On Software Support for Finite Difference Schemes Based on Index Notation
| Autor: | Kurt Otto, Krister Åhlander |
|---|---|
| Rok vydání: | 2002 |
| Předmět: |
Set-builder notation
Abuse of notation Multi-index notation Computer science Engineering notation Big O notation Penrose graphical notation Notation for differentiation Mathematical notation Einstein notation Voigt notation symbols.namesake Scientific notation Index notation symbols Big O in probability notation Calculus |
| Zdroj: | Lecture Notes in Computer Science ISBN: 9783540435945 International Conference on Computational Science (3) |
| DOI: | 10.1007/3-540-47789-6_74 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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