Closed-form analytical expressions for the potential fields generated by triangular monolayers with linearly...

Area of Science:

• Potential Theory
• Boundary Value Problems
• Computational Electromagnetics

Background:

• Mixed boundary value problems in potential theory require calculating fields from surface source distributions.
• Existing literature provides solutions for double layer sources with linear strength distributions on triangular elements.
• A gap exists in closed-form solutions for monolayer sources with similar distributions.

Purpose of the Study:

• To derive and present a closed-form analytical expression for the potential field generated by a monolayer source with linearly distributed strength over a triangular element.
• To extend the existing solutions for potential theory boundary value problems.
• To provide a computationally efficient method for analyzing potential fields.

Main Methods:

• Development of analytical expressions based on potential theory principles.
• Integration of source strength distributions over triangular surface elements.
• Validation of the derived solution for various spatial observation points.

Main Results:

• A novel closed-form analytical expression for the potential field of a linearly distributed monolayer source on a triangle has been derived.
• The solution is valid for all spatial observation points, including points on the triangle's interior, edges, and vertices.
• This complements existing solutions for double layer sources.

Conclusions:

• The derived analytical solution for monolayer sources significantly advances the field of potential theory.
• This work provides a valuable tool for solving mixed boundary value problems with monolayer distributions.
• The findings have implications for computational electromagnetics and related fields.