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Full-Text Articles in Physical Sciences and Mathematics
An Iterative Numerical Method For Multiple Scattering Using High Order Local Absorbing Boundary Conditions, Jonathan Harriman Hale
An Iterative Numerical Method For Multiple Scattering Using High Order Local Absorbing Boundary Conditions, Jonathan Harriman Hale
Theses and Dissertations
This thesis outlines an iterative approach for determining the scattered wave for two dimensional multiple acoustic scattering problems using high order local absorbing boundary conditions and second order finite difference. We seek to approximate the total wave as it is scattered off of multiple arbitrarily shaped obstacles. This is done by decomposing the scattered wave into the superposition of single scattered waves. We then repeatedly solve the single scattering system for each obstacle, while updating the boundary conditions based off the incident wave and the scattered wave off the other obstacles. We solve each single scattering by enclosing the obstacle …
High Order Numerical Methods For Problems In Wave Scattering, Dane Scott Grundvig
High Order Numerical Methods For Problems In Wave Scattering, Dane Scott Grundvig
Theses and Dissertations
Arbitrary high order numerical methods for time-harmonic acoustic scattering problems originally defined on unbounded domains are constructed. This is done by coupling recently developed high order local absorbing boundary conditions (ABCs) with finite difference methods for the Helmholtz equation. These ABCs are based on exact representations of the outgoing waves by means of farfield expansions. The finite difference methods, which are constructed from a deferred-correction (DC) technique, approximate the Helmholtz equation and the ABCs to any desired order. As a result, high order numerical methods with an overall order of convergence equal to the order of the DC schemes are …