TY - GEN
T1 - Numerical investigation of the conditioning for plane wave discontinuous Galerkin methods
AU - Congreve, Scott
AU - Gedicke, Joscha
AU - Perugia, Ilaria
N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2019.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - We present a numerical study to investigate the conditioning of the plane wave discontinuous Galerkin discretization of the Helmholtz problem. We provide empirical evidence that the spectral condition number of the plane wave basis on a single element depends algebraically on the mesh size and the wave number, and exponentially on the number of plane wave directions; we also test its dependence on the element shape. We show that the conditioning of the global system can be improved by orthogonalization of the local basis functions with the modified Gram-Schmidt algorithm, which results in significantly fewer GMRES iterations for solving the discrete problem iteratively.
AB - We present a numerical study to investigate the conditioning of the plane wave discontinuous Galerkin discretization of the Helmholtz problem. We provide empirical evidence that the spectral condition number of the plane wave basis on a single element depends algebraically on the mesh size and the wave number, and exponentially on the number of plane wave directions; we also test its dependence on the element shape. We show that the conditioning of the global system can be improved by orthogonalization of the local basis functions with the modified Gram-Schmidt algorithm, which results in significantly fewer GMRES iterations for solving the discrete problem iteratively.
UR - http://www.scopus.com/inward/record.url?scp=85060055058&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-96415-7_44
DO - 10.1007/978-3-319-96415-7_44
M3 - Contribution to proceedings
AN - SCOPUS:85060055058
SN - 9783319964140
T3 - Lecture Notes in Computational Science and Engineering
SP - 493
EP - 500
BT - Numerical Mathematics and Advanced Applications ENUMATH 2017
A2 - Radu, Florin Adrian
A2 - Kumar, Kundan
A2 - Berre, Inga
A2 - Nordbotten, Jan Martin
A2 - Pop, Iuliu Sorin
PB - Springer
T2 - European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017
Y2 - 25 September 2017 through 29 September 2017
ER -