Get updates on Eligibility, Admission, Placements Fees Structure
Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Course Overview
This Certification programme has been crafted by experts from the University of Michigan to lay extraordinary focus on formulations of Finite Element Method, which has multi-dimensional applications. The course material corresponds to introductory graduate learning with occasional references to variational calculus and functional analysis. The main aim of the course comprises the transformation of the learner from an amateur to a competent developer of Finite Element code. The course also stresses upon the mathematical basis for finite learning methods.
Candidates will discover detailed learning of Linear Algebra and classical forms of PDEs. Every module would find a brief overview of the physical phenomena of Partial Differential Equations. This course prioritises clarity with each concept and thus proceeds to advanced stages like three-dimensional problems in vectors from basics like elliptic PDEs in one dimension. Parabolic Partial Differential Equations in three dimensions follows later, along with hyperbolic equations in three dimensions.
One of the most striking features of the course is query redressal mingled in the lecture videos itself. Responses therein are related to questions put up by graduates and post-doctoral scholars who attended the live lectures. Another unique feature is the casual reference to the code framework through mathematical development.
The Highlights
- 61 hours of learning
- Totally online and self-paced
- Certification from the University of Michigan
- Course training by a PhD scholar
Programme Offerings
- video lectures
- Online Learning System
- Classroom-Based Learning
- Project Exercise.
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 2435 | yes | Coursera |
- Finite Element Method for Problems in Physics provides learning free of cost. Only the certification is chargeable.
- Candidates wishing for a Certificate post-completion ought to pay an amount of INR 2,435.
The Finite Element Method for Problems in Physics Fees Structure
| Head | Amount |
| Certificate fees | Rs. 2,435/- |
Eligibility Criteria
Education
Finite Element Method for Problems in Physics Certification Course mandates candidates to possess a fundamental knowledge regarding any programming language including FORTRAN, Matlab, C, C++ or Python).
Besides this, appreciable understanding of vectors, matrices, and partial differential equations will be beneficial.
Certification Qualifying Details
All the successful learners of Finite Element Method for Problems in Physics Certification Course shall receive a certificate at the completion of the course which can be shared elsewhere.
What you will learn
This course has been modelled to broaden the fundamentals and intermediate knowledge of mechanical engineers with respect to the Finite Learning Method in Physics. After successfully completing this course, learners will acquire skills like-
- Theoretical overview of the Finite Element Method
- Learning finite coding through coding assignments
- Discovering the mathematical origin of FEM methods for solving problems related to solid mechanics and heat/mass transfer.
- Apply the knowledge to research projects.
- Tackle real-world based Physics simulations through Finite Element Method.
Who it is for
Finite Element Method for Problems in Physics is a tailor-made online learning initiative for learning a budding branch of problem solving method in Physics and Mechanical Engineering. It is intended to benefit-
- Graduates in their initial semesters
- Individuals with basic knowledge of any programming knowledge.
- Professionals with knowledge of Linear Algebra and PDEs
- Mechanical engineers willing to learn about Finite Element Method
Admission Details
The admission process for enrolling in the course is highly streamlined and convenient. A step-by-step guide is mentioned below for assisting candidates with a smooth registration process-
Step 1: Go to the course page and select "Enroll for Free."
Step 2: Select an option from "Purchase Course" which is paid and would offer a Certificate and "Full Course, No Certificate" which has free access to course material without a certificate.
Here's the procedure if you select the first option-
Step 3: Enter your card details and make the payment.
However, if you choose the second option-
Step 4: You will simply gain access to the course material and you can begin learning thereon by clicking on “Start Learning.”
The Syllabus
Videos
- Introduction. Linear elliptic partial differential equations - I
- Introduction. Linear elliptic partial differential equations - II
- Boundary conditions
- Constitutive relations
- Strong form of the partial differential equation. Analytic solution
- Weak form of the partial differential equation - I
- Weak form of the partial differential equation - II
- Equivalence between the strong and weak forms
- Intro to C++ (running your code, basic structure, number types, vectors)
- Intro to C++ (conditional statements, “for” loops, scope)
- Intro to C++ (pointers, iterators)
Readings
- Syllabus
- Help us learn more about you!
