ESO 208A/ESO 218 COMPUTATIONAL METHODS IN ENGINEERING

COURSE STRUCTURE QUIZ-1 (10) MID-SEMESTER (30) QUIZ-2 (10) END-SEMESTER (40) TUTORIALS (10) Attendance Lectures (random) Tutorials (compulsory)

Instructor: Pranab K. Mohapatra, CE Tutors: – V. Shankar, CHE – A. Ghatak, CHE – P. Apte, CHE – Raj Pala, CHE – Shipra Verma, CHE – S. Chandra, CE – Aubha Goel, CE – Mukesh Sharma, CE – S. N. Tripathi, CE

Course Contents Introduction, Engineering Systems, Physical and Mathematical Modeling Error Analysis: Approximations and round off and Truncation errors Roots of Equations: Method of Bisection, Method of Interpolation, Secant Method, Newton Raphson method, Secant Method, Multiple roots Solution of Linear Simultaneous Equations: Direct Methods-Gauss Elimination, Gauss-Jordan, LU decomposition; lterative Methods-Gauss-Seidel, Conjugate Gradient, Banded and Sparse systems Solution of Nonlinear Simultaneous Equations Curve Fitting-Least Square regression, Interpolation including splines Fast Fourier Transforms, Regression Analysis for Multivariable Eigen Values and Eigen Vectors- Power method, Relaxation Method, Diagonalization method. Numerical Differentiation and Integration-High-Accuracy Differentiation Formulas, Derivatives of Unequal Spaced Data. The trapezoidal Rule, Simpson’s rule, Integration with unequal segments, Open Integration Formulas Ordinary Differential Equations- Finite Difference method, Method of Weighted Residuals Analytical versus Numerical Methods, Initial Value and Boundary Value Problems Euler’s method, Improvement of Euler’s method, Runge-Kutta Method, Multiple Steps Method Partial Differential Equations-Elliptic and parabolic Equations, Explicit and Implicit Methods, Crank Nicholson Method, ADI method Introduction to Finite Element Method, Applications.

BOOK(S) CHAPRA & CANALE (2012) NUM. METHODS FOR ENGINEERS, 6 TH ED., TMH GUHA & SRIVASTAVA (2012) NUM. METH. FOR ENGG. AND SCIENCE, 1 ST ED., OXFORD PRESS ET AL. (1992) NUM. RECIPES IN FORTRAN, 2 ND ED., CAMBRIDGE UNIV. PRESS

CLASS SCHEDULE LECTURE: L17 (M/W/F) 11:00 – 11:50 TUTORIAL: THU (11:00 – 11:50)

INTRODUCTION A DIVISION GIGO CAD HUMAN VS COMPUTER

MODELING PHYSICAL ANALYTICAL NUMERICAL ANALOGICAL

FACTORS TIME ACCURACY COST PHYSICAL PROCESSES DEVELOPMENT USER FRIENDLY

MATHEMATICAL MODELING GOVERNING EQUATIONS BOUNDARY CONDITIONS NUMERICAL/ANALYTICAL SOLUTION INTERPRETATION OF RESULTS IMPLEMENTATION

CHECKS GRID INDEPENDENCE CONSERVATION LAWS VALIDATION

NUMERICAL METHOD? POTENT PROBLEM SOLVING TOOLS USE OF SOFTWARES WRITE YOUR OWN PROGRAM LEARN PROGRAMMING INSIGHT TO THE PROBLEM

PRACTICAL ISSUES (NON)LINEAR SYSTEM LARGE / SMALL SYSTEM IDEAL / REAL SENSITIVITY ANALYSIS DESIGN INVERSE PROBLEM

PRACTICE EXAMPLE 1.1 (PAGE 14) EXAMPLE 1.2 (PAGE 17)