite grid method. 251-265. 1988
- Applications of the fast adaptive composite grid method 1988
- Multigrid methods on a hypercube. 63-83. 1988
- Multigrid methods on a hypercube 1988
- Multigrid, elliptic grid generation and the fast adaptive composite grid method for solving transonic potential flow equations. 365-387. 1988
- Multigrid, elliptic grid generation and the fast adaptive composite grid method for solving transonic potential flow equations 1988
- Variational multigrid theory. 131-177. 1987
- A variational theory for multilevel adaptive techniques (MLAT) 1985
- A variational theory for multilevel adaptive techniques (MLAT). 225-230. 1985
- Algebraic multigrid (AMG) for sparse matrix equations. 257-284. 1985
- Algebraic multigrid (AMG) for sparse matrix equations 1985
- Fast Adaptive Composite Grid (FAC) Methods: Theory for the Variational Case. 115-121. 1984
- Fast adaptive composite grid (FAC) methods: theory for the variational case 1984
- Discrete correction methods for operator equations. 30-97. 1981
- Mesh refinement methods for integral equations. 183-190. 1980
- A revised mesh refinement strategy for Newton’s method applied to nonlinear two-point boundary value problems. 15-23. 1978
conference proceeding
- A finite volume convergence theory for the fast adaptive composite grid methods. Applied Numerical Mathematics. 91-103. 1994
- Multilevel adaptive schemes and domain decomposition methods. 245-252. 1989
- Proceedings of the Fourth Copper Mountain Conference on Multigrid Methods. xii+438-xii+438. 1989
- Second Copper Mountain conference on multigrid methods. Applied Mathematics and Computation. 1-372. 1986
journal article
- ALGEBRAIC MULTIGRID DOMAIN AND RANGE DECOMPOSITION (AMG-DD/AMG-RD). SIAM Journal on Scientific Computing. S113-S136. 2015
- HYBRID FIRST-ORDER SYSTEM LEAST SQUARES FINITE ELEMENT METHODS WITH APPLICATION TO STOKES EQUATIONS. SIAM Journal on Numerical Analysis. 2214-2237. 2013
- Parallel adaptive mesh refinement for first-order system least squares. Numerical Linear Algebra with Applications. 343-366. 2012
- Relaxation-corrected bootstrap algebraic multigrid (rBAMG). Numerical Linear Algebra with Applications. 178-193. 2012
- [Introduction].. Revista Clínica Española. 1-2. 2011
- EFFICIENCY BASED ADAPTIVE LOCAL REFINEMENT FOR FIRST-ORDER SYSTEM LEAST-SQUARES FORMULATIONS. SIAM Journal on Scientific Computing. 1-24. 2011
- Adaptive Multigrid Algorithm for the Lattice Wilson-Dirac Operator. Physical Review Letters. 2010
- Finite element methods for quantum electrodynamics using a Helmholtz decomposition of the gauge field. Numerical Linear Algebra with Applications. 539-556. 2010
- Further results on error estimators for local refinement with first-order system least squares (FOSLS). Numerical Linear Algebra with Applications. 387-413. 2010
- Operator-based interpolation for bootstrap algebraic multigrid. Numerical Linear Algebra with Applications. 519-537. 2010
- ALGEBRAIC MULTIGRID FOR MARKOV CHAINS. SIAM Journal on Scientific Computing. 544-562. 2010
- FIRST-ORDER SYSTEM LEAST SQUARES FOR INCOMPRESSIBLE RESISTIVE MAGNETOHYDRODYNAMICS. SIAM Journal on Scientific Computing. 229-248. 2010
- LEAST-SQUARES FINITE ELEMENT METHODS FOR QUANTUM ELECTRODYNAMICS. SIAM Journal on Scientific Computing. 398-417. 2010
- NESTED ITERATION AND FIRST-ORDER SYSTEM LEAST SQUARES FOR INCOMPRESSIBLE, RESISTIVE MAGNETOHYDRODYNAMICS. SIAM Journal on Scientific Computing. 1506-1526. 2010
- SMOOTHED AGGREGATION MULTIGRID FOR MARKOV CHAINS. SIAM Journal on Scientific Computing. 40-61. 2010
