Preview

Selected image

ΕΠΙΣΤΗΜΟΝΙΚΟΙ ΥΠΟΛΟΓΙΣΜΟΙ

(TMA386) -  Χρήστος Παπαδόπουλος-Φιλέλης

Course Description

Το μάθημα Επιστημονικοί Υπολογισμοί (Scientific Computing) εισάγει βασικές αριθμητικές μεθόδους για την επίλυση σύνθετων μαθηματικών προβλημάτων με τη βοήθεια υπολογιστών. Καλύπτει την επίλυση μεγάλων γραμμικών συστημάτων με επαναληπτικές μεθόδους, τον υπολογισμό ιδιοτιμών και ιδιοδιανυσμάτων, την αριθμητική επίλυση μη γραμμικών εξισώσεων, καθώς και τη διακριτοποίηση και επίλυση μερικών διαφορικών εξισώσεων με πεπερασμένες διαφορές. Έμφαση δίνεται στην κατανόηση της σύγκλισης, της αριθμητικής ευστάθειας, της υπολογιστικής αποδοτικότητας και στην πρακτική εφαρμογή των μεθόδων σε προβλήματα επιστήμης και μηχανικής.

Creation Date

Thursday, March 10, 2011

Course page

  • Syllabus

    Βιβλιογραφία

    1. AKIN J.E. (1982): Application and implementation of finite element method, Academic Press.
    2. AMES W.F. (1977): Numerical methods for partial differential equations, Academic Press.
    3. ATKINSON K.E. (1989): An Introduction to Numerical Analysis (second edition), John Wiley & Sons.
    4. AXELSSON O. (1994): Iterative solution methods, Cambridge University Press.
    5. ΑΖΙΖ Α.Κ. (1972): The mathematical foundation of the finite element method wih applications to partial differential equations, Academic Press.
    6. BECKER E.B., CAREY G.F., ODEN J.T. (1981): Finite Elements: An Introduction, Vol. 1, Prentice-Hall.
    7. BERTSEKAS D.P. and TSITSIKLIS, J.N. (1989): Parallel and Distributed Computation, Numerical Methods, Prentice-Hall.
    8. CHAPMAN S. (2001): MATLAB Programming for Engineers, Thomson Learning.
    9. CIARLET P.G. (1977): The finite element method for elliptic problems, North Holland.
    10. COLEMAN, T.F. and C. VAN LOAN (1988): Handbook for Matrix Computations, SIAM.
    11. COLLATZ L. (1960): The Numerical treatment of differential equations, Springer-Verlag.
    12. CONTE S.D., DE BOOR C. (1980): Elementary Numerical Analysis, Mc Graw-Hill.
    13. DAHLQUIST G. and BJORCK A. (1974): Numerical Methods, Prentice-Hall.
    14. DANAILA I., JOLY P., KABER S.M. AND POSTEL M. (2006): An introduction to scientific computing: Twelve application projects solved by MATLAB, Springer.
    15. DEMMEL J. W. (1997): Applied Numerical Linear Algebra, SIAM.
    16. DUFF I.S., ERISMAN A.M. and REID J.K. (1986): Direct Methods for Sparse Matrices, Clarendon Press.
    17. EVANS, D.J. (1985): Sparsity and Applications, Cambridge University Press.
    18. EVANS D.J. (1974): Software for Numerical Mathematics, Academic Press.
    19. FADEEVA V.N. (1959): Computational methods of Linear Algebra, transl. C.D. Benster, Dover.
    20. FORSYTHE G.E., MALCOLM M., MOLER C.B. (1977): Computer Methods for mathematical Computations, Prentice Hall.
    21. FORSYTHE G.E. and MOLER C.B. (1967): Computer solution of linear algebraic systems, Prentice Hall.
    22. FOX L. AND MAYERS D.F. (1968): Computing methods for scientists and engineers, Oxford University Press.
    23. FROBERG C.E. (1969): Introduction to Numerical Analysis, Addison Wesley.
