|
| 1 | +@book{Hackbusch2015HMA, |
| 2 | + author = {Hackbusch, Wolfgang}, |
| 3 | + publisher = {Springer Berlin Heidelberg}, |
| 4 | + title = {Hierarchical Matrices: Algorithms and Analysis}, |
| 5 | + year = {2015}, |
| 6 | + series = {Springer Series in Computational Mathematics}, |
| 7 | + volume = {49}, |
| 8 | + doi = {10.1007/978-3-662-47324-5}, |
| 9 | + groups = {Compression techniques > Hierarchical matrix > General,Compression techniques > Hierarchical matrix > H matrix,Compression techniques > Hierarchical matrix > H2 matrix,Compression techniques > Hierarchical matrix > ACA} |
| 10 | +} |
| 11 | + |
| 12 | + |
| 13 | +@article{BoermGrasedyckEtAl2003IHM, |
| 14 | + author = {B{\"o}rm, Steffen and Grasedyck, Lars and Hackbusch, Wolfgang}, |
| 15 | + journal = {Engineering Analysis with Boundary Elements}, |
| 16 | + title = {Introduction to hierarchical matrices with applications}, |
| 17 | + year = {2003}, |
| 18 | + month = {may}, |
| 19 | + number = {5}, |
| 20 | + pages = {405--422}, |
| 21 | + volume = {27}, |
| 22 | + doi = {10.1016/S0955-7997(02)00152-2}, |
| 23 | + groups = {Compression techniques > Hierarchical matrix > H matrix, Compression techniques > Hierarchical matrix > H2 matrix}, |
| 24 | + publisher = {Elsevier BV} |
| 25 | +} |
| 26 | + |
| 27 | +@book{Bebendorf2008HMM, |
| 28 | + author = {Bebendorf, Mario}, |
| 29 | + publisher = {Springer Berlin Heidelberg}, |
| 30 | + title = {Hierarchical matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems}, |
| 31 | + year = {2008}, |
| 32 | + series = {Lecture Notes in Computational Science and Engineering}, |
| 33 | + volume = {63}, |
| 34 | + doi = {10.1007/978-3-540-77147-0}, |
| 35 | + groups = {Compression techniques > Hierarchical matrix > ACA, Compression techniques > Hierarchical matrix > H matrix, Compression techniques > Hierarchical matrix > General} |
| 36 | +} |
| 37 | + |
| 38 | +@book{Borm2010ENM, |
| 39 | + author = {Steffen B{\"o}rm}, |
| 40 | + publisher = {European Mathematical Society}, |
| 41 | + title = {Efficient Numerical Methods for Non-local Operators: $\mathcal{H}^2$-matrix Compression, Algorithms and Analysis}, |
| 42 | + year = {2010}, |
| 43 | + isbn = {978-3-03719-091-3}, |
| 44 | + doi = {10.4171/091}, |
| 45 | + groups = {Compression techniques > Hierarchical matrix > H2 matrix}, |
| 46 | + url = {https://www.amazon.com/Efficient-Numerical-Methods-Non-local-Operators/dp/3037190914?SubscriptionId=AKIAIOBINVZYXZQZ2U3A&tag=chimbori05-20&linkCode=xm2&camp=2025&creative=165953&creativeASIN=3037190914} |
| 47 | +} |
| 48 | + |
| 49 | + |
| 50 | + |
| 51 | +@inproceedings{JolivetHechtEtAl2013SDD, |
| 52 | + author = {Pierre Jolivet and Fr{\'{e}}d{\'{e}}ric Hecht and Fr{\'{e}}d{\'{e}}ric Nataf and Christophe Prud{\textquotesingle}homme}, |
| 53 | + booktitle = {Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis}, |
| 54 | + title = {Scalable domain decomposition preconditioners for heterogeneous elliptic problems}, |
| 55 | + year = {2013}, |
| 56 | + month = nov, |
| 57 | + pages = {1--11}, |
| 58 | + publisher = {ACM}, |
| 59 | + series = {SC13}, |
| 60 | + collection = {SC13}, |
| 61 | + doi = {10.1145/2503210.2503212}, |
| 62 | + file = {:JolivetHechtEtAl2013SDD.pdf:PDF}, |
| 63 | + groups = {PDE > DDM, Software} |
| 64 | +} |
| 65 | + |
| 66 | + |
| 67 | +@misc{h2lib, |
| 68 | + author = {Steffen Börm}, |
| 69 | + title = {H2lib}, |
| 70 | + year = {2016}, |
| 71 | + publisher = {GitHub}, |
