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; PLTMG; GitHub; FAIR.m; IFISS; Trilinos; AMRCLAW; AMReX; p4est; NewtonLib; FEAPpv; gridlib; ParaDiag; PARALAAOMPI; GradSamp; NITSOL; LFA Lab; PARI/GP; MGRIT Cited in: 63 Publications 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 88 Authors 19 Gaspar, Francisco José 19 Rodrigo, Carmen 9 He, Yunhui 6 Lisbona Cortés, Francisco Javier 5 Oosterlee, Cornelis Willebrordus 4 Chen, Ke 3 Bolten, Matthias 3 Liu, Jun 3 Luo, Peiyao 3 MacLachlan, Scott P. 3 Pinto, Marcio Augusto Villela 3 Rhebergen, Sander 2 Arrarás, Andres 2 Benzi, Michele 2 Brown, Jed 2 Chumchob, Noppadol 2 Donatelli, Marco 2 Franco, Sebastião Romero 2 Gracia, José Luis 2 Hu, Xiaozhe 2 Huckle, Thomas Kilian 2 Lu, Peipei 2 Notay, Yvan 2 Portero, Laura 2 Sun, Li 2 van der Vegt, Jaap J. W. 2 Vandewalle, Stefan G. 2 Xu, Xuejun 2 Zhang, Lili 2 Zhang, Lixiang 2 Zhu, Xingwen 1 Boonen, Tim J. 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 Erlangga, Yogi A. 1 Grandperrin, Gwenol 1 Greif, Chen 1 Guo, Pei-Ming 1 Guo, Xueping 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 Joppich, Wolfgang 1 Kahl, Karsten 1 Kintscher, Nils 1 Kravvaritis, Christos D. 1 Lauder, George V. 1 Li, Jingzhi 1 Liao, Wei 1 Luo, Lishi 1 Menickelly, Matt 1 Moghaderi, Hamid 1 Napov, Artem 1 Nicolaï, Bart M. 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, Tony 1 van Lent, Jan 1 Wang, Junshi 1 Wang, Xiangsheng 1 Wienands, Roman 1 Wild, Stefan M. 1 Wu, Jianping 1 Yang, Jinhui 1 Yin, Fukang 1 Zikatanov, Ludmil T. all top 5 Cited in 25 Serials 9 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 2 Computers & Mathematics with Applications 2 Linear Algebra and its 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 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 Computational Geosciences 1 Computational Methods in Applied Mathematics 1 S\(\vec{\text{e}}\)MA Journal 1 East Asian Journal on Applied Mathematics all top 5 Cited in 15 Fields 58 Numerical analysis (65-XX) 19 Partial differential equations (35-XX) 14 Fluid mechanics (76-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 6 Computer science (68-XX) 5 Information and communication theory, circuits (94-XX) 3 Mechanics of deformable solids (74-XX) 3 Operations research, mathematical programming (90-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Optics, electromagnetic theory (78-XX) 2 Biology and other natural sciences (92-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-XX) Citations by Year