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Laplace's equation on perturbed domains

McCollom, William A.
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Advisor
Martin, P. A.
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Date
Date Issued
2014
Date Submitted
2014
Keywords
perturbation
 Laplacian
 boundary-variation
 Harmonic functions
 Perturbation (Mathematics)
 Dirichlet problem
 Neumann problem
 Differential equations, Partial
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2010-2019 - Mines Theses & Dissertations
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Laplace's equation on perturbed domains
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https://hdl.handle.net/11124/12281
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Abstract
Laplace's equation is a prototypical elliptic PDE that appears in many electromagnetic and fluid dynamics problems. We develop two methods for solving Laplace's equation on domains that are perturbations of a circle. These methods are derived from governing equations and applied to several test cases. Both Dirichlet and Neumann boundary conditions are considered. We verify our methods by constructing exact solutions for the perturbed geometries.
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