Exploiting Zeros in Frontal Solvers
نویسنده
چکیده
An important feature of the frontal method for the solution of large sparse systems of linear equations is that the frontal matrix is held as a dense matrix. This allows efficient dense linear algebra kernels, in particular, the Level 3 Basic Linear Algebra Subprograms (BLAS) to be used during the numerical factorization. However, the frontal matrix may contain a significant number of zeros and this, in turn, leads to unnecessary operations being performed and to zeros being stored explicitly in the factors. In this paper we look at how we can take advantage of zeros within the frontal matrix. We illustrate the effects of exploiting zeros in the front on the factorization and solve times, and on the storage requirements for the Harwell Subroutine Library general frontal code MA42 using a range of problems arising from real engineering and industrial applications.
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