Reference no: EM131097998
E19: Numerical Methods for Engineering Applications Spring 2016 - HOMEWORK 12
1. Solving the steady-state heat equation
The steadystate_heat.py code on the course website solves the steady-state heat equation with given boundary conditions that we defined in class.
a. Please add comments to the program to summarize how it works. In particular:
- What are the BOUNDARY_* variables doing?
- How are they related to the boundaries array?
- What does scipy.sparse.lil_matrix do?
- What are the neighbor_deltas for?
- How the heck does the vectorized building code work?
- What does the line A = A.tocsr() do?
b. For what values of n is it advantageous to compute the 'dense' solution as opposed to the 'sparse' one? Is there any problem size for which the 'loop' building method outperforms the 'vectorized' one? Why is the sparse solver so much faster for large n?
2. Transient heat equation
The transient_heat.py code on the course website solves the transient (time-varying) heat equation.
a. Based upon the code, what are the boundary conditions for this system? What temperature are we assuming (either implicitly or explicitly) lies along the border of the plate?
b. Play with the simulation. At which value of α does the forward Euler solver blow up with the default value of n = 64?
c. Can you make the backward solver blow up?
d. Explain how modifying n (by editing the code) affects the behavior of the forward solver. Does the it get more or less stable (in terms of the maxmimum allowable value of α) as n increases?
Attachment:- Assignment.rar
|
Social networking users create the life
: Read the following article: Opinion: Farewell to Facebook's false reality by Jessa Haines. Thanks to social networking, much of a person's life is now scripted and manufactured. Many social networking users create the life they wish they had, not ..
|
|
Denominator of the standard error formula
: The quantity of the sample size has a significant influence on the standard error. Since n is the denominator of the standard error formula, as n increases, the standard error increases. The more data that you have, the more accurate you can be.
|
|
Analyze how your thinking has changed
: Analyze how your thinking has changed with regard to ethical practice - Which ethical or professional situations did you encounter in which your original viewpoint changed?
|
|
Evidence to support the shop claim
: A repair shop believes that people travel more than 3500 miles between oil changes. A random sample of 8 cars getting an oil change has a mean distance of 3375 miles since having an oil change with a standard deviation of 225 miles. At alpha = 0.0..
|
|
What are the boundary conditions for this system
: E19: Numerical Methods for Engineering Applications Spring 2016 - HOMEWORK 12. Based upon the code, what are the boundary conditions for this system? What temperature are we assuming (either implicitly or explicitly) lies along the border of the pl..
|
|
Commenting on the validity of the reasoning
: Consider the following scenarios, commenting on the validity of the reasoning that is being used. After an unusually dry autumn, a radio announcer is heard to say, "Watch out! We'll pay for these sunny days later on this winter." A batter who had ..
|
|
Produce female puppies
: A geneticist conducts her survey and calculates hat p = 0.512. Which of the following is the most correct interpretation of this statistic? a) There is a 51.2% chance that a randomly selected gamete cell will have the male chromosome.
|
|
Four model of relationship between religion and science
: Four Philosophy question that I need to be answered in paragraph style. I need them in 4 Hours
|
|
Demands in excess of initial stock
: What is the expected shortfall at the end of the week? That is, what is the expected number of demands in excess of the initial stock?
|