TY - JOUR
T1 - A Weighted Variational Formulation Based on Plane Wave Basis for Discretization of Helmholtz Equations
AU - Q. Hu & L. Yuan
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 587
EP - 607
PY - 2014
DA - 2014/11
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/543.html
KW - Helmholtz equations, wave basis functions, variational formulation, error estimate, preconditioner, iteration counts.
AB - <p style="text-align: justify;">In this paper we are concerned with numerical methods for solving Helmholtz equations. We propose a new variant of the Variational Theory of Complex Rays (VTCR) method
introduced in [15, 16]. The approximate solution generated by the new variant has higher accuracy
than that generated by the original VTCR method. Moreover, the accuracy of the resulting
approximate solution can be further increased by adding two suitable positive relaxation parameters
into the new variational formula. Besides, a simple domain decomposition preconditioner
is introduced for the system generated by the proposed variational formula. Numerical results
confirm the efficiency of the new method.</p>