LEADER 04663nam 22006611a 450 001 9911004742303321 005 20241120174745.0 010 $a1-61197-075-X 024 7 $a10.1137/1.9781611970753 035 $a(CKB)2670000000108417 035 $a(CaBNVSL)gtp00547935 035 $a(SIAM)9781611970753 035 $a(SSID)ssj0000527722 035 $a(PQKBManifestationID)12179481 035 $a(PQKBTitleCode)TC0000527722 035 $a(PQKBWorkID)10544675 035 $a(PQKB)10254186 035 $a(CaBNVSL)gtp00547935 035 $a(PPN)191741531 035 $a(EXLCZ)992670000000108417 071 50$aCL67$bSIAM 100 $a20110315d2011 uy 0 101 0 $aeng 135 $aurbn||||m|||a 181 $ctxt 182 $cc 183 $acr 200 10$aMultigrid techniques $e1984 guide with applications to fluid dynamics /$fAchi Brandt, Oren E. Livne 205 $aRev. ed. 210 $aPhiladelphia, Pa. $cSociety for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104)$d2011 215 $a1 electronic text (xxii, 218 p.) $cdigital file 225 1 $aClassics in applied mathematics ;$v67 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a1-61344-319-6 311 $a1-61197-074-1 320 $aIncludes bibliographical references and index. 327 $aList of figures -- List of tables -- Preface to Classics edition -- Preface -- Chapter 0. Introduction -- Chapter 1. Elementary acquaintance with Multigrid -- 327 $aPart I. Stages in developing fast solvers. Chapter 2. Stable discretization -- Chapter 3. Interior relaxation and smoothing factors -- Chapter 4. Interior two-level cycles -- Chapter 5. Boundary conditions and two-level cycling -- Chapter 6. Many-level cycles -- Chapter 7. Full Multi-Grid (FMG) algorithms -- Part II. Advanced techniques and insights -- Chapter 8. Full approximation scheme (FAS) and applications -- Chapter 9. Local refinements and grid adaptation -- Chapter 10. Higher-order techniques -- Chapter 11. Coarsening guided by discretization -- Chapter 12. True role of relaxation -- Chapter 13. Dealgebraization of Multigrid -- Chapter 14. Practical role of rigorous analysis and quantitative predictions -- Chapter 15. Chains of problems. frozen [tau] -- Chapter 16. Time dependent problems -- 327 $aPart II. Applications to fluid dynamics. Chapter 17. Cauchy-Riemann equations -- Chapter 18. Steady-state Stokes equations -- Chapter 19. Steady-state incompressible Navier-Stokes equations -- Chapter 20. Compressible Navier-Stokes and Euler equations -- Chapter 21. Remarks on solvers for transonic potential equations -- Appendix. Test cycle: MATLAB code -- Bibliography -- Index. 330 $aThis classic text presents the best practices of developing multigrid solvers for large-scale computational problems in science and engineering. By representing a problem at multiple scales and employing suitable interscale interactions, multigrid avoids slowdown due to stiffness and reduces the computational cost of classical algorithms by orders of magnitude. Starting from simple examples, this book guides the reader through practical stages for developing reliable multigrid solvers, methodically supported by accurate performance predictors. The revised edition presents discretization and fast solution of linear and nonlinear partial differential systems; treatment of boundary conditions, global constraints and singularities; grid adaptation, high-order approximations, and system design optimization; applications to fluid dynamics, from simple models to advanced systems; new quantitative performance predictors, a MATLABʼ sample code, and more. Readers will also gain access to the Multigrid Guide 2.0 Web site, where updates and new developments will be continually posted, including a chapter on Algebraic Multigrid. 410 0$aClassics in applied mathematics ;$v67. 606 $aFluid dynamics$xMathematics 606 $aMultigrid methods (Numerical analysis) 606 $aDifferential equations, Partial$xNumerical solutions 615 0$aFluid dynamics$xMathematics. 615 0$aMultigrid methods (Numerical analysis) 615 0$aDifferential equations, Partial$xNumerical solutions. 676 $a532/.05015182 700 $aBrandt$b Achi$0723633 701 $aLivne$b Oren E$0723632 712 02$aSociety for Industrial and Applied Mathematics. 801 0$bCaBNVSL 801 1$bCaBNVSL 801 2$bCaBNVSL 906 $aBOOK 912 $a9911004742303321 996 $aMultigrid techniques$91417838 997 $aUNINA