Some recent developments in field calculations

The paper surveys several numerical techniques, under development at the University of Manitoba, that yield improved computational efficiency in the solution of difficult magnetic field problems. The paper includes the following: a description of an isoparametric finite element method for continuously inhomogeneous and orthotropic media within curved boundaries; a description of an isoparametric boundary element method (using integral equation or source distribution techniques) for extensive or open-region problems; and coupled partial differential and integral equation techniques (i.e., picture-frame methods) which are of particular use in solving problems that involve inhomogeneous/orthotropic media within localized regions of free space. Mention is made of sparsity techniques, for the solution of large and sparse systems of equations, and of Kron's diakoptics which is a method of tearing a large system into more easily managed subsystems.