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Numerical Analysis and Computation Commons™
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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.
Multigrid For The Nonlinear Power Flow Equations, Enrique Pereira Batista
Multigrid For The Nonlinear Power Flow Equations, Enrique Pereira Batista
Mathematics Theses and Dissertations
The continuously changing structure of power systems and the inclusion of renewable
energy sources are leading to changes in the dynamics of modern power grid,
which have brought renewed attention to the solution of the AC power flow equations.
In particular, development of fast and robust solvers for the power flow problem
continues to be actively investigated. A novel multigrid technique for coarse-graining
dynamic power grid models has been developed recently. This technique uses an
algebraic multigrid (AMG) coarsening strategy applied to the weighted
graph Laplacian that arises from the power network's topology for the construction
of coarse-grain approximations to …