Abstract
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.KeywordsHelmholtz EquationFinite Difference SchemeSoftware SupportMatrix Vector MultiplicationSparsity PatternThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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