Concepedia

Helmholtz Equation

The Helmholtz Equation is a second-order linear partial differential equation that governs the spatial distribution of time-harmonic acoustic waves in a homogeneous medium, derived from the wave equation by applying a Fourier transform in time and distinguished by its characterization of monochromatic wave propagation in boundary-value problems relevant to finite element acoustics and solutions via separation of variables.

3.3K

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5.6K

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1.8K

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Publications per year

2017–2026

574

Parents

Publications

3.3K

The partition of unity finite element method: Basic theory and applications

Jens Markus Melenk, Ivo Babuška · Computer Methods in Applied Mechanics and Engineering · 1996 · 3.4K citations

, , +13

THE PARTITION OF UNITY METHOD

Ivo Babuška, Jens Markus Melenk · International Journal for Numerical Methods in Engineering · 1997 · 2.3K citations

, , +13

Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods

Thomas J.R. Hughes · Computer Methods in Applied Mechanics and Engineering · 1995 · 1.8K citations · Full text

, , +13

Polar factorization and monotone rearrangement of vector‐valued functions

Yann Brenier · Communications on Pure and Applied Mathematics · 1991 · 1.7K citations

, , +8

The fast multipole method for the wave equation: a pedestrian prescription

Ronald R. Coifman, Vladimir Rokhlin, Stephen M. Wandzura · IEEE Antennas and Propagation Magazine · 1993 · 1.5K citations

, , +12

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Authors

5.6K

  1. PL
    Peijun Li

    Purdue University West Lafayette, United States

    21 publications · 821 citations

    19

    h-index

  2. ET
    Eli Turkel

    Tel Aviv University, Israel

    21 publications · 2K citations

    19

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  3. EA
    Euan A. Spence

    University of Bath, United Kingdom

    18 publications · 950 citations

    16

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  4. LM
    Liviu Marin

    University of Leeds, United Kingdom

    19 publications · 941 citations

    16

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  5. IB
    Ivo Babuška

    University of Maryland, College Park, United States

    15 publications · 8.7K citations

    15

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Institutions

1.8K

  1. Centre National de la Recherche Scientifique

    Paris, France

    32 h-index

    196 publications

    8.7K citations

  2. University of Delaware

    Newark, United States

    26 h-index

    54 publications

    2.9K citations

  3. Stanford University

    Stanford, United States

    25 h-index

    76 publications

    5.5K citations

  4. The University of Texas at Austin

    Austin, United States

    24 h-index

    50 publications

    8.9K citations

  5. Purdue University West Lafayette

    West Lafayette, United States

    22 h-index

    48 publications

    1.8K citations

  6. Tel Aviv University

    Tel Aviv, Israel

    22 h-index

    59 publications

    3.4K citations

  7. ETH Zurich

    Zurich, Switzerland

    21 h-index

    29 publications

    7.8K citations

  8. University of Minnesota

    Minneapolis, United States

    20 h-index

    31 publications

    1.2K citations

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Venues

  1. The Journal of the Acoustical Society of America

    JASA · 194 publications · 10.6K citations

    47

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  2. 44

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  3. 39

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  4. Journal of Computational Physics

    104 publications · 6.3K citations

    39

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  5. Inverse Problems

    70 publications · 3.2K citations

    33

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