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September 26, 2023

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Description

Numerical Methods in Civil Engineering. Instructor: Prof. A. Deb, Department of Civil Engineering, IIT Kharagpur.

This course attempts to give a broad background to numerical methods common to various branches of civil engineering. It starts with core concepts of error estimate and accuracy of numerical solutions. It then introduces the student to methods of solution of linear and nonlinear equations. Both direct and iterative solution methods are discussed. Next we introduce the numerical solution of partial differential equations, after a brief review of canonical partial differential equations and well known analytical techniques for their solution, stressing when and why numerical solutions are necessary. Finite difference operators are introduced and used to solve typical initial and boundary value problems. Following this we introduce the finite element method as a generic method for the numerical solution of partial differential equations. The concepts of weak form, finite element discretization, polynomial interpolation using Lagrange polynomials and numerical quadrature are introduced. Numerical integration in the time domain is discussed, emphasizing the key requirements of stability and accuracy of time integration algorithms. Finally we discuss integral equations and introduce numerical techniques for their solution. (from nptel.ac.in)

Course Curriculum

  • Lecture 01 – Introduction to Numerical Methods Unlimited
  • Lecture 02 – Error Analysis Unlimited
  • Lecture 03 – Introduction to Linear Systems Unlimited
  • Lecture 04 – Linear Systems (cont.) Unlimited
  • Lecture 05 – Linear Systems (cont.) Unlimited
  • Lecture 06 – Linear Systems – Error Bounds Unlimited
  • Lecture 07 – Error Bounds and Iterative Methods for Solving Linear Systems Unlimited
  • Lecture 08 – Iterative Methods for Solving Linear Systems Unlimited
  • Lecture 09 – Iterative Methods (cont.) Unlimited
  • Lecture 10 – Iterative Methods (cont.) Unlimited
  • Lecture 11 – Iterative Methods for Eigenvalue Extraction Unlimited
  • Lecture 12 – Solving Nonlinear Equations Unlimited
  • Lecture 13 – Solving Nonlinear Equations (cont.) Unlimited
  • Lecture 14 – Solving Multidimensional Nonlinear Equations Unlimited
  • Lecture 15 – Solving Multidimensional Nonlinear Equations (cont.) Unlimited
  • Lecture 16 – ARC Length and Gradient Based Methods Unlimited
  • Lecture 17 – Gradient Based Methods Unlimited
  • Lecture 18 – Conjugate Gradient Method Unlimited
  • Lecture 19 – Conjugate Gradient Method (cont.) Unlimited
  • Lecture 20 – Nonlinear Conjugate Gradient and Introduction to PDEs Unlimited
  • Lecture 21 – Eigenfunction Solutions for the Wave Equation Unlimited
  • Lecture 22 – Analytical Methods for Solving the Wave Equation Unlimited
  • Lecture 23 – Analytical Methods for Hyperbolic and Parabolic PDEs Unlimited
  • Lecture 24 – Analytical Methods for Parabolic and Elliptic PDEs Unlimited
  • Lecture 25 – Analytical Methods for Elliptic PDEs Unlimited
  • Lecture 26 – Series Solutions for Elliptic PDEs and Introduction to Differential Operators Unlimited
  • Lecture 27 – Differential Operators Unlimited
  • Lecture 28 – Differential Operators (cont.) Unlimited
  • Lecture 29 – Differential Operators (cont.) Unlimited
  • Lecture 30 – Interpolation Unlimited
  • Lecture 31 – Polynomial Fitting Unlimited
  • Lecture 32 – Orthogonal Polynomials Unlimited
  • Lecture 33 – Orthogonal Polynomials (cont.) Unlimited
  • Lecture 34 – Orthogonal Polynomials (cont.) Unlimited
  • Lecture 35 – Spline Functions Unlimited
  • Lecture 36 – Orthogonal Basis Functions for Solving PDEs Unlimited
  • Lecture 37 – Orthogonal Basis Functions for Solving PDEs (cont.) Unlimited
  • Lecture 38 – Integral Equations Unlimited
  • Lecture 39 – Integral Equations (cont.) Unlimited
  • Lecture 40 – Integral Equations (cont.) Unlimited

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