- "Paper and pencil" practice assignment on strong and weak forms
Quiz
- Unit 1 Quiz
Videos
- The Galerkin, or finite-dimensional weak form
- Response to a question
- Basic Hilbert spaces - I
- Basic Hilbert spaces - II
- The finite element method for the one-dimensional, linear, elliptic partial differential equation
- Response to a question
- Basis functions - I
- Basis functions - II
- The bi-unit domain - I
- The bi-unit domain - II
- The finite dimensional weak form as a sum over element subdomains - I
- The finite dimensional weak form as a sum over element subdomains - II
- Intro to C++ (functions)
- Intro to C++ (C++ classes)
Quiz
- Unit 2 Quiz
Videos
- The matrix-vector weak form - I - I
- The matrix-vector weak form - I - II
- The matrix-vector weak form - II - I
- The matrix-vector weak form - II - II
- The matrix-vector weak form - III - I
- The matrix-vector weak form - III - II
- ct.1. Dealii.org, running deal.II on a virtual machine with Oracle VirtualBox
- ct.2. Intro to AWS, using AWS on Windows
- ct.2c. In-Video Correction
- ct.3. Using AWS on Linux and Mac OS
- The final finite element equations in matrix-vector form - I
- The final finite element equations in matrix-vector form - II
- Response to a question
- Coding assignment 1 (main1.cc, overview of C++ class in FEM1.h)
Quiz
- Unit 3 Quiz
Videos
- The pure Dirichlet problem - I
- The pure Dirichlet problem - II
- In-Video Correction
- Higher polynomial order basis functions - I
- c0. In-Video Correction
- c1. In-Video Correction
- Higher polynomial order basis functions - I - II
- Higher polynomial order basis functions - II - I
- Higher polynomial order basis functions - III
- ct. Coding assignment 1 (functions: class constructor to “basis_gradient”)
- The matrix-vector equations for quadratic basis functions - I - I
- The matrix-vector equations for quadratic basis functions - I - II
- The matrix-vector equations for quadratic basis functions - II - I
- The matrix-vector equations for quadratic basis functions - II - II
- Numerical integration -- Gaussian quadrature
- ct.1. Coding assignment 1 (functions: “generate_mesh” to “setup_system”)
- ct.2. Coding assignment 1 (functions: “assemble_system”)
Quiz
- Unit 4 Quiz
Videos
- Norms - I
- In-Video Correction
- Coding assignment 1 (functions: “solve” to “l2norm_of_error”)
- ct.2. Visualization tools
- Norms - II
- Response to a question
- Consistency of the finite element method
- The best approximation property
- The "Pythagorean Theorem"
- Response to a question
- Sobolev estimates and convergence of the finite element method
- Finite element error estimates
Quiz
- Unit 5 Quiz
Videos
- Functionals. Free energy - I
- Functionals. Free energy - II
- Extremization of functionals
- Derivation of the weak form using a variational principle
Quiz
- Unit 6 Quiz
Videos
- The strong form of steady state heat conduction and mass diffusion - I
- The strong form of steady state heat conduction and mass diffusion - II
- Response to a question
- The strong form, continued
- In-Video Correction
- The weak form
- The finite-dimensional weak form - I
- The finite-dimensional weak form - II
- Three-dimensional hexahedral finite elements
- Aside: Insight to the basis functions by considering the two-dimensional case
- In-Video Correction
- Field derivatives. The Jacobian - I
- Field derivatives. The Jacobian - II
- The integrals in terms of degrees of freedom
- The integrals in terms of degrees of freedom - continued
- The matrix-vector weak form - I
- The matrix-vector weak form II
- The matrix-vector weak form, continued - I
- In-Video Correction
- The matrix-vector weak form, continued - II
- The matrix vector weak form, continued further - I
- In-Video Correction
- The matrix-vector weak form, continued further - II
- In-Video Correction
Quiz
- Unit 7 Quiz
Videos
- Lagrange basis functions in 1 through 3 dimensions - I
- In-Video Correction
- Lagrange basis functions in 1 through 3 dimensions - II
- Coding assignment 2 (2D problem) - I
- Quadrature rules in 1 through 3 dimensions
- ct.1. Coding assignment 2 (2D problem) - II
- ct.2. Coding assignment 2 (3D problem)
