Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Fast and Memory Efficient Sparse Solver with Applications to
  Finite-Element Matrices   In this article, we introduce a fast and memory efficient solver for sparse
matrices arising from the finite element discretization of elliptic partial
differential equations (PDEs). We use a fast direct (but approximate)
multifrontal solver as a preconditioner, and use an iterative solver to achieve
a desired accuracy. This approach combines the advantages of direct and
iterative schemes to arrive at a fast, robust and accurate solver. We will show
that this solver is faster ($\sim$ 2x) and more memory efficient ($\sim$ 2--3x)
than a conventional direct multifrontal solver. Furthermore, we will
demonstrate that the solver is both a faster and more effective preconditioner
than other preconditioners such as the incomplete LU preconditioner. Specific
speed-ups depend on the matrix size and improve as the size of the matrix
increases. The solver can be applied to both structured and unstructured meshes
in a similar manner. We build on our previous work and utilize the fact that
dense frontal and update matrices, in the multifrontal algorithm, can be
represented as hierarchically off-diagonal low-rank (HODLR) matrices. Using
this idea, we replace all large dense matrix operations in the multifrontal
elimination process with $O(N)$ HODLR operations to arrive at a faster and more
memory efficient solver.

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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc