Modeling Piezoelectricity Using the Discontinuous Galerkin Method

Using the results of Problem 2.29, apply the Galerkin method to the integral equivalent of the Poisson equation with zero potential on the boundary, for the lattice of Problem 1.24, with its three independent lattice sites. Show that you get three coupled equations for the ϕi j values (ψ1, ψ2, ψ3) and solve to find the "Galerkin" approximations for the potential at these sites. Compare with the exact values and the results of the various iterations of Problem 1.24 c, Comment. [ψ=4 πϵ0  d] | Nume