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2019•DEStech Transactions on Environment Energy and Earth ScienceRequires access

21-point Finite-difference Modeling for the Helmholtz Equation

Dongsheng Cheng, Jian-jun CHEN, Baowen Chen

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Abstract

In this paper, we propose a 21-point finite-difference method for solving numerically the Helmholtz equation in 2-dimensional domain, which is a second order scheme. To discretize the Laplacian and the term of zeroth order, a weighted derivative and linear combination of the 21 points are employed respectively, with the weight parameters are determined by minimizing the numerical dispersion. Numerical simulations show that the method is more efficiency than 9-point schemes.

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What this paper is about

In this paper, we propose a 21-point finite-difference method for solving numerically the Helmholtz equation in 2-dimensional domain, which is a second order scheme. To discretize the Laplacian and the term of zeroth order, a weighted derivative and linear combination of the 21 points are employed respectively, with the weight parameters are determined by minimizing the numerical dispersion. Numerical simulations show that the method is more efficiency than 9-point schemes.

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Available abstract

In this paper, we propose a 21-point finite-difference method for solving numerically the Helmholtz equation in 2-dimensional domain, which is a second order scheme. To discretize the Laplacian and the term of zeroth order, a weighted derivative and linear combination of the 21 points are employed respectively, with the weight parameters are determined by minimizing the numerical dispersion. Numerical simulations show that the method is more efficiency than 9-point schemes.

Key concepts: Discretization, Helmholtz equation, Mathematics, Finite difference, Finite difference method, Mathematical analysis, Finite difference coefficient, Helmholtz free energy

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