Library for architecture-independent development of structured grid applications
ACM SIGPLAN Notices - Workshop on languages, compilers and run-time environments for distributed memory multiprocessors
Iterative Solution of the Helmholtz Equation by a Second-Order Method
SIAM Journal on Matrix Analysis and Applications
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 higher space dimensions, it is claimed that a band tensor formulation better corresponds to the inherent problem structure than does conventional matrix notation. Tensor algebra is commonly expressed using index notation. The standard index notation is extended with the notion of index offsets, thereby allowing the common traversal of band tensor diagonals. The transition from mathematical index notation to implementation is presented. It is emphasized that efficient band tensor computations must exploit the particular problem structure, which calls for a combination of general index notation software with special-purpose band tensor routines.