Exact Finite Difference Schemes for Solving Helmholtz Equation at any Wavenumber
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@Article{IJNAMB-2-91,
author = {C. Wen and T.-Z. Huang},
title = {Exact Finite Difference Schemes for Solving Helmholtz Equation at any Wavenumber},
journal = {International Journal of Numerical Analysis Modeling Series B},
year = {2011},
volume = {2},
number = {1},
pages = {91--108},
abstract = {In this study, we consider new finite difference schemes for solving the Helmholtz equation. Novel difference schemes which do not introduce truncation error are presented, consequently
the exact solution for the Helmholtz equation can be computed numerically. The most
important features of the new schemes are that while the resulting linear system has the same
simple structure as those derived from the standard central difference method, the technique is
capable of solving Helmholtz equation at any wavenumber without using a fine mesh. The proof
of the uniqueness for the discretized Helmholtz equation is reported. The power of this technique
is illustrated by comparing numerical solutions for solving one- and two-dimensional Helmholtz
equations using the standard second-order central finite difference and the novel finite difference
schemes.},
issn = {},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnamb/301.html}
}
TY - JOUR
T1 - Exact Finite Difference Schemes for Solving Helmholtz Equation at any Wavenumber
AU - C. Wen & T.-Z. Huang
JO - International Journal of Numerical Analysis Modeling Series B
VL - 1
SP - 91
EP - 108
PY - 2011
DA - 2011/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnamb/301.html
KW - Helmholtz equation
KW - wavenumber
KW - radiation boundary condition
KW - finite difference schemes
KW - exact numerical solution
AB - In this study, we consider new finite difference schemes for solving the Helmholtz equation. Novel difference schemes which do not introduce truncation error are presented, consequently
the exact solution for the Helmholtz equation can be computed numerically. The most
important features of the new schemes are that while the resulting linear system has the same
simple structure as those derived from the standard central difference method, the technique is
capable of solving Helmholtz equation at any wavenumber without using a fine mesh. The proof
of the uniqueness for the discretized Helmholtz equation is reported. The power of this technique
is illustrated by comparing numerical solutions for solving one- and two-dimensional Helmholtz
equations using the standard second-order central finite difference and the novel finite difference
schemes.
C. Wen and T.-Z. Huang. (2011). Exact Finite Difference Schemes for Solving Helmholtz Equation at any Wavenumber.
International Journal of Numerical Analysis Modeling Series B. 2 (1).
91-108.
doi:
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