- TOWARDS ADAPTIVE SMOOTHED AGGREGATION (αSA) FOR NONSYMMETRIC PROBLEMS. SIAM Journal on Scientific Computing. 14-39. 2010
- Weighted least-squares finite elements based on particle imaging velocimetry data. Journal of Computational Physics. 107-118. 2010
- ENHANCED MASS CONSERVATION IN LEAST-SQUARES METHODS FOR NAVIER-STOKES EQUATIONS. SIAM Journal on Scientific Computing. 2303-2321. 2009
- A generalized eigensolver based on smoothed aggregation (GES-SA) for initializing smoothed aggregation (SA) multigrid. Numerical Linear Algebra with Applications. 249-269. 2008
- Efficiency-based h- and hp-refinement strategies for finite element methods. Numerical Linear Algebra with Applications. 89-114. 2008
- MULTILEVEL ADAPTIVE AGGREGATION FOR MARKOV CHAINS, WITH APPLICATION TO WEB RANKING. SIAM Journal on Scientific Computing. 2235-2262. 2008
- An alternative least-squares formulation of the Navier-Stokes equations with improved mass conservation. Journal of Computational Physics. 994-1006. 2007
- Spatial multigrid for isotropic neutron transport. SIAM Journal on Scientific Computing. 1900-1917. 2007
- Adaptive reduction-based AMG. Numerical Linear Algebra with Applications. 599-620. 2006
- First-order system least squares for the Oseen equations. Numerical Linear Algebra with Applications. 523-542. 2006
- First-order system least-squares (FOSLS) for modeling blood flow. Medical Engineering and Physics. 495-503. 2006
- An energy-based AMG coarsening strategy. Numerical Linear Algebra with Applications. 133-148. 2006
- Adaptive algebraic multigrid. SIAM Journal on Scientific Computing. 1261-1286. 2006
- Extending the applicability of multigrid methods. Journal of Physics : Conference Series. 443-452. 2006
- First-order system least squares for geometrically nonlinear elasticity. SIAM Journal on Numerical Analysis. 2057-2081. 2006
- On mass-conserving least-squares methods. SIAM Journal on Scientific Computing. 1675-1693. 2006
- PROJECTION MULTILEVEL METHODS FOR QUASI-LINEAR PDES: V-CYCLE THEORY. SIAM: Multiscale Modeling and Simulation. 1339-1348. 2006
- Projection multilevel methods for quasilinear elliptic partial differential equations: Numerical results. SIAM Journal on Numerical Analysis. 120-138. 2006
- Projection multilevel methods for quasilinear elliptic partial differential equations: Theoretical results. SIAM Journal on Numerical Analysis. 139-152. 2006
- Adaptive smoothed aggregation (αSA) multigrid. SIAM Review. 317-346. 2005
- Algebraic multigrid for higher-order finite elements. Journal of Computational Physics. 520-532. 2005
- Analysis of first-order system least squares (FOSLS) for elliptic problems with discontinuous coefficients: Part I. SIAM Journal on Numerical Analysis. 386-408. 2005
- Analysis of first-order system least squares (FOSLS) for elliptic problems with discontinuous coefficients: Part II. SIAM Journal on Numerical Analysis. 409-436. 2005
- First-order system LL* (FOSLL*) for general scalar elliptic problems in the plane. SIAM Journal on Numerical Analysis. 2098-2120. 2005
- Numerical conservation properties of H(div)-conforming least-squares finite element methods for the Burgers equation. SIAM Journal on Scientific Computing. 1573-1597. 2005
- First-order system least squares (FOSLS) for coupled fluid-elastic problems. Journal of Computational Physics. 560-575. 2004
- A robust multilevel approach for minimizing H(div)-dominated functionals in an H-1-conforming finite element space. Numerical Linear Algebra with Applications. 115-140. 2004
- Adaptive smoothed aggregation (αSA). SIAM Journal on Scientific Computing. 1896-1920. 2004
