Interested in this College?
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 2368	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 2,368.

Fees	Amount in INR
Course Fee Without Certificate	Free
Course Fee With Certificate	2,381

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

C++Programming skills

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

Computer ProgrammerMechanical Engineer

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
8ct.1. Intro to C++ (running your code, basic structure, number types, vectors)
8ct.2. Intro to C++ (conditional statements, “for” loops, scope)
8ct.3. Intro to C++ (pointers, iterators)

Readings

Syllabus
Help us learn more about you!
"Paper and pencil" practice assignment on strong and weak forms

Practice Exercise

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
ct.1. Intro to C++ (functions)
ct.2. Intro to C++ (C++ classes)

Practice Exercise

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
ct. Coding assignment 1 (main1.cc, overview of C++ class in FEM1.h)

Practice Exercise

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”)

Practice Exercise

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

Practice Exercise

Unit 5 Quiz

Videos

Functionals. Free energy - I
Functionals. Free energy - II
Extremization of functionals
Derivation of the weak form using a variational principle

Practice Exercise

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

Practice Exercise

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

Practice Exercise

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

Practice Exercise

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

Practice Exercise

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

Practice Exercise

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

Practice Exercise

Unit 12 Quiz

Videos

Conclusion, and the Road Ahead

Practice Exercise

Post-course Survey
Keep Learning with Michigan Online

Instructors

UM–Ann Arbor Frequently Asked Questions (FAQ's)

1: Are there any additional benefits of purchasing the certificate?

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.

2: What software is required for classes?

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.

3: How much time will classes take?

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).

4: Will candidates earn a University Credit after completion?

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.

5: Are any recommended textbooks for the course?

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.