Li, Junpu; Fu, Zhuojia; Gu, Yan; Zhang, Lan Rapid calculation of large-scale acoustic scattering from complex targets by a dual-level fast direct solver. (English) Zbl 1524.65908 Comput. Math. Appl. 130, 1-9 (2023). MSC: 65N38 35J05 76Q05 65F10 65F50 65N35 78A45 35Q35 PDFBibTeX XMLCite \textit{J. Li} et al., Comput. Math. Appl. 130, 1--9 (2023; Zbl 1524.65908) Full Text: DOI
Martynenko, S. I. Numerical solving of boundary value problems on multiblock grids. (English. Russian original) Zbl 1493.65263 Comput. Math. Math. Phys. 61, No. 9, 1375-1386 (2021); translation from Zh. Vychisl. Mat. Mat. Fiz. 61, No. 9, 1403-1415 (2021). MSC: 65N55 65N12 65Y05 35J05 PDFBibTeX XMLCite \textit{S. I. Martynenko}, Comput. Math. Math. Phys. 61, No. 9, 1375--1386 (2021; Zbl 1493.65263); translation from Zh. Vychisl. Mat. Mat. Fiz. 61, No. 9, 1403--1415 (2021) Full Text: DOI
Li, Junpu; Gu, Yan; Qin, Qing-Hua; Zhang, Lan The rapid assessment for three-dimensional potential model of large-scale particle system by a modified multilevel fast multipole algorithm. (English) Zbl 1524.65909 Comput. Math. Appl. 89, 127-138 (2021). MSC: 65N38 35J05 65N80 35J25 65N55 65F50 PDFBibTeX XMLCite \textit{J. Li} et al., Comput. Math. Appl. 89, 127--138 (2021; Zbl 1524.65909) Full Text: DOI
Feng, Hongsong; Long, Guangqing; Zhao, Shan FFT-based high order central difference schemes for Poisson’s equation with staggered boundaries. (English) Zbl 1456.65140 J. Sci. Comput. 86, No. 1, Paper No. 7, 25 p. (2021). MSC: 65N06 65T50 65N85 35J05 PDFBibTeX XMLCite \textit{H. Feng} et al., J. Sci. Comput. 86, No. 1, Paper No. 7, 25 p. (2021; Zbl 1456.65140) Full Text: DOI
Yang, Xiang; Mittal, Rajat Efficient relaxed-Jacobi smoothers for multigrid on parallel computers. (English) Zbl 1380.65243 J. Comput. Phys. 332, 135-142 (2017). MSC: 65M55 35J05 PDFBibTeX XMLCite \textit{X. Yang} and \textit{R. Mittal}, J. Comput. Phys. 332, 135--142 (2017; Zbl 1380.65243) Full Text: DOI
Abide, Stéphane; Zeghmati, Belkacem Multigrid defect correction and fourth-order compact scheme for Poisson’s equation. (English) Zbl 1372.65321 Comput. Math. Appl. 73, No. 7, 1433-1444 (2017). MSC: 65N55 65N06 35J05 PDFBibTeX XMLCite \textit{S. Abide} and \textit{B. Zeghmati}, Comput. Math. Appl. 73, No. 7, 1433--1444 (2017; Zbl 1372.65321) Full Text: DOI HAL
Ghaffar, Fazal; Badshah, Noor; Islam, Saeed; Khan, Muhammad Altaf Multigrid method based on transformation-free high-order scheme for solving 2D Helmholtz equation on nonuniform grids. (English) Zbl 1422.65313 Adv. Difference Equ. 2016, Paper No. 19, 16 p. (2016). MSC: 65N06 65N55 35J05 65F10 65N12 PDFBibTeX XMLCite \textit{F. Ghaffar} et al., Adv. Difference Equ. 2016, Paper No. 19, 16 p. (2016; Zbl 1422.65313) Full Text: DOI
Moghaderi, Hamid; Dehghan, Mehdi; Hajarian, Masoud A fast and efficient two-grid method for solving \(d\)-dimensional Poisson equations. (English) Zbl 1342.65226 Numer. Algorithms 72, No. 3, 483-537 (2016). MSC: 65N55 65N06 35K20 PDFBibTeX XMLCite \textit{H. Moghaderi} et al., Numer. Algorithms 72, No. 3, 483--537 (2016; Zbl 1342.65226) Full Text: DOI
