Hierarchical interpolative factorization for elliptic operators: integral equations
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Publication:2812291
DOI10.1002/CPA.21577zbMATH Open1344.65123arXiv1307.2666OpenAlexW2950678188MaRDI QIDQ2812291
Author name not available (Why is that?)
Publication date: 16 June 2016
Published in: (Search for Journal in Brave)
Abstract: This paper introduces the hierarchical interpolative factorization for integral equations (HIF-IE) associated with elliptic problems in two and three dimensions. This factorization takes the form of an approximate generalized LU decomposition that permits the efficient application of the discretized operator and its inverse. HIF-IE is based on the recursive skeletonization algorithm but incorporates a novel combination of two key features: (1) a matrix factorization framework for sparsifying structured dense matrices and (2) a recursive dimensional reduction strategy to decrease the cost. Thus, higher-dimensional problems are effectively mapped to one dimension, and we conjecture that constructing, applying, and inverting the factorization all have linear or quasilinear complexity. Numerical experiments support this claim and further demonstrate the performance of our algorithm as a generalized fast multipole method, direct solver, and preconditioner. HIF-IE is compatible with geometric adaptivity and can handle both boundary and volume problems. MATLAB codes are freely available.
Full work available at URL: https://arxiv.org/abs/1307.2666
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