H-Index & Metrics Best Publications

H-Index & Metrics

Discipline name H-index Citations Publications World Ranking National Ranking
Mathematics D-index 36 Citations 7,363 135 World Ranking 1381 National Ranking 592

Research.com Recognitions

Awards & Achievements

2009 - SIAM Fellow For contributions to iterative methods for linear systems and numerical methods for partial differential equations.

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Algebra
  • Partial differential equation

Thomas A. Manteuffel spends much of his time researching Applied mathematics, Mathematical analysis, Multigrid method, Partial differential equation and Finite element method. His work carried out in the field of Applied mathematics brings together such families of science as Linear system and Iterative method, Numerical analysis, Eigenvalues and eigenvectors, Algebra. He interconnects Least squares and Pure mathematics in the investigation of issues within Mathematical analysis.

His Multigrid method research integrates issues from Algebraic equation and Mathematical optimization. The various areas that Thomas A. Manteuffel examines in his Partial differential equation study include Boundary value problem and Differential equation. The study incorporates disciplines such as Discretization, Norm and Elliptic partial differential equation in addition to Finite element method.

His most cited work include:

  • First-order system least squares for second-order partial differential equations: part I (316 citations)
  • An incomplete factorization technique for positive definite linear systems (306 citations)
  • The Tchebychev iteration for nonsymmetric linear systems (253 citations)

What are the main themes of his work throughout his whole career to date?

His primary scientific interests are in Multigrid method, Mathematical analysis, Applied mathematics, Finite element method and Linear system. His Multigrid method research entails a greater understanding of Partial differential equation. His studies deal with areas such as Positive-definite matrix, Domain decomposition methods and Iterative method, Mathematical optimization, Conjugate gradient method as well as Applied mathematics.

In his study, Discrete mathematics is inextricably linked to Eigenvalues and eigenvectors, which falls within the broad field of Iterative method. His Finite element method research is multidisciplinary, incorporating perspectives in Conservation of mass, Navier–Stokes equations, Norm and Least squares. Thomas A. Manteuffel has included themes like Reduction and Relaxation in his Linear system study.

He most often published in these fields:

  • Multigrid method (47.65%)
  • Mathematical analysis (37.65%)
  • Applied mathematics (35.29%)

What were the highlights of his more recent work (between 2016-2021)?

  • Multigrid method (47.65%)
  • Applied mathematics (35.29%)
  • Linear system (21.76%)

In recent papers he was focusing on the following fields of study:

Multigrid method, Applied mathematics, Linear system, Finite element method and Solver are his primary areas of study. The Multigrid method study combines topics in areas such as Geometry, Numerical analysis, Reduction and Library science. His Applied mathematics research is multidisciplinary, relying on both Unit cube, Plane, Partial differential equation and Ideal.

His Finite element method research includes elements of Computational fluid dynamics, Data mining, Least squares and Noise. The concepts of his Solver study are interwoven with issues in Polygon mesh and Discretization, Polynomial, Mathematical analysis, Parallel transport. His research in Discretization intersects with topics in Positive-definite matrix and Iterative method.

Between 2016 and 2021, his most popular works were:

  • Multigrid Reduction in Time for Nonlinear Parabolic Problems: A Case Study (31 citations)
  • Nonsymmetric Algebraic Multigrid Based on Local Approximate Ideal Restriction ($ll$AIR) (19 citations)
  • Nonsymmetric Reduction-Based Algebraic Multigrid (17 citations)

In his most recent research, the most cited papers focused on:

  • Mathematical analysis
  • Algebra
  • Geometry

Thomas A. Manteuffel mainly investigates Multigrid method, Applied mathematics, Linear system, Reduction and Solver. His Applied mathematics study combines topics in areas such as Ideal, Finite element method, Numerical analysis, Least squares and Scaling. His Linear system research is multidisciplinary, relying on both Discrete mathematics, Directed graph and Laplace operator.

His research investigates the connection with Reduction and areas like Supercomputer which intersect with concerns in Algorithm. His Solver study combines topics in areas such as Discretization, Elliptic pdes, Algebraic number and Positive-definite matrix. His study in Discretization is interdisciplinary in nature, drawing from both Iterative method and Partial differential equation.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

An incomplete factorization technique for positive definite linear systems

T. A. Manteuffel.
Mathematics of Computation (1980)

547 Citations

The Tchebychev iteration for nonsymmetric linear systems

Thomas A. Manteuffel.
Numerische Mathematik (1977)

457 Citations

Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method

Vance Faber;Thomas Manteuffel.
SIAM Journal on Numerical Analysis (1984)

446 Citations

First-order system least squares for second-order partial differential equations: part I

Z. Cai;R. Lazarov;T. A. Manteuffel;S. F. McCormick.
SIAM Journal on Numerical Analysis (1994)

429 Citations

A taxonomy for conjugate gradient methods

Steven F. Ashby;Thomas A. Manteuffel;Paul E. Saylor.
SIAM Journal on Numerical Analysis (1990)

387 Citations

Algebraic Multigrid Based on Element Interpolation (AMGe)

M. Brezina;A. J. Cleary;R. D. Falgout;V. E. Henson.
SIAM Journal on Scientific Computing (2000)

313 Citations

The numerical solution of second-order boundary value problems on nonuniform meshes

Thomas A Manteuffel;Andrew B White.
Mathematics of Computation (1986)

238 Citations

Robustness and Scalability of Algebraic Multigrid

Andrew J. Cleary;Robert D. Falgout;Van Emden Henson;Jim E. Jones.
SIAM Journal on Scientific Computing (1999)

237 Citations

First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

Z. Cai;T. A. Manteuffel;S. F. McCormick.
SIAM Journal on Numerical Analysis (1997)

230 Citations

Adaptive procedure for estimating parameters for the nonsymmetric Tchebychev iteration

Thomas A. Manteuffel.
Numerische Mathematik (1978)

221 Citations

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