A fast direct solver for boundary integral equations in two dimensions

By Per-Gunnar Martinsson, Vladimir Rokhlin. 2003

358 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/d9dc4ac6390ccc88023c37a5b42ea9cf573cc7d7

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In Atomic and Molecular Physics, and Optics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Fast Direct Methods for Gaussian Processes (2014, methodology): “Index Terms—Covariance function, Gaussian process, hierarchical off-diagonal low-rank, direct solver, fast multipole method, Bayesian analysis, likelihood, evidence F”
On the Compression of Low Rank Matrices (2005, methodology): “We do this by compressing the interaction between Γi and an artificial contour Γartif that surrounds Γi (as shown in Figure 2(b)) combined with the parts of the other contours that penetrate it. This procedure works for any potential problem for which the Green’s identities hold. For details, see [ ”
An adaptive fast direct solver for boundary integral equations in two dimensions (2009, neutral): “When applied to boundary integral equations in two dimensions arising from partial differential equations for which a Green’s function is non-oscillatory (or, weakly oscillatory, as defined in [21]), the complexity of the solver is reduced to O (N log2 N).”
Fast algorithms for hierarchically semiseparable matrices (2010, background): “These matrices have been shown very efiective in solving linear systems [9, 10, 12, 16], least squares problems [6], eigenvalue problems [3, 13, 21, 36, 37, 44], PDEs [2, 28, 29, 47], integral equations [26, 41 , 42], etc.”
Likelihood approximation with hierarchical matrices for large spatial datasets (2017, neutral): “on the recursive skeletonization factorization procedure [33, 47].”
A fast algorithm for the inversion of general Toeplitz matrices (2004, methodology): “Section 4 contains the proof that the Fourier representation of a Toeplitz matrix possesses the properties required for the fast inversion scheme of [ 11 ] to be applicable.”
Numerical construction of Green's functions in high dimensional elliptic problems with variable coefficients and analysis of renewable energy data via sparse and separable approximations (2012, methodology): “These methods include fast multipole (FMM) [63, 38], panel clustering [64, 121], Hmatrices [65, 67], matrix skeletonization [99, 37], and hierarchically semiseparable (HSS) matrices [33, 32, 149, 98].”
Diffusion Wavelets (2004, methodology): “In [42,43] techniques for compressing low-rank matrices (see also [63]) are applied to the problem of obtaining an explicit sparse inverse, in particular for the solution of integral equations arising from boundary value problems of elliptic PDEs.”
Randomized numerical linear algebra: Foundations and algorithms (2020, methodology): “On top of that, the algorithms used to compute the ID can result in answers that are still further away from the optimal value (Cheng, Gimbutas, Martinsson and Rokhlin 2005).”