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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 …