Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number | Zendy

Hafiz Abdul Wajid | Zendy; Naseer Ahmed | Zendy; Hifza Iqbal | Zendy; Muhammad Sarmad Arshad | Zendy

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Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number

Author(s) -

Hafiz Abdul Wajid,

Naseer Ahmed,

Hifza Iqbal,

Muhammad Sarmad Arshad

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/673106

Subject(s) - helmholtz equation , finite difference , mathematics , finite difference method , helmholtz free energy , finite difference coefficient , grid , wave equation , mathematical analysis , finite difference scheme , compact finite difference , boundary (topology) , boundary value problem , finite element method , geometry , mixed finite element method , physics , quantum mechanics , thermodynamics

We construct modified forward, backward, and central finite difference schemes, specifically for the Helmholtz equation, by using the Bloch wave property. All of these modified finite difference approximations provide exact solutions at the nodes of the uniform grid for the second derivative present in the Helmholtz equation and the first derivative in the radiation boundary conditions for wave propagation. The most important feature of the modified schemes is that they work for large as well as low wave numbers, without the common requirement of a very fine mesh size. The superiority of the modified finite difference schemes is illustrated with the help of numerical examples by making a comparison with standard finite difference schemes

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