AILU swMATH ID: 41207 Software Authors: Gander, Martin J.; Nataf, Frédéric Description: AILU: a preconditioner based on the analytic factorization of the elliptic operator. We investigate a new type of preconditioner for large systems of linear equations stemming from the discretization of elliptic symmetric partial differential equations. Instead of working at the matrix level, we construct an analytic factorization of the elliptic operator into two parabolic factors and we identify the two parabolic factors with the LU factors of an exact block LU decomposition at the matrix level. Since these factorizations are nonlocal, we introduce a second order local approximation of the parabolic factors. We analyze the approximate factorization at the continuous level and optimize its performance which leads to the new AILU (Analytic ILU) preconditioner with convergence rate effectiveness of the new approach. Homepage: https://www.unige.ch/~gander/Preprints/AILUNLAA.pdf Keywords: block preconditioner; ILU; analytic parabolic factorization; frequency filtering; incomplete LU factorization; iterative methods; convergence; numerical experiments Related Software: clique; PSP; STRUMPACK; MUMPS; UMFPACK; CGS; ILUT; PARDISO; SuperLU; FreeFem++; DRIC; MIQR; LFA; Wesseling; symrcm; CARP-CG; SuperLU-DIST; Hm-toolbox; HssMatrices.jl; hlib Cited in: 27 Publications Standard Articles 2 Publications describing the Software, including 2 Publications in zbMATH Year Ailu for Helmholtz problems: a new preconditioner based on the analytic parabolic factorization. Zbl 1360.76181Gander, Martin J.; Nataf, Frédéric 2001 AILU: a preconditioner based on the analytic factorization of the elliptic operator. Zbl 1051.65054Gander, Martin J.; Nataf, Frédéric 2000 all top 5 Cited by 36 Authors 10 Gander, Martin Jakob 4 Nataf, Frédéric 3 Demanet, Laurent 3 Erlangga, Yogi A. 3 Zepeda-Núñez, Leonardo 2 Dolean, Victorita 2 Oosterlee, Cornelis Willebrordus 2 Vuik, Cornelis 2 Ying, Lexing 2 Zhang, Hui 1 Appelö, Daniel 1 Bonev, Boris 1 Chaouqui, Faycal 1 Claeys, Xavier 1 Conen, Lea 1 Du, Kui 1 Gao, Rong 1 Garcia, Fortino 1 Halpern, Laurence 1 Harari, Isaac 1 Hesthaven, Jan S. 1 Hewett, Russell J. 1 Kim, Seungil 1 Krause, Rolf H. 1 Lang, Chao 1 Liu, Yongxiang 1 Lu, Linzhang 1 Martin, Véronique 1 Niu, Qiang 1 Qiu, Chujun 1 Runborg, Olof 1 Saad, Yousef 1 Santugini-Repiquet, Kévin 1 Taus, Matthias 1 Xi, Yuanzhe 1 Xu, Yingxiang all top 5 Cited in 15 Serials 5 SIAM Journal on Scientific Computing 3 Journal of Computational Physics 3 Applied Numerical Mathematics 2 Applied Mathematics and Computation 1 Computer Methods in Applied Mechanics and Engineering 1 Mathematics of Computation 1 Journal of Computational and Applied Mathematics 1 Journal of Scientific Computing 1 Numerical Algorithms 1 SIAM Review 1 Numerical Linear Algebra with Applications 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Archives of Computational Methods in Engineering 1 Multiscale Modeling & Simulation 1 Journal of Computational Acoustics Cited in 5 Fields 25 Numerical analysis (65-XX) 17 Partial differential equations (35-XX) 4 Fluid mechanics (76-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Optics, electromagnetic theory (78-XX) Citations by Year