Simulations of the Helmholtz equation at any wave number for adaptive grids using a modified central finite difference scheme | Zendy

Hafiz Abdul Wajid | Zendy

Open Access

Simulations of the Helmholtz equation at any wave number for adaptive grids using a modified central finite difference scheme

Author(s) -

Hafiz Abdul Wajid

Publication year - 2016

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1506-24

Subject(s) - mathematics , helmholtz equation , grid , scheme (mathematics) , finite difference , helmholtz free energy , finite difference scheme , wave equation , mathematical analysis , homogeneous , variety (cybernetics) , finite difference method , central differencing scheme , domain (mathematical analysis) , finite difference coefficient , finite element method , geometry , mixed finite element method , boundary value problem , physics , combinatorics , statistics , quantum mechanics , thermodynamics

In this paper, a modified central finite difference scheme for a three-point nonuniform grid is presented for the one-dimensional homogeneous Helmholtz equation using the Bloch wave property. The modified scheme provides highly accurate solutions at the nodes of the nonuniform grid for very small to very large range of wave numbers irrespective of how the grid is adapted throughout the domain. A variety of numerical examples are considered to validate the superiority of the modified scheme for a nonuniform grid over a standard central finite difference scheme.

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