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

A. Idesman

doi:10.1007/s00419-020-01744-w

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 ◽

Cited By ~ 1

Author(s):

A. Idesman

Keyword(s):

Numerical Approach ◽

Irregular Domains ◽

Poisson Equations ◽

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 ◽

Cited By ~ 3

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 ◽

Cited By ~ 2

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 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 ◽

Cited By ~ 7

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 ◽

Cited By ~ 1

Author(s):

B. Dey ◽

A. Idesman

Keyword(s):

Numerical Simulations ◽

Numerical Approach ◽

Irregular Domains ◽

Cartesian Meshes ◽

Optimal Accuracy

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A high-order numerical approach with Cartesian meshes for modeling of wave propagation and heat transfer on irregular domains with inhomogeneous materials

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2020.113249 ◽

2020 ◽

Vol 370 ◽

pp. 113249

Author(s):

A. Idesman ◽

B. Dey

Keyword(s):

Heat Transfer ◽

Wave Propagation ◽

Numerical Approach ◽

High Order ◽

Inhomogeneous Materials ◽

Irregular Domains ◽

Cartesian Meshes

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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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Poisson equations in irregular domains with Robin boundary conditions — Solver with second-order accurate gradients

Journal of Computational Physics ◽

10.1016/j.jcp.2018.03.022 ◽

2018 ◽

Vol 365 ◽

pp. 1-6 ◽

Cited By ~ 7

Author(s):

Victoria Arias ◽

Daniil Bochkov ◽

Frederic Gibou

Keyword(s):

Boundary Conditions ◽

Second Order ◽

Robin Boundary Conditions ◽

Irregular Domains ◽

Poisson Equations ◽

Robin Boundary

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A high-order immersed interface method free of derivative jump conditions for Poisson equations on irregular domains

Journal of Computational Physics ◽

10.1016/j.jcp.2020.109791 ◽

2020 ◽

Vol 423 ◽

pp. 109791

Author(s):

Marilaine Colnago ◽

Wallace Casaca ◽

Leandro Franco de Souza

Keyword(s):

High Order ◽

Jump Conditions ◽

Irregular Domains ◽

Immersed Interface Method ◽

Immersed Interface ◽

Poisson Equations

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The Fast 3D Immersed Interface Method for Poisson Equations on Irregular Domains

International Journal of Applied Science and Technology ◽

10.30845/ijast.v10n3p1 ◽

2020 ◽

Vol 10 (3) ◽

Author(s):

Elgaddafi Elamami

Keyword(s):

Irregular Domains ◽

Immersed Interface Method ◽

Immersed Interface ◽

Poisson Equations

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