- Triangular and tetrahedral elements - Linears - I
- Triangular and tetrahedral elements - Linears - II
Quiz
- Unit 8 Quiz
Videos
- The finite-dimensional weak form and basis functions - I
- The finite-dimensional weak form and basis functions - II
- The matrix-vector weak form
- In-Video Correction
- The matrix-vector weak form - II
- In-Video Correction
Quiz
- Unit 9 Quiz
Videos
- The strong form of linearized elasticity in three dimensions - I
- The strong form of linearized elasticity in three dimensions - II
- In-Video Correction
- The strong form, continued
- The constitutive relations of linearized elasticity
- The weak form - I
- Response to a question
- The weak form - II
- The finite-dimensional weak form - Basis functions - I
- The finite-dimensional weak form - Basis functions - II
- Element integrals - I
- In-Video Correction
- Element integrals - II
- The matrix-vector weak form - I
- The matrix-vector weak form - II
- Assembly of the global matrix-vector equations - I
- Assembly of the global matrix-vector equations - II
- In Video Correction
- ct.1. Coding assignment 3 - I
- ct.2. Coding assignment 3 - II
- Dirichlet boundary conditions - I
- Dirichlet boundary conditions - II
Quiz
- Unit 10 Quiz
Videos
- The strong form
- In-Video Correction
- The weak form, and finite-dimensional weak form - I
- The weak form, and finite-dimensional weak form - II
- Basis functions, and the matrix-vector weak form - I
- In-Video Correction
- Basis functions, and the matrix-vector weak form - II
- Response to a question
- Dirichlet boundary conditions; the final matrix-vector equations
- Time discretization; the Euler family - I
- Time discretization; the Euler family - II
- The v-form and d-form
- ct.1. Coding assignment 4 - I
- ct.2. Coding assignment 4 - II
- Analysis of the integration algorithms for first order, parabolic equations; modal decomposition - I
- Analysis of the integration algorithms for first order, parabolic equations; modal decomposition - II
- In-Video Correction
- Modal decomposition and modal equations - I
- 11.13. Modal decomposition and modal equations - II
- Modal equations and stability of the time-exact single degree of freedom systems - I
- Modal equations and stability of the time-exact single degree of freedom systems - II
- Response to a question
- Stability of the time-discrete single degree of freedom systems
- Behavior of higher-order modes; consistency - I
- Behavior of higher-order modes; consistency - II
- Convergence - I
- Convergence - II
Quiz
- Unit 11 Quiz
Videos
- The strong and weak forms
- The finite-dimensional and matrix-vector weak forms - I
- The finite-dimensional and matrix-vector weak forms - II
- The time-discretized equations
- Stability - I
- Stability - II
- Behavior of higher-order modes 19m
- Convergence
- In-Video Correction
Quiz
- Unit 12 Quiz
Videos
- Conclusion, and the Road Ahead
Quiz
- Post-course Survey
- Keep Learning with Michigan Online
Instructors
UM–Ann Arbor Frequently Asked Questions (FAQ's)
Candidates with a paid course shall also gain access to graded assignments along with all the course materials. The certificate can be posted on LinkedIn for professional connections.
Computing resources can be from 13MB download of tarred and gzipped files to 45MB for a serial MacOSX binary, and 192MB for a parallel MacOSX binary. Candidates will require a specific visualization program of minimum 1GB. A Virtual Machine Interface could be an alternative.
Candidates must invest at least 5 to 10 hours each week for the Finite Element Method for Problems in Physics course. (excluding the time spent in lectures).
Not by default, however, it depends on the university. Learners may correspond with their institution. Mastertrack™ Certificates and Online Degrees on Coursera give university credit.
There are three prescribed books-
- The Finite Element Method: Its Basis and Fundamentals, O.C. Zienkiewicz, R.L. Taylor and
- The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, T.J.R.
- J.Z. Zhu, Butterworth-Heinemann, 2005.
- A First Course in Finite Elements, J. Fish and T. Belytschko, Wiley, 2007.
- Hughes, Dover Publications, 2000.