| 72 | + journal = {GitHub repository}, |
| 73 | + url = {https://github.com/H2Lib/H2Lib/tree/v3.0} |
| 74 | +} |
| 75 | + |
| 76 | +@misc{hmat_oss, |
| 77 | + key = {hmat-oss}, |
| 78 | + title = {{hmat-oss}}, |
| 79 | + year = {2024}, |
| 80 | + publisher = {GitHub}, |
| 81 | + journal = {GitHub repository}, |
| 82 | + url = {https://github.com/jeromerobert/hmat-oss} |
| 83 | +} |
| 84 | + |
| 85 | +@article{AmbikasaranSinghEtAl2019HLH, |
| 86 | + author = {Ambikasaran, Sivaram and Singh, Karan and Sankaran, Shyam}, |
| 87 | + journal = {Journal of Open Source Software}, |
| 88 | + title = {HODLRlib: A Library for Hierarchical Matrices}, |
| 89 | + year = {2019}, |
| 90 | + issn = {2475-9066}, |
| 91 | + month = feb, |
| 92 | + number = {34}, |
| 93 | + pages = {1167}, |
| 94 | + volume = {4}, |
| 95 | + doi = {10.21105/joss.01167}, |
| 96 | + publisher = {The Open Journal} |
| 97 | +} |
| 98 | + |
| 99 | +@article{ZampiniBoukaramEtAl2022HDM, |
| 100 | + author = {Zampini, Stefano and Boukaram, Wajih and Turkiyyah, George and Knio, Omar and Keyes, David}, |
| 101 | + journal = {Advances in Computational Mathematics}, |
| 102 | + title = {H2Opus: a distributed-memory multi-GPU software package for non-local operators}, |
| 103 | + year = {2022}, |
| 104 | + issn = {1572-9044}, |
| 105 | + month = may, |
| 106 | + number = {31}, |
| 107 | + volume = {48}, |
| 108 | + doi = {10.1007/s10444-022-09942-6}, |
| 109 | + groups = {Compression techniques > Hierarchical matrix > H2 matrix}, |
| 110 | + publisher = {Springer Science and Business Media LLC} |
| 111 | +} |
| 112 | + |
| 113 | + |
| 114 | +@article{IskeLeBorneEtAl2017HMA, |
| 115 | + author = {Iske, Armin and Le Borne, Sabine and Wende, Michael}, |
| 116 | + journal = {{SIAM} Journal on Scientific Computing}, |
| 117 | + title = {Hierarchical Matrix Approximation for Kernel-Based Scattered Data Interpolation}, |
| 118 | + year = {2017}, |
| 119 | + issn = {1095-7197}, |
| 120 | + month = {jan}, |
| 121 | + number = {5}, |
| 122 | + pages = {A2287--A2316}, |
| 123 | + volume = {39}, |
| 124 | + doi = {10.1137/16m1101167}, |
| 125 | + file = {:IskeBorneEtAl2017HMA.pdf:PDF}, |
| 126 | + groups = {Compression techniques > Hierarchical matrix > H matrix, RBF > Data interpolation}, |
| 127 | + publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})} |
| 128 | +} |
| 129 | + |
| 130 | + |
| 131 | +@inbook{AinsworthGlusa2018TEF, |
| 132 | + author = {Mark Ainsworth and Christian Glusa}, |
| 133 | + pages = {17--57}, |
| 134 | + editor = {Dick, Josef and Kuo, Frances Y. and Wo{\'{z}}niakowski, Henryk}, |
| 135 | + publisher = {Springer International Publishing}, |
| 136 | + title = {Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains}, |
| 137 | + year = {2018}, |
| 138 | + isbn = {9783319724560}, |
| 139 | + booktitle = {Contemporary Computational Mathematics - A Celebration of the 80th Birthday of {Ian Sloan}}, |
| 140 | + doi = {10.1007/978-3-319-72456-0_2}, |
| 141 | + file = {:AinsworthGlusa2018TEF.pdf:PDF}, |
| 142 | + groups = {FDE > FEM} |
| 143 | +} |
| 144 | + |
| 145 | + |
| 146 | +@article{GreengardRokhlin1987FAP, |
| 147 | + author = {L Greengard and V Rokhlin}, |
| 148 | + journal = {Journal of Computational Physics}, |
| 149 | + title = {A fast algorithm for particle simulations}, |
| 150 | + year = {1987}, |
| 151 | + month = {dec}, |
| 152 | + number = {2}, |
| 153 | + pages = {325--348}, |
| 154 | + volume = {73}, |
| 155 | + doi = {10.1016/0021-9991(87)90140-9}, |
