On a modular architecture for finite element systems. I. Sequential codes

The paper discusses basic principles for the modular design of sequential finite element codes. The emphasis is put on computational kernels, considering pre- and post-processing as separate programs. Four fundamental modules (subsystems) of computational kernels are identified for the four main tasks: problem definition, approximation, mesh manipulation and linear system solution. Example interfaces between the four modules that can accommodate a broad range of application areas, approximation methods, mesh types and existing solvers are presented and discussed. The extensions for other modules and for interfaces with external environments are considered. The paper prepares ground for the next article considering the architecture of parallel finite element systems.