ALL SLIDES COVERED
,Lecture 1: What we will learn
➢ Why is engineering analysis important?
➢ What are the main steps in engineering analysis?
▪ Verification and Validation
▪ Sanity Checks
Copyright ©
➢ Essentials of MECHENG
▪ What it teaches you
Sandip
6507 Mazumder
The Ohio
▪ What State
it does not teach you University
➢ Classification of Partial Differential Equations
1
,Why Engineering Analysis?
• Troubleshoot problems
• Improve existing designs Why do things work the way they do?
• Explore new designs
One way (perhaps, the best way) to learn why and how things work is
Copyright © Sandip Mazumder
through observations (or experiments).
However, performing experiments has its own challenges
The Ohio State University
• Expensive (material and equipment cost, labor)
• Time-consuming (hours spent in making and breaking, too many
permutations and combinations)
• Intrusive: cannot always do in situ measurements, ex situ
measurements provide limited understanding
• Extremely difficult at small (sub-micron) or large scales
Alternative: MODELING and SIMULATION (analysis)
2
, Engineering Analysis
Most engineering analyses involve one or more of the following
basic class of computations:
➢ Finding roots of equations (single or simultaneous, linear or non-
linear)
➢ Solving ODEs (single or simultaneous)
Copyright © Sandip Mazumder
➢ Solving PDEs (single or simultaneous)
➢ Statistical analysis
The
The typeOhio State
of calculation University
performed can also be broadly categorized
into two types:
➢ Deterministic: the same solution is obtained every time if the same
equation is solved, e.g., finite difference, finite element, etc.
➢ Stochastic: The solution is different each time, e.g., Monte Carlo
method
A stochastic method is a better representation of the real-life
scenario because it has uncertainty built into it. However, usually it
is tedious to use because it requires extra data processing. 3
,Lecture 1: What we will learn
➢ Why is engineering analysis important?
➢ What are the main steps in engineering analysis?
▪ Verification and Validation
▪ Sanity Checks
Copyright ©
➢ Essentials of MECHENG
▪ What it teaches you
Sandip
6507 Mazumder
The Ohio
▪ What State
it does not teach you University
➢ Classification of Partial Differential Equations
1
,Why Engineering Analysis?
• Troubleshoot problems
• Improve existing designs Why do things work the way they do?
• Explore new designs
One way (perhaps, the best way) to learn why and how things work is
Copyright © Sandip Mazumder
through observations (or experiments).
However, performing experiments has its own challenges
The Ohio State University
• Expensive (material and equipment cost, labor)
• Time-consuming (hours spent in making and breaking, too many
permutations and combinations)
• Intrusive: cannot always do in situ measurements, ex situ
measurements provide limited understanding
• Extremely difficult at small (sub-micron) or large scales
Alternative: MODELING and SIMULATION (analysis)
2
, Engineering Analysis
Most engineering analyses involve one or more of the following
basic class of computations:
➢ Finding roots of equations (single or simultaneous, linear or non-
linear)
➢ Solving ODEs (single or simultaneous)
Copyright © Sandip Mazumder
➢ Solving PDEs (single or simultaneous)
➢ Statistical analysis
The
The typeOhio State
of calculation University
performed can also be broadly categorized
into two types:
➢ Deterministic: the same solution is obtained every time if the same
equation is solved, e.g., finite difference, finite element, etc.
➢ Stochastic: The solution is different each time, e.g., Monte Carlo
method
A stochastic method is a better representation of the real-life
scenario because it has uncertainty built into it. However, usually it
is tedious to use because it requires extra data processing. 3
