An extrapolation accelerated multiscale Newton-MG method for fourth-order compact discretizations of semilinear Poisson equations
An extrapolation accelerated multiscale Newton-multigrid (EMNMG) method is proposed to solve two-dimensional semilinear Poisson equations. The nine-point fourth-order compact schemes are used to approximate the nonlinear Poisson equations. In order to accelerate Newton-MG method for calculating the...
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| Veröffentlicht in: | Computers & mathematics with applications (1987) Jg. 113; S. 189 - 197 |
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01.05.2022
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| Abstract | An extrapolation accelerated multiscale Newton-multigrid (EMNMG) method is proposed to solve two-dimensional semilinear Poisson equations. The nine-point fourth-order compact schemes are used to approximate the nonlinear Poisson equations. In order to accelerate Newton-MG method for calculating the finite difference (FD) solution on the finest grid, a quite good initial guess is constructed from the fourth-order FD solutions at two coarse levels by using Richardson extrapolation and bi-quartic polynomial interpolation, which greatly reduces the number of Newton iterations required. A completed extrapolation technique is adopted to generate a sixth-order extrapolated solution on entire finest grid cheaply. Numerical results are given to show that our proposed EMNMG algorithm can achieve high accuracy and keep less cost simultaneously. |
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| AbstractList | An extrapolation accelerated multiscale Newton-multigrid (EMNMG) method is proposed to solve two-dimensional semilinear Poisson equations. The nine-point fourth-order compact schemes are used to approximate the nonlinear Poisson equations. In order to accelerate Newton-MG method for calculating the finite difference (FD) solution on the finest grid, a quite good initial guess is constructed from the fourth-order FD solutions at two coarse levels by using Richardson extrapolation and bi-quartic polynomial interpolation, which greatly reduces the number of Newton iterations required. A completed extrapolation technique is adopted to generate a sixth-order extrapolated solution on entire finest grid cheaply. Numerical results are given to show that our proposed EMNMG algorithm can achieve high accuracy and keep less cost simultaneously. |
| Author | Hu, Hongling Li, Ming Wu, Pinxia Pan, Kejia |
| Author_xml | – sequence: 1 givenname: Hongling surname: Hu fullname: Hu, Hongling organization: MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, China – sequence: 2 givenname: Ming orcidid: 0000-0003-4183-2404 surname: Li fullname: Li, Ming email: mathlm@126.com organization: Department of Mathematics and Statistics, Honghe University, Mengzi, Yunnan 661199, China – sequence: 3 givenname: Kejia orcidid: 0000-0001-5768-7972 surname: Pan fullname: Pan, Kejia organization: School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, China – sequence: 4 givenname: Pinxia surname: Wu fullname: Wu, Pinxia organization: School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, China |
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| Cites_doi | 10.1016/j.cam.2014.03.021 10.1016/j.jcp.2010.04.048 10.1016/j.camwa.2013.06.008 10.1006/jcph.1996.5466 10.1006/jcph.2002.7049 10.1007/s10915-016-0275-9 10.1002/num.20529 10.1002/cnm.1640090502 10.1016/j.jcp.2021.110794 10.1016/j.jcp.2017.04.069 10.1016/j.camwa.2017.05.023 10.1016/j.jcp.2011.02.027 10.1137/S1064827501357190 10.1007/s11425-008-0119-7 10.4208/eajam.090120.260320 10.1137/13092349X 10.1016/j.camwa.2017.02.020 10.1002/(SICI)1099-0887(199707)13:7<573::AID-CNM84>3.0.CO;2-6 10.1016/j.jcp.2008.09.002 10.1137/0905005 10.1016/j.camwa.2015.12.007 10.1137/040615195 10.1016/j.camwa.2018.12.024 10.1007/s11075-015-0018-2 |
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| Keywords | Extrapolation Poisson equation Fourth-order compact scheme Nonlinear term Multigrid algorithm |
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| Snippet | An extrapolation accelerated multiscale Newton-multigrid (EMNMG) method is proposed to solve two-dimensional semilinear Poisson equations. The nine-point... |
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| SubjectTerms | Algorithms Discretization Extrapolation Finite difference method Fourth-order compact scheme Interpolation Multigrid algorithm Nonlinear term Poisson equation Polynomials |
| Title | An extrapolation accelerated multiscale Newton-MG method for fourth-order compact discretizations of semilinear Poisson equations |
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