Library for architecture-independent development of structured grid applications
ACM SIGPLAN Notices - Workshop on languages, compilers and run-time environments for distributed memory multiprocessors
Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
Iterative Solution of the Helmholtz Equation by a Second-Order Method
SIAM Journal on Matrix Analysis and Applications
ISCOPE '98 Proceedings of the Second International Symposium on Computing in Object-Oriented Parallel Environments
On the Role of Mathematical Abstractions for Scientific Computing
Proceedings of the IFIP TC2/WG2.5 Working Conference on the Architecture of Scientific Software
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A formulation of finite difference schemes based on the index notation of tensor algebra is advocated. Finite difference operators on regular grids may be described as sparse, banded, "tensors". Especially for 3D, it is claimed that index notation better corresponds to the inherent problem structure than does conventional matrix notation. The transition from mathematical index notation to implementation is discussed. Software support for index notation that obeys the Einstein summation convention has been implemented in the C++ package Ein-Sum. The extension of EinSum to support typical data structures of finite difference schemes is outlined. A combination of general index notation software and special-purpose routines for instance for fast transforms is envisioned.