Ghaffar, Fazal; Badshah, Noor; Islam, Saeed Multigrid method for solution of 3D Helmholtz equation based on HOC schemes. (English) Zbl 1474.65420 Abstr. Appl. Anal. 2014, Article ID 954658, 14 p. (2014). MSC: 65N06 65F10 65N22 65N55 35J05 PDFBibTeX XMLCite \textit{F. Ghaffar} et al., Abstr. Appl. Anal. 2014, Article ID 954658, 14 p. (2014; Zbl 1474.65420) Full Text: DOI
Patil, Dhiraj V.; Premnath, Kannan N.; Banerjee, Sanjoy Multigrid lattice Boltzmann method for accelerated solution of elliptic equations. (English) Zbl 1349.76725 J. Comput. Phys. 265, 172-194 (2014). MSC: 76M28 65N55 65N75 PDFBibTeX XMLCite \textit{D. V. Patil} et al., J. Comput. Phys. 265, 172--194 (2014; Zbl 1349.76725) Full Text: DOI
Ge, Yongbin; Cao, Fujun; Zhang, Jun A transformation-free HOC scheme and multigrid method for solving the 3D Poisson equation on nonuniform grids. (English) Zbl 1284.35146 J. Comput. Phys. 234, 199-216 (2013). MSC: 35J05 65N55 65N06 PDFBibTeX XMLCite \textit{Y. Ge} et al., J. Comput. Phys. 234, 199--216 (2013; Zbl 1284.35146) Full Text: DOI
Rodrigo, C.; Gaspar, F. J.; Lisbona, F. J. Multicolor Fourier analysis of the multigrid method for quadratic FEM discretizations. (English) Zbl 1280.65139 Appl. Math. Comput. 218, No. 22, 11182-11195 (2012). MSC: 65N55 65N30 35J05 PDFBibTeX XMLCite \textit{C. Rodrigo} et al., Appl. Math. Comput. 218, No. 22, 11182--11195 (2012; Zbl 1280.65139) Full Text: DOI
Jackson, R. H.; Wu, A. C. F.; Verboncoeur, J. P. Numerical solution of the cylindrical Poisson equation using the local Taylor polynomial technique. (English) Zbl 1251.65167 J. Comput. Phys. 231, No. 16, 5421-5442 (2012). MSC: 65N75 35Q05 65N30 35J05 PDFBibTeX XMLCite \textit{R. H. Jackson} et al., J. Comput. Phys. 231, No. 16, 5421--5442 (2012; Zbl 1251.65167) Full Text: DOI
Fraysse, F.; de Vicente, J.; Valero, E. The estimation of truncation error by \(\tau \)-estimation revisited. (English) Zbl 1242.65222 J. Comput. Phys. 231, No. 9, 3457-3482 (2012). MSC: 65N15 65L70 35J05 65N55 65N08 65L10 34B05 35J60 65L12 34B15 PDFBibTeX XMLCite \textit{F. Fraysse} et al., J. Comput. Phys. 231, No. 9, 3457--3482 (2012; Zbl 1242.65222) Full Text: DOI Link
Napov, Artem; Notay, Yvan Algebraic analysis of aggregation-based multigrid. (English) Zbl 1249.65270 Numer. Linear Algebra Appl. 18, No. 3, 539-564 (2011). Reviewer: Ivana Pultarová (Praha) MSC: 65N55 65F08 65N22 35J05 65N12 65F50 65F10 PDFBibTeX XMLCite \textit{A. Napov} and \textit{Y. Notay}, Numer. Linear Algebra Appl. 18, No. 3, 539--564 (2011; Zbl 1249.65270) Full Text: DOI Link
Chen, Zhongying; Cheng, Dongsheng; Feng, Wei; Wu, Tingting; Yang, Hongqi A multigrid-based preconditioned Krylov subspace method for the Helmholtz equation with PML. (English) Zbl 1231.65198 J. Math. Anal. Appl. 383, No. 2, 522-540 (2011). Reviewer: Murli Gupta (Washington, D. C.) MSC: 65N06 65N55 35J05 65F10 65F08 PDFBibTeX XMLCite \textit{Z. Chen} et al., J. Math. Anal. Appl. 383, No. 2, 522--540 (2011; Zbl 1231.65198) Full Text: DOI
Chaigne, Benoît; Désidéri, Jean-Antoine Convergence of a two-level ideal algorithm for a parametric shape inverse model problem. (English) Zbl 1220.65075 Inverse Probl. Sci. Eng. 19, No. 3, 363-393 (2011). MSC: 65K10 49Q10 49M05 49N45 49M25 PDFBibTeX XMLCite \textit{B. Chaigne} and \textit{J.-A. Désidéri}, Inverse Probl. Sci. Eng. 19, No. 3, 363--393 (2011; Zbl 1220.65075) Full Text: DOI
