TY - JOUR
T1 - A Solver for Helmholtz System Generated by the Discretization of Wave Shape Functions
AU - Yuan , Long
AU - Hu , Qiya
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 791
EP - 808
PY - 2013
DA - 2013/05
SN - 5
DO - http://doi.org/10.4208/aamm.12-m12142
UR - https://global-sci.org/intro/article_detail/aamm/96.html
KW - Helmholtz equation, ultra weak variational formulation, wave shape functions, preconditioner, iteration counts.
AB - <p style="text-align: justify;">An interesting discretization method for Helmholtz equations was
introduced in B. Després [1]. This method is based on the
ultra weak variational formulation (UWVF) and the wave shape
functions, which are exact solutions of the governing Helmholtz
equation. In this paper we are concerned with fast solver for the
system generated by the method in [1]. We propose a new
preconditioner for such system, which can be viewed as a combination
between a coarse solver and the block diagonal preconditioner
introduced in [13]. In our numerical experiments, this
preconditioner is applied to solve both two-dimensional and
three-dimensional Helmholtz equations, and the numerical results
illustrate that the new preconditioner is much more efficient than
the original block diagonal preconditioner.</p>