| 156 | + groups = {Compression techniques > FMM}, |
| 157 | + publisher = {Elsevier {BV}} |
| 158 | +} |
| 159 | + |
| 160 | +@inproceedings{Hebeker1990PSA, |
| 161 | + author = {Friedrich K. Hebeker}, |
| 162 | + booktitle = {Domain Decomposition Methods for Partial Differential Equations}, |
| 163 | + title = {On a parallel Schwarz algorithm for symmetric strongly elliptic integral equations}, |
| 164 | + year = {1990}, |
| 165 | + editor = {Roland Glowinski and Yuri A. Kuznetsov and G\'erard Meurant and Jacques P\'eriaux and Olaf B. Widlund}, |
| 166 | + organization = {SIAM}, |
| 167 | + pages = {382--393}, |
| 168 | + groups = {BIE > Schwarz methods} |
| 169 | +} |
| 170 | + |
| 171 | +@article{StephanTran1998DDA, |
| 172 | + author = {Stephan, Ernst P. and Tran, Thanh}, |
| 173 | + journal = {SIAM Journal on Scientific Computing}, |
| 174 | + title = {Domain decomposition algorithms for indefinite hypersingular integral equations: the h and p versions}, |
| 175 | + year = {1998}, |
| 176 | + issn = {1095-7197}, |
| 177 | + month = jul, |
| 178 | + number = {4}, |
| 179 | + pages = {1139--1153}, |
| 180 | + volume = {19}, |
| 181 | + doi = {10.1137/S1064827595296161}, |
| 182 | + file = {Stephan1998.pdf:StephanTran1998DDA.pdf:PDF}, |
| 183 | + groups = {BIE > Schwarz methods > Double layer}, |
| 184 | + publisher = {SIAM} |
| 185 | +} |
| 186 | + |
| 187 | + |
| 188 | +@article{Heuer1996EA, |
| 189 | + author = {Heuer, Norbert}, |
| 190 | + journal = {Journal of Integral Equations and Applications}, |
| 191 | + title = {Efficient Algorithms for the $p$-Version of the Boundary Element Method}, |
| 192 | + year = {1996}, |
| 193 | + month = sep, |
| 194 | + number = {3}, |
| 195 | + pages = {337--361}, |
| 196 | + volume = {8}, |
| 197 | + doi = {10.1216/jiea/1181075956}, |
| 198 | + groups = {BIE > BEM > p-version, BIE > Schwarz methods > Single layer}, |
| 199 | + publisher = {Rocky Mountain Mathematics Consortium} |
| 200 | +} |
| 201 | + |
| 202 | +@article{MarchandClaeysEtAl2020TLP, |
| 203 | + author = {Pierre Marchand and Xavier Claeys and Pierre Jolivet and Fr{\'{e}}d{\'{e}}ric Nataf and Pierre-Henri Tournier}, |
| 204 | + journal = {Numerische Mathematik}, |
| 205 | + title = {Two-level preconditioning for h-version boundary element approximation of hypersingular operator with {GenEO}}, |
| 206 | + year = {2020}, |
| 207 | + month = {sep}, |
| 208 | + number = {3}, |
| 209 | + pages = {597--628}, |
| 210 | + volume = {146}, |
| 211 | + doi = {10.1007/s00211-020-01149-5}, |
| 212 | + groups = {BIE > Schwarz methods > Double layer}, |
| 213 | + publisher = {Springer Science and Business Media {LLC}} |
| 214 | +} |
| 215 | + |
| 216 | +@phdthesis{Marchand2020SMB, |
| 217 | + author = {Marchand, Pierre}, |
| 218 | + school = {{Sorbonne Universit{\'e}}}, |
| 219 | + title = {{Schwarz methods and boundary integral equations}}, |
| 220 | + year = {2020}, |
| 221 | + month = Jan, |
| 222 | + type = {Theses}, |
| 223 | + keywords = {Hierarchical matrices ; Two-level preconditioners ; Boundary element method ; Boundary integral equations ; Schwarz methods ; Domain decomposition methods ; Numerical analysis ; Equations int{\'e}grales de fronti{\`e}re ; M{\'e}thodes de Schwarz ; M{\'e}thodes de d{\'e}composition de domaine ; Analyse num{\'e}rique ; M{\'e}thode des {\'e}l{\'e}ments finis de fronti{\`e}re ; Pr{\'e}conditionneurs {\`a} deux niveaux ; Matrices hi{\'e}rarchiques}, |