Guillet, Thomas; Teyssier, Romain A simple multigrid scheme for solving the Poisson equation with arbitrary domain boundaries. (English) Zbl 1220.65171 J. Comput. Phys. 230, No. 12, 4756-4771 (2011). MSC: 65N55 65N06 35J05 65N50 65N12 65F10 PDFBibTeX XMLCite \textit{T. Guillet} and \textit{R. Teyssier}, J. Comput. Phys. 230, No. 12, 4756--4771 (2011; Zbl 1220.65171) Full Text: DOI arXiv Link
Zubair, H. Bin; MacLachlan, S. P.; Oosterlee, C. W. A geometric multigrid method based on \(L\)-shaped coarsening for PDEs on stretched grids. (English) Zbl 1240.65365 Numer. Linear Algebra Appl. 17, No. 6, 871-894 (2010). MSC: 65N55 65N08 65N50 35J05 65Y20 65N12 PDFBibTeX XMLCite \textit{H. B. Zubair} et al., Numer. Linear Algebra Appl. 17, No. 6, 871--894 (2010; Zbl 1240.65365) Full Text: DOI
Reps, Bram; Vanroose, Wim; bin Zubair, Hisham On the indefinite Helmholtz equation: Complex stretched absorbing boundary layers, iterative analysis, and preconditioning. (English) Zbl 1210.65182 J. Comput. Phys. 229, No. 22, 8384-8405 (2010). Reviewer: Adrian Carabineanu (Bucureşti) MSC: 65N06 35J05 65N55 65F08 65F10 PDFBibTeX XMLCite \textit{B. Reps} et al., J. Comput. Phys. 229, No. 22, 8384--8405 (2010; Zbl 1210.65182) Full Text: DOI arXiv
Ge, Yongbin Multigrid method and fourth-order compact difference discretization scheme with unequal meshsizes for 3D Poisson equation. (English) Zbl 1197.65169 J. Comput. Phys. 229, No. 18, 6381-6391 (2010). MSC: 65N06 35J05 65F10 65F50 65N50 65N55 65Y20 PDFBibTeX XMLCite \textit{Y. Ge}, J. Comput. Phys. 229, No. 18, 6381--6391 (2010; Zbl 1197.65169) Full Text: DOI
Umetani, N.; MacLachlan, S. P.; Oosterlee, C. W. A multigrid-based shifted Laplacian preconditioner for a fourth-order Helmholtz discretization. (English) Zbl 1224.65078 Numer. Linear Algebra Appl. 16, No. 8, 603-626 (2009). Reviewer: Roman Kohut (Ostrava) MSC: 65F08 65F10 65N55 35J05 65N06 65N12 PDFBibTeX XMLCite \textit{N. Umetani} et al., Numer. Linear Algebra Appl. 16, No. 8, 603--626 (2009; Zbl 1224.65078) Full Text: DOI
Wang, Yin; Zhang, Jun Sixth order compact scheme combined with multigrid method and extrapolation technique for 2D Poisson equation. (English) Zbl 1157.65469 J. Comput. Phys. 228, No. 1, 137-146 (2009). MSC: 65N06 65N55 PDFBibTeX XMLCite \textit{Y. Wang} and \textit{J. Zhang}, J. Comput. Phys. 228, No. 1, 137--146 (2009; Zbl 1157.65469) Full Text: DOI
MacLachlan, S. P.; Tang, J. M.; Vuik, C. Fast and robust solvers for pressure-correction in bubbly flow problems. (English) Zbl 1317.76062 J. Comput. Phys. 227, No. 23, 9742-9761 (2008). MSC: 76M25 76T10 65F10 65M06 65M55 65M22 PDFBibTeX XMLCite \textit{S. P. MacLachlan} et al., J. Comput. Phys. 227, No. 23, 9742--9761 (2008; Zbl 1317.76062) Full Text: DOI Link
Erlangga, Yogi A. Advances in iterative methods and preconditioners for the Helmholtz equation. (English) Zbl 1158.65078 Arch. Comput. Methods Eng. 15, No. 1, 37-66 (2008). Reviewer: Sui Sun Cheng (Hsinchu) MSC: 65N06 65F10 65N55 65F35 35J05 PDFBibTeX XMLCite \textit{Y. A. Erlangga}, Arch. Comput. Methods Eng. 15, No. 1, 37--66 (2008; Zbl 1158.65078) Full Text: DOI