- Asynchronous fast adaptive composite-grid methods for elliptic problems: Theoretical foundations. SIAM Journal on Numerical Analysis. 130-152. 2004
- First-order system least squares and electrical impedance tomography. SIAM Journal on Numerical Analysis. 461-483. 2004
- Least-squares finite element methods and algebraic multigrid solvers for linear hyperbolic PDEs. SIAM Journal on Scientific Computing. 31-54. 2004
- Improved discretization error estimates for first-order system least squares. East West Journal of Numerical Mathematics. 163-177. 2003
- Asynchronous fast adaptive composite-grid methods: Numerical results. SIAM Journal on Scientific Computing. 682-700. 2003
- Multilevel first-order system least squares for elliptic grid generation. SIAM Journal on Numerical Analysis. 2210-2232. 2003
- Multilevel first-order system least squares for nonlinear elliptic partial differential equations. SIAM Journal on Numerical Analysis. 2197-2209. 2003
- Spectral AMGe (ρAMGe). SIAM Journal on Scientific Computing. 1-26. 2003
- First-order system least squares for elastohydrodynamics with application to flow in compliant blood vessels.. Biomedical sciences instrumentation. 277-282. 2002
- First-order system LL (FOSLL*): Scalar elliptic partial differential equations. SIAM Journal on Numerical Analysis. 1418-1445. 2001
- First-order system least squares (FOSLS) for spatial linear elasticity: Pure traction. SIAM Journal on Numerical Analysis. 1454-1482. 2000
- A nonlinear multigrid solver for a semi-Lagrangian potential vorticity-based shallow-water model on the sphere. SIAM Journal on Scientific Computing. 2381-2395. 2000
- First-order system least squares for linear elasticity: Numerical results. SIAM Journal on Scientific Computing. 1706-1727. 2000
- First-order system least squares for the Stokes and linear elasticity equations: Further results. SIAM Journal on Scientific Computing. 1728-1739. 2000
- First-order system least-squares for the Helmholtz equation. SIAM Journal on Scientific Computing. 1927-1949. 2000
- Robustness and scalability of algebraic multigrid. SIAM Journal on Scientific Computing. 1886-1908. 2000
- Algebraic multigrid based on element interpolation (AMGE). SIAM Journal on Scientific Computing. 1570-1592. 2000
- Analysis of velocity-flux least-squares principles for the Navier-Stokes equations: Part II. SIAM Journal on Numerical Analysis. 1125-1144. 1999
- First-order system least squares (FOSLS) for convection-diffusion problems: Numerical results. SIAM Journal on Scientific Computing. 1958-1979. 1998
- Analysis of velocity-flux first-order system least-squares principles for the Navier-Stokes equations: Part I. SIAM Journal on Numerical Analysis. 990-1009. 1998
- First-order system least squares (FOSLS) for planar linear elasticity: Pure traction problem. SIAM Journal on Numerical Analysis. 320-335. 1998
- First-order system least squares for the Stokes equations, with application to linear elasticity. SIAM Journal on Numerical Analysis. 1727-1741. 1997
- Introduction 1997
- First-order system least squares for second-order partial differential equations .2.. SIAM Journal on Numerical Analysis. 425-454. 1997
- Multigrid Methods for Nearly Singular Linear Equations and Eigenvalue Problems. SIAM Journal on Numerical Analysis. 178-200. 1997
- Control-volume mixed finite element methods. Annals of Software Engineering. 289-315. 1997
- Local error estimates and adaptive refinement for first-order system least squares (FOSLS). Electronic Transactions on Numerical Analysis. 35-43 (electronic). 1997
- A fast multigrid algorithm for isotropic transport problems .2. With absorption. SIAM Journal on Scientific Computing. 1449-1474. 1996
