The numerical solution of the 3D Helmholtz equation with optimal accuracy on irregular domains and unfitted Cartesian meshes

Engineering With Computers ◽

10.1007/s00366-021-01547-9 ◽

2021 ◽

Author(s):

A. Idesman ◽

B. Dey

Keyword(s):

Helmholtz Equation ◽

Numerical Solution ◽

Irregular Domains ◽

Cartesian Meshes ◽

Optimal Accuracy

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A new numerical approach to the solution of the 2-D Helmholtz equation with optimal accuracy on irregular domains and Cartesian meshes

Computational Mechanics ◽

10.1007/s00466-020-01814-4 ◽

2020 ◽

Vol 65 (4) ◽

pp. 1189-1204 ◽

Author(s):

A. Idesman ◽

B. Dey

Keyword(s):

Helmholtz Equation ◽

Numerical Approach ◽

Irregular Domains ◽

Cartesian Meshes ◽

Optimal Accuracy

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The treatment of the Neumann boundary conditions for a new numerical approach to the solution of PDEs with optimal accuracy on irregular domains and Cartesian meshes

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2020.112985 ◽

2020 ◽

Vol 365 ◽

pp. 112985 ◽

Author(s):

A. Idesman ◽

B. Dey

Keyword(s):

Boundary Conditions ◽

Neumann Boundary ◽

Numerical Approach ◽

Neumann Boundary Conditions ◽

Irregular Domains ◽

Cartesian Meshes ◽

Optimal Accuracy

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A new numerical approach to the solution of PDEs with optimal accuracy on irregular domains and Cartesian meshes—Part 1: the derivations for the wave, heat and Poisson equations in the 1-D and 2-D cases

Archive of Applied Mechanics ◽

10.1007/s00419-020-01744-w ◽

2020 ◽

Vol 90 (12) ◽

pp. 2621-2648 ◽

Author(s):

A. Idesman

Keyword(s):

Numerical Approach ◽

Irregular Domains ◽

Poisson Equations ◽

Cartesian Meshes ◽

Optimal Accuracy

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A new 3-D numerical approach to the solution of PDEs with optimal accuracy on irregular domains and Cartesian meshes

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2019.05.049 ◽

2019 ◽

Vol 354 ◽

pp. 568-592 ◽

Author(s):

A. Idesman ◽

B. Dey

Keyword(s):

Numerical Approach ◽

Irregular Domains ◽

Cartesian Meshes ◽

Optimal Accuracy

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A NEW NUMERICAL APPROACH TO THE SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS WITH OPTIMAL ACCURACY ON IRREGULAR DOMAINS AND CARTESIAN MESHES

Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2015) ◽

10.7712/120119.7021.18485 ◽

2019 ◽

Author(s):

Alexander Idesman

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Numerical Approach ◽

Irregular Domains ◽

Partial Differential ◽

Cartesian Meshes ◽

Optimal Accuracy

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A new numerical approach to the solution of PDEs with optimal accuracy on irregular domains and Cartesian meshes—part 2: numerical simulations and comparison with FEM

Archive of Applied Mechanics ◽

10.1007/s00419-020-01742-y ◽

2020 ◽

Vol 90 (12) ◽

pp. 2649-2674 ◽

Author(s):

B. Dey ◽

A. Idesman

Keyword(s):

Numerical Simulations ◽

Numerical Approach ◽

Irregular Domains ◽

Cartesian Meshes ◽

Optimal Accuracy

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Numerical solution of a generalized boundary value problem for the modified Helmholtz equation in two dimensions

Mathematics and Computers in Simulation ◽

10.1016/j.matcom.2021.05.013 ◽

2021 ◽

Author(s):

Olha Ivanyshyn Yaman ◽

Gazi Özdemir

Keyword(s):

Boundary Value Problem ◽

Helmholtz Equation ◽

Numerical Solution ◽

Boundary Value ◽

Two Dimensions ◽

Modified Helmholtz Equation

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Numerical solution of 3-D Neuman problem for scalar Helmholtz equation at the bodies of complex shapes

MMET 96 VIth International Conference on Mathematical Methods in Electromagnetic Theory Proceedings MMET-96 ◽

10.1109/mmet.1996.565728 ◽

2002 ◽

Author(s):

I. Lifanov ◽

I. Lifanov ◽

S. Novikov

Keyword(s):

Helmholtz Equation ◽

Numerical Solution ◽

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A direct numerical solution to a one-dimensional helmholtz equation

Journal of Computational Physics ◽

10.1016/0021-9991(69)90062-x ◽

1969 ◽

Vol 3 (4) ◽

pp. 544-546 ◽

Author(s):

James J O'brien

Keyword(s):

Helmholtz Equation ◽

Numerical Solution ◽

One Dimensional ◽

Direct Numerical Solution

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An efficient method for the numerical solution of Hammerstein mixed VF integral equations on 2D irregular domains

Applied Mathematics and Computation ◽

10.1016/j.amc.2018.10.003 ◽

2019 ◽

Vol 344-345 ◽

pp. 46-56 ◽

Author(s):

H. Laeli Dastjerdi ◽

M. Nili Ahmadabadi

Keyword(s):

Numerical Solution ◽

Integral Equations ◽

Efficient Method ◽

Irregular Domains

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