Kasbah, Safaa J.; Damaj, Issam W.; Haraty, Ramzi A. Multigrid solvers in reconfigurable hardware. (English) Zbl 1131.65096 J. Comput. Appl. Math. 213, No. 1, 79-94 (2008). MSC: 65N55 35J05 65F10 65N06 65N12 65Y05 65Y15 PDFBibTeX XMLCite \textit{S. J. Kasbah} et al., J. Comput. Appl. Math. 213, No. 1, 79--94 (2008; Zbl 1131.65096) Full Text: DOI arXiv
Wang, Jie; Zhong, Weijun; Zhang, Jun A general meshsize fourth-order compact difference discretization scheme for 3D Poisson equation. (English) Zbl 1109.65090 Appl. Math. Comput. 183, No. 2, 804-812 (2006). MSC: 65N06 35J05 65N50 65F10 65F50 65N12 PDFBibTeX XMLCite \textit{J. Wang} et al., Appl. Math. Comput. 183, No. 2, 804--812 (2006; Zbl 1109.65090) Full Text: DOI
Singh, K. M.; Williams, J. J. R. A parallel fictitious domain multigrid preconditioner for the solution of Poisson’s equation in complex geometries. (English) Zbl 1093.65104 Comput. Methods Appl. Mech. Eng. 194, No. 45-47, 4845-4860 (2005). MSC: 65N06 65Y05 80M20 76F35 65N55 65F10 65F35 80A20 76M20 35J05 PDFBibTeX XMLCite \textit{K. M. Singh} and \textit{J. J. R. Williams}, Comput. Methods Appl. Mech. Eng. 194, No. 45--47, 4845--4860 (2005; Zbl 1093.65104) Full Text: DOI
Patidar, Kailash C. Dispersion induced by the pollution for the wave equation. (English) Zbl 1063.65126 Appl. Math. Comput. 160, No. 2, 329-341 (2005). MSC: 65N30 35J05 PDFBibTeX XMLCite \textit{K. C. Patidar}, Appl. Math. Comput. 160, No. 2, 329--341 (2005; Zbl 1063.65126) Full Text: DOI
Mohr, Marcus; Wienands, Roman Cell-centred multigrid revisited. (English) Zbl 1070.65128 Comput. Vis. Sci. 7, No. 3-4, 129-140 (2004). MSC: 65N55 35J25 92C55 35J05 65N30 PDFBibTeX XMLCite \textit{M. Mohr} and \textit{R. Wienands}, Comput. Vis. Sci. 7, No. 3--4, 129--140 (2004; Zbl 1070.65128) Full Text: DOI
Singh, K. M.; Williams, J. J. R. Application of the additive Schwarz method to large scale Poisson problems. (English) Zbl 1038.65137 Commun. Numer. Methods Eng. 20, No. 3, 193-205 (2004). MSC: 65N55 65F10 65N06 65Y05 35J05 65F35 PDFBibTeX XMLCite \textit{K. M. Singh} and \textit{J. J. R. Williams}, Commun. Numer. Methods Eng. 20, No. 3, 193--205 (2004; Zbl 1038.65137) Full Text: DOI
Eroshin, A. E. Investigation of the convergence rate of multigrid method on quasi-nested adaptive grids. (English) Zbl 1083.65101 Russ. J. Numer. Anal. Math. Model. 18, No. 5, 377-395 (2003). Reviewer: Ramaz Botchorishvili (Tbilisi) MSC: 65N12 65N55 65N30 35J05 65N50 PDFBibTeX XMLCite \textit{A. E. Eroshin}, Russ. J. Numer. Anal. Math. Model. 18, No. 5, 377--395 (2003; Zbl 1083.65101) Full Text: DOI
Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray Parallel multigrid smoothing: Polynomial versus Gauss–Seidel. (English) Zbl 1022.65030 J. Comput. Phys. 188, No. 2, 593-610 (2003). MSC: 65F10 65Y05 65N55 35J05 35Q80 35Q72 PDFBibTeX XMLCite \textit{M. Adams} et al., J. Comput. Phys. 188, No. 2, 593--610 (2003; Zbl 1022.65030) Full Text: DOI
Zhang, Jun Multigrid method and fourth-order compact scheme for 2D Poisson equation with unequal mesh-size discretization. (English) Zbl 1005.65137 J. Comput. Phys. 179, No. 1, 170-179 (2002). MSC: 65N55 65N12 65N06 65F10 35J05 PDFBibTeX XMLCite \textit{J. Zhang}, J. Comput. Phys. 179, No. 1, 170--179 (2002; Zbl 1005.65137) Full Text: DOI Link
