Scalable, finite element analysis of electromagnetic scattering and radiation: Error estimation and H-adaptivity

In this paper a method for simulating electromagnetic fields scattered from complex objects is reviewed; namely, an unstructured finite element code that does not use traditional mesh partitioning algorithms. The complete software package is implemented on the Cray T3D massively parallel processor using both Cray Adaptive FORTRAN (CRAFT) compiler constructs to simplify portions of the code that operate on the irregular data, and optimized message passing constructs on portions of the code that operate on regular data and require optimum machine performance. The above finite element solution package is then integrated into an error estimation and adaptive mesh refinement algorithm. An error for the fields over the mesh is estimated and used to drive an adaptive mesh refinement algorithm that refines the mesh where errors are above a given tolerance. This refined mesh is then used once again for a finite element solution of the fields. After estimating the error a second time, the mesh is again refined as needed. This process continues until the error is reduced to an allowable level.