#### Research Title

#### Keywords

electromagnetics, volume, integral, equation, electric field, inhomogeneous, electrical, engineering, volume integral equation, computation

#### Presentation Type

Event

#### Research Abstract

Solving complex electric field problems can lead researchers to a host of electronic characteristics about an inhomogeneous, complex object. However due to the complexity of these electric fields, a computer needs to be used in order to solve them. Due to the size of the matrices for some problems, methods for improving speed and performance for these algorithms are absolutely necessary. A Volume Integral Equation was used to solve the Electric Field Displacement, D, and approximate the differential term in this equation. The problem was next discretized using phasors, so that it can computationally be solved. Data used to form the matrices was ultimately used to solve a complex Electric Field problem, and compared against known results of a sphere. Due to the universality of the equation used to model the problem, the same method could be applied to any shape of varying characteristics. More in depth research should be done before any conclusive results can be established. If this method proves to work, it could lead to substantial benefits, including performance increases, while still maintaining accuracy.

#### Recommended Citation

Ryan Nobis, Dan Jiao, and Saad Omar,
"An Approximation Method for Solving Complex Electromagnetics Problems using the Volume Integral Equation"
().
*The Summer Undergraduate Research Fellowship (SURF) Symposium.*
Paper 129.

https://docs.lib.purdue.edu/surf/2013/presentations/129

An Approximation Method for Solving Complex Electromagnetics Problems using the Volume Integral Equation

Solving complex electric field problems can lead researchers to a host of electronic characteristics about an inhomogeneous, complex object. However due to the complexity of these electric fields, a computer needs to be used in order to solve them. Due to the size of the matrices for some problems, methods for improving speed and performance for these algorithms are absolutely necessary. A Volume Integral Equation was used to solve the Electric Field Displacement, D, and approximate the differential term in this equation. The problem was next discretized using phasors, so that it can computationally be solved. Data used to form the matrices was ultimately used to solve a complex Electric Field problem, and compared against known results of a sphere. Due to the universality of the equation used to model the problem, the same method could be applied to any shape of varying characteristics. More in depth research should be done before any conclusive results can be established. If this method proves to work, it could lead to substantial benefits, including performance increases, while still maintaining accuracy.