- Multilevel image reconstruction with natural pixels. SIAM Journal on Scientific Computing. 193-216. 1996
- A global shallow-water numerical model based on the semi-Lagrangian advection of potential vorticity. Quarterly Journal of the Royal Meteorological Society. 1981-2005. 1995
- MULTILEVEL ADAPTIVE METHODS FOR SEMIIMPLICIT SOLUTION OF SHALLOW-WATER EQUATIONS ON A SPHERE. Monthly Weather Review. 2197-2205. 1995
- A FAST MULTIGRID ALGORITHM FOR ISOTROPIC TRANSPORT PROBLEMS .1. PURE SCATTERING. SIAM Journal on Scientific Computing. 601-635. 1995
- ACCURATE DISCRETIZATION FOR SINGULAR PERTURBATIONS - THE ONE-DIMENSIONAL CASE. SIAM Journal on Numerical Analysis. 83-109. 1995
- First-order system least squares for velocity-vorticity-pressure form of the Stokes equations, with application to linear elasticity. Electronic Transactions on Numerical Analysis. 150-159 (electronic). 1995
- 1ST-ORDER SYSTEM LEAST-SQUARES FOR 2ND-ORDER PARTIAL-DIFFERENTIAL EQUATIONS .1.. SIAM Journal on Numerical Analysis. 1785-1799. 1994
- MULTILEVEL ADAPTIVE METHODS FOR ELLIPTIC EIGENPROBLEMS - A 2-LEVEL CONVERGENCE THEORY. SIAM Journal on Numerical Analysis. 1731-1745. 1994
- Multilevel methods for temporal and spatial flow transition simulation in a rough channel. International Journal for Numerical Methods in Fluids. 23-40. 1994
- A PARALLEL VERSION OF A MULTIGRID ALGORITHM FOR ISOTROPIC TRANSPORT-EQUATIONS. SIAM Journal on Scientific Computing. 474-493. 1994
- Multigrid solution of a linearized, regularized least-squares problem in electrical impedance tomography. Inverse Problems. 697-713. 1993
- Multilevel adaptive methods for laminar diffusion flames. Journal of Scientific Computing. 341-355. 1993
- An efficient multigrid scheme for elliptic equations with discontinuous coefficients. Communications in Applied Numerical Methods. 621-631. 1992
- Multilevel adaptive methods for incompressible flow in grooved channels. Journal of Computational and Applied Mathematics. 283-295. 1991
- Multigrid methods for flow transition in a planar channel. Computer Physics Communications. 188-200. 1991
- The Finite Volume Element Method for Diffusion Equations on General Triangulations. SIAM Journal on Numerical Analysis. 392-402. 1991
- ON LOCAL REFINEMENT HIGHER ORDER METHODS FOR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS. International Journal of High Speed Computing. 311-334. 1990
- On the Accuracy of the Finite Volume Element Method for Diffusion Equations on Composite Grids. SIAM Journal on Numerical Analysis. 636-655. 1990
- Computational complexity of the fast adaptive composite grid (FAC) method. Applied Numerical Mathematics. 315-327. 1990
- The Realization Problem for a Class of Nonlinear Systems. SIAM Journal on Matrix Analysis and Applications. 113-127. 1990
- Asynchronous multilevel adaptive methods for solving partial differential equations on multiprocessors: Basic ideas. Parallel Computing. 131-144. 1989
- Asynchronous multilevel adaptive methods for solving partial differential equations on multiprocessors: Performance results. Parallel Computing. 145-156. 1989
- COMPUTATIONAL COMPLEXITY OF THE SCHWARZ ALTERNATING PROCEDURE. International Journal of High Speed Computing. 1-28. 1989
- A multilevel variational method for Au = λBu on composite grids. Journal of Computational Physics. 442-452. 1989
- An Algebraic Theory for Multigrid Methods for Variational Problems. SIAM Journal on Numerical Analysis. 91-110. 1988
- The fast adaptive composite-grid method (FAC): algorithms for advanced computers. Applied Mathematics and Computation. 103-125. 1986
