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Full-Text Articles in Logic and Foundations of Mathematics

Spatial Relations Between Conscious And Unconscious Thought, John Shannon Hendrix Jan 2024

Spatial Relations Between Conscious And Unconscious Thought, John Shannon Hendrix

Architecture, Art, and Historic Preservation Faculty Publications

No abstract provided.


Numerical Solution Of The Helmholtz Equation For The Superellipsoid Via The Galerkin Method For The Dirichlet Problem, Yajni Warnapala, Hy Dinh Jan 2013

Numerical Solution Of The Helmholtz Equation For The Superellipsoid Via The Galerkin Method For The Dirichlet Problem, Yajni Warnapala, Hy Dinh

Arts & Sciences Faculty Publications

The objective of this work was to find the numerical solution of the Dirichlet problem for the Helmholtz equation fora smooth superellipsoid. The superellipsoid is a shape that is controlled by two parameters. There are some numerical issues in this type of an analysis; any integration method is affected by the wave number k, because of the oscillatory behavior of the fundamental solution. In this case we could only obtain good numerical results for super ellipsoids that were more shaped like super cones, which is a narrow range of super ellipsoids. The formula for these shapes was: x = cos …


Solving The Helmholtz Equation For The Neumann Boundary Condition For The Pseudosphere By The Galerkin Method, Jane Pleskunas May 2011

Solving The Helmholtz Equation For The Neumann Boundary Condition For The Pseudosphere By The Galerkin Method, Jane Pleskunas

Mathematics Theses

In this paper, the Helmholtz equation for the exterior Neumann boundary condition for the pseudosphere in three dimensions using the global Galerkin method is studied. The Galerkin method will be used to solve Jones’ modified integral equation approach (modified as a series of radiating waves will be added to the fundamental solution) for the Neumann problem for the Helmholtz equation, which uses a series of double sums to approximate the integral. A Fortran 77 program is used and some required subroutines from the Naval Warfare Center are called to help increase ouraccuracy since these boundary integrals are difficult to solve. …