2 research outputs found
Compressed absorbing boundary conditions via matrix probing
Absorbing layers are sometimes required to be impractically thick in order to
offer an accurate approximation of an absorbing boundary condition for the
Helmholtz equation in a heterogeneous medium. It is always possible to reduce
an absorbing layer to an operator at the boundary by layer-stripping
elimination of the exterior unknowns, but the linear algebra involved is
costly. We propose to bypass the elimination procedure, and directly fit the
surface-to-surface operator in compressed form from a few exterior Helmholtz
solves with random Dirichlet data. The result is a concise description of the
absorbing boundary condition, with a complexity that grows slowly (often,
logarithmically) in the frequency parameter.Comment: 29 pages with 25 figure
Compressed Absorbing Boundary Conditions for the Helmholtz Equation
Absorbing layers are sometimes required to be impractically thick in order to
offer an accurate approximation of an absorbing boundary condition for the
Helmholtz equation in a heterogeneous medium. It is always possible to reduce
an absorbing layer to an operator at the boundary by layer-stripping
elimination of the exterior unknowns, but the linear algebra involved is
costly. We propose to bypass the elimination procedure, and directly fit the
surface-to-surface operator in compressed form from a few exterior Helmholtz
solves with random Dirichlet data. We obtain a concise description of the
absorbing boundary condition, with a complexity that grows slowly (often,
logarithmically) in the frequency parameter. We then obtain a fast (nearly
linear in the dimension of the matrix) algorithm for the application of the
absorbing boundary condition using partitioned low rank matrices. The result,
modulo a precomputation, is a fast and memory-efficient compression scheme of
an absorbing boundary condition for the Helmholtz equation.Comment: PhD thesi