- The Fast Adaptive Composite Grid (FAC) Method for Elliptic Equations. Mathematics of Computation. 439-439. 1986
- Multigrid Methods for Variational Problems: General Theory for the V-Cycle. SIAM Journal on Numerical Analysis. 634-643. 1985
- Multigrid Methods for Variational Problems: Further Results. SIAM Journal on Numerical Analysis. 255-263. 1984
- Unigrid for Multigrid Simulation. Mathematics of Computation. 43-43. 1983
- Multigrid Methods for Differential Eigenproblems. SIAM Journal on Scientific Computing. 244-260. 1983
- An adaptive differential-correction algorithm. Journal of Approximation Theory. 197-211. 1983
- Multigrid methods for variation problems: The V-cycle. Mathematics and Computers in Simulation. 63-65. 1983
- Discrete Defect Corrections: Basic Ideas. Journal of Applied Mathematics and Mechanics (ZAMM). 371-377. 1983
- Successive overrelaxation, multigrid, and preconditioned conjugate gradients algorithms for solving a diffusion problem on a vector computer. Applied Mathematics and Computation. 285-309. 1983
- Unigrid methods for boundary value problems with nonrectangular domains. Journal of Computational Physics. 412-422. 1982
- Multigrid Methods for Variational Problems. SIAM Journal on Numerical Analysis. 924-929. 1982
- Uniform rational approximation on large data sets. International Journal for Numerical Methods in Engineering. 1569-1575. 1982
- An Algebraic Interpretation of Multigrid Methods. SIAM Journal on Numerical Analysis. 548-560. 1982
- Evaluation of functions on microcomputers: ln (X). Computers and Mathematics with Applications. 389-392. 1982
- A Mesh Refinement Method for Ax = λBx. Mathematics of Computation. 485-485. 1981
- Evaluation of functions on microcomputers: exp(x). Computers and Mathematics with Applications. 503-508. 1981
- Simultaneous rayleigh-quotient minimization methods for Ax=λBx. Linear Algebra and Its Applications. 195-234. 1980
- A general mesh independence principle for Newton's method applied to second order boundary value problems. Computing. 233-246. 1979
- Evaluation of functions on microcomputers: rational approximation of kth roots. Computers and Mathematics with Applications. 163-167. 1979
- Evaluation of functions on microcomputers: square root. Computers and Mathematics with Applications. 359-367. 1978
- Newton’s method with mesh refinements for numerical solution of nonlinear two-point boundary value problems. Numerische Mathematik. 237-260. 1978
- Simultaneous iteration for the matrix eigenvalue problem. 43-56. 1977
- The methods of Kaczmarz and row orthogonalization for solving linear equations and least squares problems in Hilbert space. Indiana University Mathematics Journal. 1137-1150. 1977
- Some convergence results on the method of gradients for Ax=λBx. Journal of Computer and System Sciences. 213-222. 1976
- A uniform approach to gradient methods for linear operator equations. Journal of Mathematical Analysis and Applications. 275-285. 1975
- An iterative procedure for the solution of constrained nonlinear equations with application to optimization problems. Numerische Mathematik. 371-385. 1975
- A general approach to one-step iterative methods with application to eigenvalue problems. Journal of Computer and System Sciences. 354-372. 1972

Background

education and training

Ph.D., University of Southern California 1971
B.A., San Diego State University 1966

awards and honors

Fellow, conferred by Society for Industrial and Applied Mathematics, 2010

International Activities

geographic focus

New Zealand Country