    24. FROBERG C.E. (1985): Numerical Mathematics: Theory and Computer Applications, Benjamin/Cummings Publishing Company.
    25. GEORGE J.A. and LIU J.W.H. (1981): Computer Solution of Large Sparse Positive Definite Systems, Prentice Hall.
    26. GERALD C.F., WHEATLEY P.O. (1984): Applied Numerical Analysis, Addison Wesley.
    27. GILBERT J., MOLER C. AND SCHREIBER R. (1992): Sparse Matrices in MATLAB: Design and Implementation, SIAM J. on Matrix Analysis and Applications, 13, pp. 333-356.
    28. GOLUB G.H., VAN LOAN C.F. (1996): Matrix Computations, John Hopkins University Press.
    29. ΓΡΑΒΒΑΝΗΣ Γ.Α. και ΓΙΑΝΝΟΥΤΑΚΗΣ Κ.Μ. (2009): Προγραμματισμός με τη χρήση MATLAB, Εκδόσεις Γκιούρδας.
    30. ΓΡΑΒΒΑΝΗΣ Γ.Α. και ΓΙΑΝΝΟΥΤΑΚΗΣ Κ.Μ. (2010): Εισαγωγή στο MATHEMATICA, Εκδόσεις: Εταιρεία Αξιοποίησης και Διαχείρισης της Περιουσίας του Δημοκρίτειου Πανεπιστημίου Θράκης.
    31. GREENBAUM A. (1997): Iterative methods for solving linear systems, SIAM.
    32. HAGEMAN L.A. and YOUNG D.M. (1981): Applied Iterative Methods, Academic Press.
    33. HENRICI P. (1964): Elements of Numerical Analysis, Wiley & Sons.
    34. HILDERBRAND F.B. (1974): Introduction to Numerical Analysis, Mc Graw-Hill.
    35. HOUSEHOLDER A.S. (1964): The theory of Matrices in Numerical Analysis, Blaisdell Publ Company.
    36. ISAACSON E., KELLER H.B. (1966): Analysis of Numerical Methods, Wiley & Sons.
    37. JENNINGS A. (1977): Matrix Computations for Engineers and Scientists, Wiley.
    38. KAHANER D., MOLER C. and NASH S. (1989): Numerical Methods and Software, Prentice-Hall.
    39. KINCAID D., CHENEY W. (1991): Numerical Analysis: Mathematics of Scientific Computing, Brooks-Cole.
    40. KINCAID D.R. and HAYES L.J. (1990): Iterative methods for large linear Systems, Academic Press.
    41. LAKSHMIKANTHAM V., TRIGIANTE D. (1988): Theory of difference equations, numerical methods and examples, Academic Press.
    42. LINDFIELD G. AND PENNY J. (1999): Numerical methods using MATLAB, Prentice Hall.
    43. ΛΥΠΙΤΑΚΗΣ Η.Α. (2006): Μαθηματικά πληροφορικής: Θέματα εφαρμοσμένης αριθμητικής ανάλυσης, Υπολογιστικές μέθοδοι και αλγοριθμικές τεχνικές επιστημονικών υπολογισμών, Τόμος 2 και 3, ΛΕΑ Εκδόσεις.
    44. MALEK-MADANI R. (1998): Advanced Engineering Mathematics with Mathematica and MATLAB, Pearson Higher Education.
    45. MITCHELL A.R. (1969): Computational Methods for Partial Differential Equations, John Wiley & Sons.
    46. MITCHELL A.R. and WAIT R. (1977): The finite element method, Wiley.
    47. MOLER C.B. (2004): Numerical Computing with MATLAB, SIAM.
    48. ΜΠΑΚΟΠΟΥΛΟΣ Α. (1981): Πεπερασμένα στοιχεία, Εκδόσεις Συμεών.
    49. NORRIE D.H., de VRIES G. (1973): The finite element method, Academic Press.
    50. NORRIE D.H., de VRIES G. (1975): The finite element method for engineers, Wiley.
    51. ODEN J.T. (1979): Applied Functional Analysis, Prentice Hall.
    52. ODEN J.T., REDDY J.N. (1976): An introduction to the mathematical theory of Finite Elements, Wiley.
    53. ORTEGA J.M. (1972): Numerical Analysis: A second course, Academic Press.
    54. ORTEGA J.M., RHEINBOLDT W.C. (1966): Iterative solution of non-linear equations in several variables, Academic Press.
