On one method of solving the Helmholtz equation. I
I. L. Verbitskii
Source abstract
A method is suggested to solve the Helmholtz equation in an arbitrary domain with general form boundary conditions. The method permits reducing this equation to that of Poisson and an infinite set of simultaneous linear algebraic equations. Convergence of the method is proved for any wave number. Thus, it becomes possible to solve the Helmholtz equation by using any known method developed to solve the Poisson equation. As an illustration, an effective algorithm is constructed to solve the two dimensional diffraction problem on the arbitrary periodic boundary for any wavelength by using the conformal mapping techniques. If the boundary contains irregular points, then the field in all approximations has in all these points singularities of the needed type.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.