SOLUTION OF LAPLACE S EQUATION FOR ASYMMETRIC GEOMETRIES USING COMSOL MULTIPHYSICS

Laplace s and Poisson s equation are partial di erential equations which can besolved for some geometries by analytical techniques. In electromagnetic theory onemight has studied solutions of Laplace s and Poissons equations for various geometriesthat have usually high symmetry. However, more complex problems can be solved bya computer. The two most frequently used numerical methods to solve Poissons orLaplaces equation are the nite di erence method and the nite element method.Using Comsol Multiphysics software, in this paper we obtain a solution of Laplace sequation, ∇r2u = 0, where u is the potential. The easiest way to solve this problem is tochoose the application mode Laplace s equation from the subsection Classical PDEs.A solution of Laplaces equation is known to be entirely determined by its boundaryconditions which are in fact the Dirichlet boundary conditions here. Therefore, weassign potential values to the boundary settings step by step on each of the threedi erent boundaries by clicking them, respectively.

کلیدواژه ها:

Laplace s equation ، COMSOL ، Electric potential