AI Article Synopsis
- Elliptic boundary value problems are challenging near singularities like edges and corners, such as the concentration of electrical charge on conductors.
- A rapid method is presented that combines Green's-function-based Monte Carlo diffusion methods with a diffusion algorithm.
- This approach successfully calculates the charge distribution near the edge and corner of a conducting cube, addressing a benchmark problem effectively.
Article Abstract
Elliptic boundary value problems are difficult to treat in the vicinity of singularities, i.e., edges and corners, of the boundary. The concentration of electrical charge on the edges and corners of a conductor is perhaps the simplest example of such problems. Here we provide a rapid method for accurate treatment of these problems. It utilizes a Green's-function-based implementation of last-passage Monte Carlo diffusion methods. This is combined with a diffusion algorithm for the scaling of solutions to the Laplace equation near a corner singularity to yield the solution of a benchmark problem: the charge distribution near the edge and corner of a conducting cube.
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| http://dx.doi.org/10.1103/PhysRevE.68.046128 | DOI Listing |
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