TY - JOUR
T1 - Non-iterative domain decomposition for the Helmholtz equation with strong material discontinuities
AU - North, Evan
AU - Tsynkov, Semyon
AU - Turkel, Eli
N1 - Publisher Copyright:
© 2021 IMACS
PY - 2022/3
Y1 - 2022/3
N2 - Many wave propagation problems involve discontinuous material properties. We propose to solve such problems by non-overlapping domain decomposition combined with the method of difference potentials (MDP). The MDP reduces the Helmholtz equation on each subdomain to a Calderon's boundary equation with projection on the boundary. The unknowns for the Calderon's equation are the Dirichlet and Neumann data. Coupling between neighboring subdomains is rendered by applying their respective Calderon's equations to the same data at the common interface. Solutions on individual subdomains are computed concurrently using a direct solver. Our method proves to be insensitive to large jumps in the wavenumber for transmission problems, as well as interior cross-points and mixed boundary conditions, which may be a challenge to many other domain decomposition methods.
AB - Many wave propagation problems involve discontinuous material properties. We propose to solve such problems by non-overlapping domain decomposition combined with the method of difference potentials (MDP). The MDP reduces the Helmholtz equation on each subdomain to a Calderon's boundary equation with projection on the boundary. The unknowns for the Calderon's equation are the Dirichlet and Neumann data. Coupling between neighboring subdomains is rendered by applying their respective Calderon's equations to the same data at the common interface. Solutions on individual subdomains are computed concurrently using a direct solver. Our method proves to be insensitive to large jumps in the wavenumber for transmission problems, as well as interior cross-points and mixed boundary conditions, which may be a challenge to many other domain decomposition methods.
KW - Calderon's operators
KW - Compact finite difference schemes
KW - Complexity bounds
KW - Difference potentials
KW - Direct solution
KW - Discontinuous coefficients
KW - Exact coupling between subdomains
KW - High-order accuracy
KW - Interior cross-points
KW - Non-overlapping domain decomposition
KW - Spectral representation at the boundary
KW - Time-harmonic waves
UR - http://www.scopus.com/inward/record.url?scp=85119594319&partnerID=8YFLogxK
U2 - 10.1016/j.apnum.2021.10.024
DO - 10.1016/j.apnum.2021.10.024
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AN - SCOPUS:85119594319
SN - 0168-9274
VL - 173
SP - 51
EP - 78
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
ER -