SPIKE is a polyalgorithm that uses many different strategies for solving large banded linear systems in parallel. Existing parallel algorithms and software using direct methods for banded matrices are mostly based on LU factorizations. In contrast, SPIKE uses a novel decomposition method (i.e., DS factorization) to balance communication overhead with arithmetic cost to achieve better scalability than other methods. The SPIKE algorithm is similar to a domain decomposition technique that allows performing independent calculations on each subdomain or partition of the linear system, while the interface problem leads to a reduced linear system of much smaller size than that of the original one. Direct, iterative, or approximate schemes can then be used to handle the reduced system in a different way depending on the characteristics of the linear system and the parallel computing platform.
Many science and engineering applications, particularly those...
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