A highly-accurate finite element method with exponentially compressed meshes for the solution of the Dirichlet problem of the generalized Helmholtz equation with corner singularities

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2019.04.004 ◽

2019 ◽

Vol 361 ◽

pp. 227-235 ◽

Cited By ~ 2

Author(s):

Emine Celiker ◽

Ping Lin

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Dirichlet Problem ◽

Helmholtz Equation ◽

Corner Singularities ◽

Element Method

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A Generalized Finite Element Method for solving the Helmholtz equation in two dimensions with minimal pollution

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/0045-7825(95)00890-x ◽

1995 ◽

Vol 128 (3-4) ◽

pp. 325-359 ◽

Cited By ~ 260

Author(s):

Ivo Babuška ◽

Frank Ihlenburg ◽

Ellen T. Paik ◽

Stefan A. Sauter

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Helmholtz Equation ◽

Two Dimensions ◽

Generalized Finite Element Method ◽

Generalized Finite Element ◽

Element Method

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Finite Element Method and its Analysis for a Nonlinear Helmholtz Equation with High Wave Numbers

SIAM Journal on Numerical Analysis ◽

10.1137/17m111314x ◽

2018 ◽

Vol 56 (3) ◽

pp. 1338-1359 ◽

Cited By ~ 1

Author(s):

Haijun Wu ◽

Jun Zou

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Helmholtz Equation ◽

High Wave ◽

Its Analysis ◽

Wave Numbers ◽

Element Method

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A weak Galerkin mixed finite element method for the Helmholtz equation with large wave numbers

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22242 ◽

2018 ◽

Vol 34 (3) ◽

pp. 1009-1032 ◽

Cited By ~ 7

Author(s):

Ruishu Wang ◽

Xiaoshen Wang ◽

Qilong Zhai ◽

Kai Zhang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Helmholtz Equation ◽

Mixed Finite Element ◽

Mixed Finite Element Method ◽

Weak Galerkin ◽

Large Wave ◽

Wave Numbers ◽

Element Method

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Preconditionning Techniques for the Solution of the Helmholtz Equation by the Finite Element Method

Computational Science and Its Applications — ICCSA 2003 - Lecture Notes in Computer Science ◽

10.1007/3-540-44843-8_92 ◽

2003 ◽

pp. 847-858

Author(s):

Riyad Kechroud ◽

Azzeddine Soulaimani ◽

Yousef Saad

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Helmholtz Equation ◽

The Finite Element Method ◽

Element Method

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L 2 estimates for the finite element method for the Dirichlet problem with singular data

Numerische Mathematik ◽

10.1007/bf01389461 ◽

1985 ◽

Vol 47 (4) ◽

pp. 627-632 ◽

Cited By ~ 47

Author(s):

Eduardo Casas

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Dirichlet Problem ◽

The Finite Element Method ◽

Singular Data ◽

Element Method

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A smoothed finite element method for exterior Helmholtz equation in two dimensions

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2017.09.006 ◽

2017 ◽

Vol 84 ◽

pp. 237-252 ◽

Cited By ~ 24

Author(s):

Yingbin Chai ◽

Zhixiong Gong ◽

Wei Li ◽

Tianyun Li ◽

Qifan Zhang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Helmholtz Equation ◽

Two Dimensions ◽

Smoothed Finite Element Method ◽

Element Method

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A mixed finite element method for a nonlinear Dirichlet problem

IMA Journal of Numerical Analysis ◽

10.1093/imanum/18.1.121 ◽

1998 ◽

Vol 18 (1) ◽

pp. 121-132 ◽

Cited By ~ 25

Author(s):

M Farhloul

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Dirichlet Problem ◽

Mixed Finite Element ◽

Mixed Finite Element Method ◽

Nonlinear Dirichlet Problem ◽

Element Method

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The generalized finite element method for Helmholtz equation: Theory, computation, and open problems

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2005.09.019 ◽

2006 ◽

Vol 195 (37-40) ◽

pp. 4711-4731 ◽

Cited By ~ 123

Author(s):

Theofanis Strouboulis ◽

Ivo Babuška ◽

Realino Hidajat

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Helmholtz Equation ◽

Generalized Finite Element Method ◽

Open Problems ◽

Generalized Finite Element ◽

Element Method

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A two-level finite element method and its application to the Helmholtz equation

International Journal for Numerical Methods in Engineering ◽

10.1002/(sici)1097-0207(19980915)43:1<23::aid-nme383>3.0.co;2-n ◽

1998 ◽

Vol 43 (1) ◽

pp. 23-32 ◽

Cited By ~ 41

Author(s):

Leopoldo P. Franca ◽

Antonini P. Macedo

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Helmholtz Equation ◽

Element Method

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Implementation of the Finite Element Method with Optimal Choice of Basic Functions for Dirichlet Problem for Poisson Equation

Journal of Automation and Information Sciences ◽

10.1615/jautomatinfscien.v47.i9.50 ◽

2015 ◽

Vol 47 (9) ◽

pp. 42-62

Author(s):

Oleg N. Lytvyn ◽

Konstantin V. Nosov ◽

Tatyana A. Baranova

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Dirichlet Problem ◽

Poisson Equation ◽

Optimal Choice ◽

The Finite Element Method ◽

Basic Functions ◽

Element Method

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