    55. PARLETT B. (1980): The Symmetric Eigenvalue Problem, Prentice Hall.
    56. PARTER S. (1985): Large Scale scientific computations, Academic Press.
    57. PRESS W.H., TEUKOLSKY S., FLANNERY B., VETTERLING W. (1986): Numerical Recipes: The Art of Scientific Computing, Cambridge University Press.
    58. PRESS W.H., TEUKOLSKY S., FLANNERY B., VETTERLING W. (1986): Numerical Recipes: the art of scientific computing (Fortran), Cambridge University Press.
    59. PRESS W.H., TEUKOLSKY S., FLANNERY B., VETTERLING W. (1986): Numerical Recipes: the art of scientific computing in C, Cambridge University Press.
    60. QUARTERONI A. AND SALERI F. (2006): Scientific Computing with MATLAB and OCTAVE, Springer.
    61. RALSTON A., RABINOWITZ P. (1978): A first course in numerical analysis, Mc Graw-Hill.
    62. RICE J.R. (1983): Numerical methods, software and Analysis, McGraw-Hill.
    63. RICE J.R. (1983): Matrix Computations and mathematical software, McGraw-Hill.
    64. SAAD Y. (1996): Iterative methods for sparse linear systems, PWS.
    65. SMITH G.D. (1978): Numerical Solution of Partial Differential Equations: Finite Difference Methods, Clarendon Press.
    66. STRANG G. (1980): Linear Algebra and its Applications, Academic Press, 2nd edition.
    67. STRANG G. and FIX G.J. (1973): An analysis of the finite element method, Prentice Hall.
    68. TREFETHEN L. N. AND BAU D. (1997): Numerical Linear Algebra, SIAM.
    69. VARGA R.S. (1962): Matrix Iterative Analysis, Prentice Hall.
    70. WAIT R. (1979): The numerical solution of algebraic equations, John Wiley.
    71. WALL H.S. (1948): Analytic Theory of Continued Fractions, Van Nostrand.
    72. WATSON G.A. (1980): Approximation Theory and numerical methods, John Wiley.
    73. WHITEMAN J.R. (1973): Some aspects of the mathematics of FE, in the Mathematics of FE and Applications I, MAFELAP, Academic Press.
    74. WHITEMAN J.R. (1975): Some aspects of the mathematics of FE, in the Mathematics of FE and Applications II, MAFELAP, Academic Press.
    75. WILKINSON J.H. (1963): Rounding Errors in Algebraic Processes, H.M. Stationery Office, London.
    76. WILKINSON J.H. (1965): The Algebraic Eigenvalue Problem, Clarendon Press.
    77. WILKINSON J.H., REINSCH C. (1971): Linear Algebra: Handbook for Automatic Computation, v. 2, Springer-Verlag.
    78. YOUNG D.M. (1971): Iterative solution of Large Linear Systems, Academic Press.
    79. YOUNG D.M., GREGORY R.T. (1973): A survey of numerical mathematics, Vol II, Addison Wesley.
    80. YOUNG D.M., GREGORY R.T. (1972): A survey of numerical mathematics, Vol I, Addison Wesley.
    81. ZIENKIEWICZ O.C. (1977): The finite element method, Mc Graw-Hill.
    82. ZIENKIEWICZ O., MORGAN K. (1983): Finite Elements and Approximations, Wiley & Sons.

    Μέθοδοι αξιολόγησης

    Η αξιολόγηση του μαθήματος πραγματοποιείται με γραπτή εργασία που αντιστοιχεί στο 100% του τελικού βαθμού. Η εργασία συνοδεύεται από παρουσίαση και προφορική εξέταση από το διδάσκοντα.

    Προαπαιτούμενα

    • Λογισμός μιας Μεταβλητής - Γραμμική Άλγεβρα
    • Λογισμός Πολλών Μεταβλητών
    • Διαφορικές Εξισώσεις και Μετασχηματισμοί
    • Αριθμητική Ανάλυση