New Advances in the Modeling of High-temperature Superconductors

In this paper, we present a new discrete formulation that maintains discrete invariance and is suitable for use on nonorthogonal meshes. This formulation, unlike its predecessors , allows us to easily use adaptive mesh reenement to concentrate grid points where error contributions are large (near vortex centers). In this way we reduce the total number of grid points required to accurately capture vortex conngurations and allow the possibility of solving problems previously considered intractable. To solve these large problems, we require the memory capabilities and computational power of state-of-the-art parallel computers. To use these machines, we have developed scal-able libraries for adaptive mesh reenement and partitioning on two-dimensional triangular grids. This general-purpose software uses bisection of the longest side to reene triangles in which error contributions are large. These adaptive meshes are both unstructured and dynamic, and we present a new geometric partitioning algorithm that strives to minimize communication cost by ensuring good partition aspect ratios. We present computational results showing the ee-ciency of these adaptive techniques for a superconductivity application.