NDLI: INTERNATIONAL JOURNAL OF c © 2011 Institute for Scientific NUMERICAL ANALYSIS AND MODELING, SERIES B Computing and Information Volume 2, Number 1, Pages 91–108 EXACT FINITE DIFFERENCE SCHEMES FOR SOLVING HELMHOLTZ EQUATION AT ANY WAVENUMBER

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INTERNATIONAL JOURNAL OF c © 2011 Institute for Scientific NUMERICAL ANALYSIS AND MODELING, SERIES B Computing and Information Volume 2, Number 1, Pages 91–108 EXACT FINITE DIFFERENCE SCHEMES FOR SOLVING HELMHOLTZ EQUATION AT ANY WAVENUMBER

Content Provider	CiteSeerX
Author	Li, Guangrui Shu, Yau
Abstract	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, conse-quently 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. Key words. Helmholtz equation, wavenumber, radiation boundary condition, finite difference schemes, exact numerical solution. 1.
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Access Restriction	Open
Subject Keyword	Novel Difference Scheme Novel Finite Difference Scheme Two-dimensional Helmholtz Equation Finite Difference Scheme Radiation Boundary Condition Exact Numerical Solution Scientific Numerical Analysis Modeling Truncation Error Discretized Helmholtz Equation Helmholtz Equation Standard Second-order Central Finite Difference Fine Mesh New Finite Difference Scheme Series Computing Standard Central Difference Method
Content Type	Text
Resource Type	Article

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