TY - JOUR
T1 - Compact Fourth-Order Finite Difference Schemes for Helmholtz Equation with High Wave Numbers
AU - Yiping Fu
JO - Journal of Computational Mathematics
VL - 1
SP - 98
EP - 111
PY - 2008
DA - 2008/02
SN - 26
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8613.html
KW - Helmholtz equation, Compact difference scheme, FFT algorithm, Convergence.
AB - <p style="text-align: justify;">In this paper, two fourth-order accurate compact difference schemes are presented for solving the Helmholtz equation in two space dimensions when the corresponding wave numbers are large. The main idea is to derive and to study a fourth-order accurate compact difference scheme whose leading truncation term, namely, the $\mathcal O(h^4)$ term, is independent of the wave number and the solution of the Helmholtz equation. The convergence property of the compact schemes are analyzed and the implementation of solving the resulting linear algebraic system based on a FFT approach is considered. Numerical results are presented, which support our theoretical predictions.</p>