Separable Coordinate Systems for PDEs
Abstract
Using the symmetry groups of the equations governing acoustic and electromagnetic scattering (the Helmholtz and vector Helmholtz equations, respectively) we studied new methods for separating the equations into ordinary differential equations and generating new classes of solutions in novel geometries. There are many methods for generating solutions to partial differential equations, including finite elements and finite difference numerical techniques. The oldest method, and one of the most powerful, is the method of separation of variables, invented by Bernoulli. We define separation of variables to mean the decomposition of a partial differential equation into a set of uncoupled ordinary differential equations. This is useful, as the solution of ordinary differential equations by numerical techniques is much easier and faster than the solution of partial differential equations. We attacked two specific problems with these methods: electromagnetic scattering from paraboloidal surfaces; and acoustic wave interaction with unusual shapes.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1990
- Accession Number
- ADA223052
Entities
People
- Craig Lindberg
- Freeman Gilbert
Organizations
- Scripps Institution of Oceanography