The Modified Galerkin Method for the Modified Wave Equation for the Shape of Superellipsoid
Journal of Advances in Mathematics and Computer Science · pp. 2676–2685 · Published 8 Jul 2014
10.9734/BJMCS/2014/11580Abstract
The objective of this work was to find the numerical solution of the Impendence problem for the Helmholtz equation for a 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. The Helmholtz equation, which is the modified wave equation, is used in many scattering problems. This project was funded by NASA RI Space Grant for testing of the Robin boundary condition for the shape of the superellipsoid. One practical value of all these computations can be getting a shape for the engine nacelles in a ray tracing the space shuttle. We significantly reduced the number of terms in the infinite series needed to modify the original integral equation and used the Green's theorem to solve the integral equation for the boundary of the surface.
Cited by 0
No indexed citations yet.
Related research
- Analytical Investigation for the Displacement of Beams with Flexible Supports — shares topic coverage
- Galerkin RBF for Integro-Differential Equations — shares topic coverage
- Computation of Eigenvalues of the Fourth Order Sturm-Liouville BVP by Galerkin Weighted Residual Method — shares topic coverage
- Numerical Approaches for Tenth and Twelfth Order Linear and Nonlinear Differential Equations — shares topic coverage
Article metrics
Real usage data collected on this platform.
0
Page views
0
PDF downloads
0
Outbound clicks
0
Citations
Views by country
Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".
No views recorded yet.
Traffic sources
Referring site, by host.
No traffic recorded yet.
Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.