The least squares boundary residual method in electrostatic and eddy current problems

The applicability of the least-squares boundary residual method is demonstrated on several problems in electrostatics (the Laplace equation) and eddy currents, both harmonic and nonharmonic (the Helmholtz and general parabolic equation). For all of them, the method showed a great advantage over other methods. It gave a continual solution, the programming was easy, and the accuracy was very high, even with a relatively small number of modes. The only difficulty which might appear is the choice of appropriate basis functions; however, in many problems this choice is quite obvious. As expected, in the nonharmonic eddy current problems, where both space and time boundary conditions were included, the weighting factor played an important role.