Course11310600334 lectures
Computational Methods in Materials Science and Engineering
Prof. Saswata Bhattacharya and Prof. Anuj Goyal · IIT Hyderabad
About
Computational Methods in Materials Science and Engineering provides a comprehensive introduction to numerical techniques essential for solving complex problems in materials design. The course covers fundamentals of linear algebra, solutions to linear and nonlinear systems, numerical optimization, and methods for solving ODEs and PDEs using finite difference and spectral approaches for both initial and boundary value problems. Students will explore key algebraic and differential equations used in multiscale modeling, including the many-electron Schrödinger equation and classical molecular dynamics in multi-atom systems. The course also introduces Monte Carlo simulations for modeling diffusion and phase transformations, along with numerical solutions to the Allen-Cahn and Cahn-Hilliard equations, which form the foundation of phase-field modeling for microstructural evolution. Additionally, students will learn optimization techniques for identifying local and global minima in free energy landscapes and other complex scenarios. The course emphasizes hands-on implementation, equipping students with practical skills in Python and C, as well as training in open-source software such as Quantum Espresso, LAMMPS, and MicroSim for real-world computational materials science applications.
Intended audience: 3rd/4th year BTech and 1st year MTech
Prerequisites: Course is meant for UG (3rd and 4th year), PG/PhD (1st year). No pre-requisite for other courses.
Lectures
Week 1
- Programming Foundations for Computational Methods.
- Python Programming Practice Workbook
- From core Python to NumPy to C: Matrix Multiplication and Performance
Week 2
- Systems of Linear Equations
- Direct Methods to Solve Systems of Linear Equations - Part 1
- Direct Methods to Solve Systems of Linear Equations - Part 2
Week 3
Week 4
- Numerical Interpolation and Differentiation Part 1
- Numerical Interpolation and Differentiation Part 2
- Numerical Integration
Week 5
- Implementation of Numerical Interpolation, Least Squares, Differentiation Part 1
- Implementation of Numerical Interpolation, Least Squares, Differentiation Part 2
- Gaussian Quadrature - Theory and Implementation
- Implementation of Numerical Integration
Week 6
- Understanding Least Squares Part 1
- Understanding Least Squares Part 2
- Introduction to Ordinary and Partial Differential Equations - Part 1
- Numerical Methods to Solve ODEs - Initial Value Problems - Part 1
WEEK 7
- Numerical Methods to Solve ODEs - Initial Value Problems - Part 1B
- Implementation of Numerical Methods to Solve ODEs - Initial Value Problems
- Introduction to the Monte Carlo Method for integration
Week 8
- Solving Systems of Ordinary Differential Equations
- Matrix Eigenvalue Problems
- Introduction to Optimization Part 1
- Inroduction to Optimization Part 2
Week 9
- Introduction to Numerical Methods to Solve Boundary Value Problems
- Optimization Part 3: Steepest Descent Technique
Week 10
- Introduction to Partial differential equations
- Optimization Part 4
- Numerical methods to solve partial differential equations -1
Week 11
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT Hyderabad
- Department
- Metallurgy and Material Science
- Taught by
- Prof. Saswata Bhattacharya, Prof. Anuj Goyal
- Level
- Undergraduate
- Language
- English
- Subjects
- Engineering
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed