Marching Methods for Elliptic Problems: Part 1

References

• Hockney , R. W. 1965 . A Fast Direct Solution of Poisson's Equation Using Fourier Analysis . J. Assoc. Comput. Mach. , vol. 12 : 95 – 113 .
   Web of Science ®Google Scholar
• Hockney , R. W. 1970 . “ The Potential Calculation and Some Applications ” . In Methods in Computational Physics, Vol. 9, Plasma Physics , Edited by: Alder , B. , Fernbach , S. and Rotenberg , M. 134 – 210 . New York : Academic Press .
   Google Scholar
• Buneman , O. May 1969 . A Compact Non-Iterative Poisson Solver , May , Stanford, Calif. : Stanford Univ. . SUIPR Rept. 294
   Google Scholar
• Buzbee , B. L. , Golub , G. H. and Nielson , C. W. 1969 . The Method of Odd-Even Reduction and Factorization with Application to Poisson's Equation Los Alamos Sci. Lab. Rept. LA-4141, Los Alamos, N. M.
   Google Scholar
• Dorr , F. W. 1970 . The Direct Solution of the Discrete Poisson Equation on a Rectangle . SIAM Rev. , vol. 12 ( 2 ) Apr. : 248 – 263 .
   Google Scholar
• LeBail , R. C. 1972 . Use of Fast Fourier Transforms for Solving Partial Differential Equations in Physics . J. Comput. Phys. , vol. 9 ( 3 ) June : 440 – 465 .
   Google Scholar
• Weinberger , H. F. 1965 . Partial Differential Equations , 51 New York : Blaisdell Publishing Co. .
   Google Scholar
• Roache , P. J. . A New Direct Method for the Discretized Poisson Equation . Lecture Notes in Physics, Vol. 8, Proc. Second International Conference on Numerical Methods in Fluid Mechanics . Edited by: Holt , M. pp. 48 – 53 . New York : Springer .
   Google Scholar
• Roache , P. J. 1971 . A Direct Method for the Discretized Poisson Equation, Sandia Labs Rept. SC-RR-70–579, Albuquerque, N. M.
   Google Scholar
• Roache , P. J. 1976 . Computational Fluid Dynamics, , rev. printing , Albuquerque, N. M. : Hermosa Publishers .
   Google Scholar
• Ishizaki , H. Aug. 1957 . On the Numerical Solution of Harmonic, Biharmonic and Similar Equations by the Difference Method Not through Successive Approximations , Aug. , Kyoto, , Japan : Kyoto Univ. . Disaster Prevention Research Inst. Bull. 18
   Google Scholar
• Bickley , W. G. and McNamee , J. 1960 . Matrix and Other Direct Methods for the Solution of Systems of Linear Difference Equations . Proc. Roy. Soc. London, Ser. A , vol. 252 Jan. : 69 – 131 .
   Google Scholar
• Booy , M. L. 1966 . A Noniterative Numerical Solution of Poisson's and Laplace's Equations with Applications to Slow Viscous Flow . J. Basic Eng. , Dec. : 725 – 733 .
   Google Scholar
• Hirota , I. , Tokioka , T. and Nishiguchi , M. 1970 . A Direct Solution of Poisson's Equation by Generalized Sweep-Out Method . J. Meteorol. Soc. Jpn., Ser. II , vol. 48 ( 2 ) Apr. : 161 – 167 .
   Google Scholar
• Schechter , S. 1960 . Quasi-Tridiagonal Matrices and Type-Insensitive Difference Equations . Q. Appl. Math. , vol. 19 : 285 – 295 .
   Google Scholar
• Lucey , J. W. and Hansen , K. F. 1964 . A Stable Method of Matrix Factorization . Trans. Am. Nucl. Soc. , vol. 7 : 259
   Google Scholar
• Coleman , R. 1968 . The Numerical Solution of Linear Elliptic Equations . J. Lubr. Technol., Ser. F , vol. 90 : 773 – 776 .
   Google Scholar
• Angel , E. and Bellman , R. 1972 . Dynamic Programming and Partial Differential Equations , New York : Academic Press .
   Google Scholar
• Dorr , F. W. 1975 . The Direct Solution of the Discrete Poisson Equation in O(N2) Operations . SIAM Rev. , vol. 17 ( 3 ) : 412 – 415 .
   Google Scholar
• Bank , R. E. and Rose , D. J. 1975 . An O(n2) Method for Solving Constant Coefficient Boundary Value Problems in Two Dimensions . SIAM J. Numer. Anal. , vol. 12 ( 4 ) : 529 – 539 .
   Google Scholar
• Dietrich , D. , McDonald , B. E. and Warn-Varnas , A. 1975 . Optimized Block-Implicit Relaxation . J. Comput. Phys. , vol. 18 ( 4 ) : 421 – 439 .
   Google Scholar
• Yee , S. Y. K. 1976 . An Efficient Method for a Finite-Difference Solution of the Poisson Equation on the Surface of a Sphere . J. Comput. Phys. , vol. 22 ( 2 ) : 215 – 228 .
   Google Scholar
• Bank , R. E. and Rose , D. J. 1975 . Marching Algorithms for Elliptic Boundary Value Problems. I. The Constant Coefficient Case , Cambridge, Mass. : Harvard Univ. . Aiken Computation Lab. TR 14–75
   Google Scholar
• Bank , R. E. 1975 . Marching Algorithms for Elliptic Boundary Value Problems. II. The Non-Constant Coefficient Case , Cambridge, Mass. : Harvard Univ. . Aiken Computation Lab. TR 16–75
   Google Scholar
• Bank , R. E. . Marching Algorithms and Block Gaussian Elimination . Proc. Argonne Conference on Sparse Matrix Computations . Argonne, III..
   Google Scholar
• Blum , E. K. 1972 . Numerical Analysis and Computation: Theory and Practice , 109 Reading, Mass. : Addison-Wesley Publishing Co. .
   Google Scholar
• Dahlquist , G. and Björck , Å. 1974 . Numerical Methods , Edited by: Anderson , N. Englewood Cliffs, N. J. : Prentice-Hall, Inc. .
   Google Scholar
• Bailey , C. B. Jan. 1970 . A Guide to the Sandia Mathematical Program Library Jan. , Albuquerque, N. M. Sandia Labs. Rept. SC-M-69–337
   Google Scholar
• Salvodori , M. G. and Baron , M. L. 1961 . Numerical Methods in Engineering, , 2nd ed. , Englewood Cliffs, N. J. : Prentice-Hall .
   Google Scholar
• Roache , P. J. Dec. 1972 . Finite Difference Methods for the Steady-State Navier-Stokes Equations, Sandia Labs Dec. , Albuquerque, N. M. Rept. SC-RR-72–0419. (See also Lecture Notes in Physics, vol. 18, pp. 138–145, Springer, New York, 1973.)
   Google Scholar
• Roache , P. J. 1975 . The LAD, NOS and Split NOS Methods for the Steady-State Navier-Stokes Equations . Comput. Fluids , vol. 3 : 179 – 195 .
   Google Scholar
• Roache , P. J. . The Split NOS and BID Methods for the Steady-State Navier-Stokes Equations . Lecture Notes in Physics, Vol. 35, Proc. Fourth International Conference on Numerical Methods in Fluid Dynamics . Edited by: Richtmyer , R. D. pp. 347 – 352 . New York : Springer .
   Google Scholar
• Roache , P. J. and Ellis , M. A. 1975 . The BID Method for the Steady-State Navier-Stokes Equations . Comput. Fluids , vol. 3 : 305 – 320 .
   Google Scholar
• Roache , P. J. 1977 . A Semidirect Method for Internal Flows in Flush Inlets, AIAA Pap. 77–647 . Proc. 3rd AIAA Conference on Computational Fluid Dynamics . June 27–28 1977 , Albuquerque, N. M..
   Google Scholar
• Price , H. S. , Varga , R. S. and Warren , J. E. 1966 . Applications of Oscillation Matrices to Diffusion-Convection Equations . J. Math. Phys. , vol. 45 : 301 – 311 .
   Web of Science ®Google Scholar
• Warming , R. F. and Beam , R. M. 1976 . Upwind Second-Order Difference Schemes and Applications in Aerodynamic Flows . AIAA J. , vol. 14 ( 9 ) Sept. : 1241 – 1249 .
   Google Scholar
• Atias , M. , Wolfshtein , M. and Israeli , M. 1977 . Efficiency of Navier-Stokes Solvers . AIAA J. , vol. 15 ( 2 ) Feb. : 263 – 266 .
   Google Scholar
• Harris , J. E. and Morris , D. J. 1975 . “ Solution of Three-Dimensional Boundary-Layer Equations with Comparisons to Experimental Data ” . In Lecture Notes in Physics, Vol. 35, Proc. Fourth International Conference on Numerical Methods in Fluid Dynamics , Edited by: Richtmyer , R. D. 204 – 211 . New York : Springer .
   Google Scholar
• Keller , H. B. and Cebeci , T. 1972 . Accurate Numerical Methods for Boundary Layer Flows. II. Two-Dimensional Turbulent Flows . AIAA J. , vol. 10 ( 9 ) Sept. : 1193 – 1199 .
   Google Scholar
• Hildebrand , F. B. 1968 . Finite-Difference Equations and Simulations , 95 Englewood Cliffs, N. J. : Prentice-Hall .
   Google Scholar
• Abramovitch , M. and Stegun , I. A. , eds. 1970 . Handbook of Mathematical Functions , 884 New York : Dover Publications . 9th printing, equation 25.3.27
   Google Scholar