The Invertibility of the Double Layer Potential Operator in the Space of Continuous Functions Defined on a Polyhedron: The Panel Method

Abstract

We consider the double layer potential operator W defined on the polyhedral boundary of an infinite cone and prove the invertibility of (I±2W) in the space of continuous functions. To do this we define an operator-valued symbol function for W and show that the spectral radii of its values are less than one half. In the last part of this paper we consider a piecewise constant collocation method for the numerical solution of the double layer potential equation over the boundary of a bounded polyhedron.

Keywords:

• Layers
• potentials
• polyhedral domain
• boundry integral equation
• panel method

AMS:

• 31B10
• 45E10
• 65R20