Analysis Of Heat Flow In Resistive Switching Devices Using Boundary Integral Equation

Abstract

In this thesis, we analyze the Boundary Integral Equation(BIE) methods for the poisson equation with Dirichlet Boundary Conditions in three dimensions where the boundary is smooth. We present a formulation of solving the BIEs reformulated from the poisson boundary value problems. BIE is particularly attractive in developing integral equation methods, it reduces the dimensions of the problem and often transforms a problem in an infinite domain to integrals on the finite boundary. A BoundaryvalueproblemforPartialDifferentialEquationwithaconstantcoefficientcanbereducedto aBIEbyusingthefundamentalsolutionandGreensrepresentationformula,wereducedtheboundary value problem into Boundary Integral Equations. Boundary integral equation Method is developed for the problem of heat conduction in a geometry composed of an insulator between two metallic electrodes, with multiple cuboidal heat sources within the insulator.