TY - UNPB
T1 - A comparison of coarse spaces for Helmholtz problems in the high frequency regime
AU - Bootland, Niall
AU - Dolean, Victorita
AU - Jolivet, Pierre
AU - Tournier, Pierre-Henri
PY - 2021/2/5
Y1 - 2021/2/5
N2 - Solving time-harmonic wave propagation problems in the frequency domain and within heterogeneous media brings many mathematical and computational challenges, especially in the high frequency regime. We will focus here on computational challenges and try to identify the best algorithm and numerical strategy for a few well-known benchmark cases arising in applications. The aim is to cover, through numerical experimentation and consideration of the best implementation strategies, the main two-level domain decomposition methods developed in recent years for the Helmholtz equation. The theory for these methods is either out of reach with standard mathematical tools or does not cover all cases of practical interest. More precisely, we will focus on the comparison of three coarse spaces that yield two-level methods: the grid coarse space, DtN coarse space, and GenEO coarse space. We will show that they display different pros and cons, and properties depending on the problem and particular numerical setting.
AB - Solving time-harmonic wave propagation problems in the frequency domain and within heterogeneous media brings many mathematical and computational challenges, especially in the high frequency regime. We will focus here on computational challenges and try to identify the best algorithm and numerical strategy for a few well-known benchmark cases arising in applications. The aim is to cover, through numerical experimentation and consideration of the best implementation strategies, the main two-level domain decomposition methods developed in recent years for the Helmholtz equation. The theory for these methods is either out of reach with standard mathematical tools or does not cover all cases of practical interest. More precisely, we will focus on the comparison of three coarse spaces that yield two-level methods: the grid coarse space, DtN coarse space, and GenEO coarse space. We will show that they display different pros and cons, and properties depending on the problem and particular numerical setting.
KW - Helmholtz equations
KW - domain decomposition methods
KW - two level lmethods
KW - coarse spaces
KW - high frequency
UR - https://arxiv.org/abs/2012.02678
M3 - Working paper
BT - A comparison of coarse spaces for Helmholtz problems in the high frequency regime
CY - Ithaca, N.Y.
ER -