TY  - JOUR
KW  - Helmholtz equation
KW  -  finite element method
KW  -  coercive variational formulation
KW  - 
pollution effect
KW  -  wavenumber-explicit analysis
KW  -  GMRES
AV  - public
JF  - Journal of Computational and Applied Mathematics
SN  - 1879-1778
SP  - 110
ID  - discovery10071583
N2  - A new, coercive formulation of the Helmholtz equation was introduced in [1]. In this paper we
investigate h-version Galerkin discretisations of this formulation, and the iterative solution of the
resulting linear systems. We find that the coercive formulation behaves similarly to the standard
formulation in terms of the pollution effect (i.e. to maintain accuracy as k ? ?, h must decrease
with k at the same rate as for the standard formulation). We prove k-explicit bounds on the
number of GMRES iterations required to solve the linear system of the new formulation when it
is preconditioned with a prescribed symmetric positive-definite matrix. Even though the number
of iterations grows with k, these are the first such rigorous bounds on the number of GMRES
iterations for a preconditioned formulation of the Helmholtz equation, where the preconditioner is
a symmetric positive-definite matrix.
EP  - 131
A1  - Diwan, GC
A1  - Moiola, A
A1  - Spence, EA
UR  - https://doi.org/10.1016/j.cam.2018.11.035
VL  - 352
Y1  - 2019/05/15/
TI  - Can coercive formulations lead to fast and accurate solution of the Helmholtz equation?
PB  - ELSEVIER SCIENCE BV
N1  - This version is the author accepted manuscript. For information on re-use, please refer to the publisher?s terms and conditions.
ER  -