Kouatchou, Jules; Zhang, Jun Optimal injection operator and high order schemes for multigrid solution of 3D Poisson equation. (English) Zbl 0968.65103 Int. J. Comput. Math. 76, No. 2, 173-190 (2000). Reviewer: Gerald W.Hedstrom (Pleasanton) MSC: 65N55 65N06 65F10 35J05 PDFBibTeX XMLCite \textit{J. Kouatchou} and \textit{J. Zhang}, Int. J. Comput. Math. 76, No. 2, 173--190 (2000; Zbl 0968.65103) Full Text: DOI
Griebel, Michael; Zumbusch, Gerhard Parallel adaptive subspace correction schemes with applications to elasticity. (English) Zbl 0980.74079 Comput. Methods Appl. Mech. Eng. 184, No. 2-4, 303-332 (2000). MSC: 74S99 74B05 65Y05 65N55 PDFBibTeX XMLCite \textit{M. Griebel} and \textit{G. Zumbusch}, Comput. Methods Appl. Mech. Eng. 184, No. 2--4, 303--332 (2000; Zbl 0980.74079) Full Text: DOI
Othman, M.; Abdullah, A. R. An efficient multigrid Poisson solver. (English) Zbl 0958.65129 Int. J. Comput. Math. 71, No. 4, 541-553 (1999). Reviewer: Steve F.McCormick (Boulder) MSC: 65N55 65N06 35J05 65F10 PDFBibTeX XMLCite \textit{M. Othman} and \textit{A. R. Abdullah}, Int. J. Comput. Math. 71, No. 4, 541--553 (1999; Zbl 0958.65129) Full Text: DOI Link
Zhang, Jun VML: a class of virtual multi-level iterative methods for solving partial differential equations. (English) Zbl 0942.65035 Appl. Math. Comput. 92, No. 1, 29-48 (1998). MSC: 65F10 65N06 65N55 35J05 PDFBibTeX XMLCite \textit{J. Zhang}, Appl. Math. Comput. 92, No. 1, 29--48 (1998; Zbl 0942.65035) Full Text: DOI
Zhang, Jun Two-grid analysis of minimal residual smoothing as a multigrid acceleration technique. (English) Zbl 0943.65150 Appl. Math. Comput. 96, No. 1, 27-45 (1998). MSC: 65N55 65F10 35J05 65N06 65N12 PDFBibTeX XMLCite \textit{J. Zhang}, Appl. Math. Comput. 96, No. 1, 27--45 (1998; Zbl 0943.65150) Full Text: DOI
Othman, Mohamed Bin; Abdullah, Abdul Rahman Bin The halfsweeps multigrid method as a fast multigrid Poisson solver. (English) Zbl 0936.65143 Int. J. Comput. Math. 69, No. 3-4, 319-329 (1998). MSC: 65N55 65F10 35J25 65N06 PDFBibTeX XMLCite \textit{M. B. Othman} and \textit{A. R. B. Abdullah}, Int. J. Comput. Math. 69, No. 3--4, 319--329 (1998; Zbl 0936.65143) Full Text: DOI Link
Zhang, Jun Fast and high accuracy multigrid solution of the three dimensional Poisson equation. (English) Zbl 0927.65141 J. Comput. Phys. 143, No. 2, 449-461 (1998). Reviewer: M.Jung (Chemnitz) MSC: 65N55 65N06 65F10 35J05 65N12 PDFBibTeX XMLCite \textit{J. Zhang}, J. Comput. Phys. 143, No. 2, 449--461 (1998; Zbl 0927.65141) Full Text: DOI Link
Zhang, Jun A cost-effective multigrid projection operator. (English) Zbl 0873.65106 J. Comput. Appl. Math. 76, No. 1-2, 325-333 (1996). Reviewer: W.Gander (Zürich) MSC: 65N55 65F10 35J05 65N06 PDFBibTeX XMLCite \textit{J. Zhang}, J. Comput. Appl. Math. 76, No. 1--2, 325--333 (1996; Zbl 0873.65106) Full Text: DOI
Zhang, Jun Acceleration of five-point red-black Gauss-Seidel in multigrid for Poisson equation. (English) Zbl 0870.65023 Appl. Math. Comput. 80, No. 1, 73-93 (1996). Reviewer: A.Meister (Hamburg) MSC: 65F10 35J05 65N06 65N55 PDFBibTeX XMLCite \textit{J. Zhang}, Appl. Math. Comput. 80, No. 1, 73--93 (1996; Zbl 0870.65023) Full Text: DOI