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Full-Text Articles in Numerical Analysis and Computation
A Fast Method For Computing Volume Potentials In The Galerkin Boundary Element Method In 3d Geometries, Sasan Mohyaddin
A Fast Method For Computing Volume Potentials In The Galerkin Boundary Element Method In 3d Geometries, Sasan Mohyaddin
Mathematics Theses and Dissertations
We discuss how the Fast Multipole Method (FMM) applied to a boundary concentrated mesh can be used to evaluate volume potentials that arise in the boundary element method. If $h$ is the meshwidth near the boundary, then the algorithm can compute the potential in nearly $\Ord(h^{-2})$ operations while maintaining an $\Ord(h^p)$ convergence of the error. The effectiveness of the algorithms are demonstrated by solving boundary integral equations of the Poisson equation.