Use of a multigrid solver in the MAFIA module S3 for electro- and magnetostatic problems

The MAFIA codes are fully 3-D codes for solving Maxwell´s equations by the finite integration algorithm. SOR schemes are a well tested standard for finite-difference (FD) methods in electromagnetic calculations. Since for 3-D problems requiring high accuracy, the necessary fine meshes give a large number of unknowns and so SOR becomes very slow, therefore a multigrid (MG) scheme, a technique developed for the solution of problems with many unknowns, has been incorporated into the S3 code. The performance and accuracy of the new scheme has been compared to that of SOR. The tests demonstrated that multigrid is much faster and more accurate than SOR. It also converges for matrices where SOR fails