Integral finite-element approach for solving the Laplace equation

So far, numerical methods for solving the Laplace equation have consisted mainly of either a finite-difference or a variational finite-element scheme. The variational approach, however, always dealt with a positive-definite differential operator ¿¿2. In this letter, a new integral method for solution is suggested. The differential problem is transferred into an integral equation with a kernel that defines a positive-definite operator. Then, by the Ritz method,1 the solution is given as the limit of a converging sequence of approximations. Two examples are presented: a boundary-value problem for which there is an exact solution, and the square parallel-plate capacitor fundamental in the study of microstrip-line propagation.