LFA swMATH ID: 19092 Software Authors: Wienands, Roman; Joppich, Wolfgang Description: Practical Fourier analysis for multigrid methods. With CD-ROM. A practical Fourier analysis for multigrid methods is performed. The theoretical framework is necessary for the successful use of multigrid methods for systems of partial differential equations. The local Fourier analysis can be obtained by a simple mouse click, courtesy of accompanying software (LFA) and GUI (xlfa). The studies are for two- and three-dimensioal problems, including Poisson, convection diffusion, biharmonic equation, the Oseen and Stokes equations, a linear shell problem and elasticity systems. The book enables understanding of basic principles of multigrid and local Fourier analysis, allowing investigation of real multigrid effects Homepage: https://www.crcpress.com/Practical-Fourier-Analysis-for-Multigrid-Methods/Wienands-Joppich/p/book/9781584884927 Keywords: multigrid method; Fourier analysis; Poisson equation; convection-diffusion equation; Oseen equation; Stokes equation; textbook; software package; biharmonic equation; linear shell problem; elasticity systems Related Software: Wesseling; FEATFLOW; GitHub; PETSc; IFISS; PLTMG; libCEED; MFEM; FAIR.m; Trilinos; hyper.deal; deal.ii; Energy_Spectrum; QHDFoam; LFAToolkit.jl; Julia; HAZMATH; PCPATCH; PyTorch; iFEM Cited in: 73 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Practical Fourier analysis for multigrid methods. With CD-ROM. Zbl 1062.65133Wienands, Roman; Joppich, Wolfgang 2005 all top 5 Cited by 109 Authors 19 Gaspar, Francisco José 19 Rodrigo, Carmen 11 He, Yunhui 6 Lisbona Cortés, Francisco Javier 5 Oosterlee, Cornelis Willebrordus 4 Bolten, Matthias 4 Chen, Ke 4 MacLachlan, Scott P. 3 Brown, Jed 3 Donatelli, Marco 3 Hu, Xiaozhe 3 Liu, Jun 3 Luo, Peiyao 3 Notay, Yvan 3 Pinto, Marcio Augusto Villela 3 Rhebergen, Sander 3 Zhang, Lixiang 3 Zhu, Xingwen 2 Arrarás, Andres 2 Benzi, Michele 2 Chumchob, Noppadol 2 Franco, Sebastião Romero 2 Gracia, José Luis 2 Huckle, Thomas Kilian 2 Lu, Peipei 2 Portero, Laura 2 Sun, Li 2 van der Vegt, Jaap J. W. 2 Vandewalle, Stefan G. 2 Xu, Xuejun 2 Zhang, Lili 1 Adler, James H. 1 Ahn, Hyung Taek 1 Bacq, Pierre-Loïc 1 Boonen, Tim J. 1 Borzì, Alfio 1 Brabazon, K. J. 1 Chantrapornchai, Chantana 1 Chen, Huangxin 1 De La Riva, Alvaro Pe 1 De Sterck, Hans 1 Dehghan Takht Fooladi, Mehdi 1 Deparis, Simone 1 Di Santo, Valentina 1 Diskin, Boris 1 Dong, Haibo 1 Drzisga, Daniel 1 Erlangga, Yogi A. 1 Ferrari, Paola 1 Furci, Isabella 1 Gathungu, Duncan Kioi 1 Grandperrin, Gwenol 1 Greif, Chen 1 Guo, Pei-Ming 1 Guo, Xueping 1 Habibi, Noora 1 Hajarian, Masoud 1 Hocking, L. Robert 1 Huang, Yumei 1 Hubbard, Matthew E. 1 Irion, Klaus L. 1 Jewprasert, Sopida 1 Jimack, Peter K. 1 Jodlbauer, Daniel 1 Joppich, Wolfgang 1 Kahl, Karsten 1 Kavouklis, Christos 1 Kintscher, Nils 1 Köppl, Tobias 1 Kravvaritis, Christos D. 1 Langer, Ulrich 1 Lauder, George V. 1 Li, Jingzhi 1 Liao, Wei 1 Luo, Lishi 1 Menickelly, Matt 1 Mesforush, Ali 1 Moghaderi, Hamid 1 Napov, Artem 1 Nguyen, Thi Quynh 1 Nicolaï, Bart M. 1 Ohm, Peter 1 Pan, Yu 1 Peng, Jun 1 Peng, Yan 1 Pillwein, Veronika 1 Quarteroni, Alfio M. 1 Ren, Zhi-Ru 1 Rittich, Hannah 1 Rosseel, Eveline 1 Salinas, Pablo 1 Serra-Capizzano, Stefano 1 Seynaeve, Bert 1 Takacs, Stefan 1 Thompson, Jeremy L. 1 Thompson, Tony 1 van Lent, Jan 1 Wang, Junshi 1 Wang, Xiangsheng 1 Wick, Thomas ...and 9 more Authors all top 5 Cited in 31 Serials 13 SIAM Journal on Scientific Computing 8 Journal of Computational Physics 8 Applied Numerical Mathematics 6 Journal of Computational and Applied Mathematics 3 Applied Mathematics and Computation 3 BIT 3 SIAM Journal on Matrix Analysis and Applications 3 Linear Algebra and its Applications 2 Computers & Mathematics with Applications 2 Mathematical Problems in Engineering 2 Archives of Computational Methods in Engineering 1 Computer Methods in Applied Mechanics and Engineering 1 Mathematics of Computation 1 Numerische Mathematik 1 Journal of Symbolic Computation 1 Applied Mathematics Letters 1 Journal of Scientific Computing 1 Numerical Algorithms 1 International Journal of Computer Mathematics 1 Numerical Linear Algebra with Applications 1 Computational and Applied Mathematics 1 ETNA. Electronic Transactions on Numerical Analysis 1 Computing and Visualization in Science 1 International Journal of Computational Fluid Dynamics 1 Computational Geosciences 1 Computational Methods in Applied Mathematics 1 Numerical Insights 1 S\(\vec{\text{e}}\)MA Journal 1 East Asian Journal on Applied Mathematics 1 Journal of Mathematical Modeling 1 Results in Applied Mathematics all top 5 Cited in 15 Fields 68 Numerical analysis (65-XX) 24 Partial differential equations (35-XX) 20 Fluid mechanics (76-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 6 Computer science (68-XX) 5 Information and communication theory, circuits (94-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Mechanics of deformable solids (74-XX) 3 Operations research, mathematical programming (90-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Operator theory (47-XX) 2 Optics, electromagnetic theory (78-XX) 2 Biology and other natural sciences (92-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Probability theory and stochastic processes (60-XX) Citations by Year