| 224 | + url = {https://hal.archives-ouvertes.fr/tel-02922455} |
| 225 | +} |
| 226 | + |
| 227 | +@article{Hecht2012NDF, |
| 228 | + author = {Hecht, Fr{\'e}d{\'e}ric}, |
| 229 | + journal = {Journal of numerical mathematics}, |
| 230 | + title = {New development in {FreeFem++}}, |
| 231 | + year = {2012}, |
| 232 | + number = {3-4}, |
| 233 | + pages = {251--265}, |
| 234 | + volume = {20}, |
| 235 | + comment = {FreeFEM}, |
| 236 | + doi = {10.1515/jnum-2012-0013}, |
| 237 | + groups = {Software} |
| 238 | +} |
| 239 | + |
| 240 | +@techreport{BalayAbhyankarEtAl2020PUM, |
| 241 | + author = {Satish Balay and Shrirang Abhyankar and Mark~F. Adams and Steven Benson and Jed Brown and Peter Brune and Kris Buschelman and Emil Constantinescu and Lisandro Dalcin and Alp Dener and Victor Eijkhout and Jacob Faibussowitsch and William~D. Gropp and V\'{a}clav Hapla and Tobin Isaac and Pierre Jolivet and Dmitry Karpeev and Dinesh Kaushik and Matthew~G. Knepley and Fande Kong and Scott Kruger and Dave~A. May and Lois Curfman McInnes and Richard Tran Mills and Lawrence Mitchell and Todd Munson and Jose~E. Roman and Karl Rupp and Patrick Sanan and Jason Sarich and Barry~F. Smith and Hansol Suh and Stefano Zampini and Hong Zhang and Hong Zhang and Junchao Zhang}, |
| 242 | + institution = {Argonne National Laboratory}, |
| 243 | + title = {{PETSc/TAO} Users Manual}, |
| 244 | + year = {2025}, |
| 245 | + number = {ANL-21/39 - Revision 3.24}, |
| 246 | + doi = {10.2172/2998643} |
| 247 | +} |
| 248 | + |
| 249 | + |
| 250 | +@article{SpillaneDoleanEtAl2013ARC, |
| 251 | + author = {Spillane, Nicole and Dolean, Victorita and Hauret, Patrice and Nataf, Frédéric and Pechstein, Clemens and Scheichl, Robert}, |
| 252 | + journal = {Numerische Mathematik}, |
| 253 | + title = {Abstract robust coarse spaces for systems of {PDEs} via generalized eigenproblems in the overlaps}, |
| 254 | + year = {2013}, |
| 255 | + issn = {0945-3245}, |
| 256 | + month = aug, |
| 257 | + number = {4}, |
| 258 | + pages = {741--770}, |
| 259 | + volume = {126}, |
| 260 | + abstract = {Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities in the PDE coefficients, especially for systems of PDEs. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems in the overlaps of subdomains that isolate the terms responsible for slow convergence. We prove a general theoretical result that rigorously establishes the robustness of the new coarse space and give some numerical examples on two and three dimensional heterogeneous PDEs and systems of PDEs that confirm this property.}, |
| 261 | + doi = {10.1007/s00211-013-0576-y}, |
| 262 | + file = {Spillane2014a.pdf:SpillaneDoleanEtAl2014ARC.pdf:PDF}, |
| 263 | + groups = {PDE > DDM > Adaptive coarse space > GenEO}, |
| 264 | + publisher = {Springer Science and Business Media LLC} |
| 265 | +} |
| 266 | + |
| 267 | + |
| 268 | +@article{JolivetRomanEtAl2021KPE, |
| 269 | + author = {Pierre Jolivet and Jose E. Roman and Stefano Zampini}, |
| 270 | + journal = {Computers {\&} Mathematics with Applications}, |
| 271 | + title = {{KSPHPDDM} and {PCHPDDM}: Extending {PETSc} with advanced {Krylov} methods and robust multilevel overlapping {Schwarz} preconditioners}, |
| 272 | + year = {2021}, |
| 273 | + month = {feb}, |
| 274 | + pages = {277--295}, |
| 275 | + volume = {84}, |
| 276 | + doi = {10.1016/j.camwa.2021.01.003}, |
| 277 | + groups = {Software}, |
| 278 | + publisher = {Elsevier {BV}} |
| 279 | +} |
0 commit comments