TY - JOUR
T1 - Solving the Helmholtz equation for general smooth geometry using simple grids
AU - Medvinsky, M.
AU - Tsynkov, S.
AU - Turkel, E.
N1 - Publisher Copyright:
© 2015 Elsevier B.V.
PY - 2016/4/1
Y1 - 2016/4/1
N2 - The method of difference potentials was originally proposed by Ryaben'kii, and is a generalized discrete version of the method of Calderon's operators. It handles non-conforming curvilinear boundaries, variable coefficients, and non-standard boundary conditions while keeping the complexity of the solver at the level of a finite-difference scheme on a regular structured grid. Compact finite difference schemes enable high order accuracy on small stencils and so require no additional boundary conditions beyond those needed for the differential equation itself. Previously, we have used difference potentials combined with compact schemes for solving transmission/scattering problems in regions of a simple shape. In this paper, we generalize our previous work to incorporate smooth general shaped boundaries and interfaces, including a formulation that involves multiple scattering.
AB - The method of difference potentials was originally proposed by Ryaben'kii, and is a generalized discrete version of the method of Calderon's operators. It handles non-conforming curvilinear boundaries, variable coefficients, and non-standard boundary conditions while keeping the complexity of the solver at the level of a finite-difference scheme on a regular structured grid. Compact finite difference schemes enable high order accuracy on small stencils and so require no additional boundary conditions beyond those needed for the differential equation itself. Previously, we have used difference potentials combined with compact schemes for solving transmission/scattering problems in regions of a simple shape. In this paper, we generalize our previous work to incorporate smooth general shaped boundaries and interfaces, including a formulation that involves multiple scattering.
KW - Boundary projections
KW - Calderon's operators
KW - Curvilinear boundaries
KW - Difference potentials
KW - High order compact differencing
KW - Multiple scattering
UR - http://www.scopus.com/inward/record.url?scp=84958663605&partnerID=8YFLogxK
U2 - 10.1016/j.wavemoti.2015.12.004
DO - 10.1016/j.wavemoti.2015.12.004
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AN - SCOPUS:84958663605
SN - 0165-2125
VL - 62
SP - 75
EP - 97
JO - Wave Motion
JF - Wave Motion
ER -