Ask Electrical & Electronics Expert

problem 1: Figure below shows two first-order triangular finite elements used to solve the Laplace equation for electrostatic potential. Find out a local S-matrix for each triangle, and a global S-matrix for the mesh which comprises of just these two triangles. The local (disjoint) and global (conjoint) node-numberings are shown in figure (a) and (b), respectively. Also, figure (a) shows the (x, y)-coordinates of the element vertices in meters.

2339_laplace for electrostatic equation.jpg

problem 2: Figure below shows the cross-section of an electrostatic problem with translational symmetry: a rectangular coaxial cable. The inner conductor is held at 10 volts and the outer conductor is grounded.
 
a) Use the two-element mesh shown in Figure 1(b) as a 'building block' to construct a finite element mesh for one-quarter of the cross-section of the coaxial cable. Specify the mesh, comprising boundary conditions, in an input file following the format for the SIMPLE2D program.
 
b) Use the SIMPLE2D program with the mesh from part (a) to find out the electrostatic potential solution. Find out the potential at (x, y) = (0.06, 0.04) from the data in the output file of the program.
 
(c) Caculate the capacitance per unit length of the system using the solution obtained from SIMPLE2D.
 
Note: The SIMPLE2D program and related utility programs are available from the myCourse page for this course or on the World-Wide-Web at:

http://www.cambridge.org/catalogue/catalogue.asp?isbn=0521449537&ss=res

Please read the file README.1ST before using the software.

345_simple 2d program.jpg

problem 3: prepare a program implementing the conjugate gradient method (un-preconditioned). Solve the matrix equation corresponding to a finite difference node-spacing, h = 0.02m in x and y directions for the same one-quarter cross-section of the system shown in figure above that considered in problem 2 above. Use a starting solution of zero.

a) Test your matrix by using your Choleski decomposition program which you wrote for problem 1 to make sure that it is positive definite. If it is not, suggest how you could modify the matrix equation in order to use the conjugate gradient method for this problem.

b) Once you have modified the problem so that the matrix is positive definite, solve the matrix equation first by using the Choleski decomposition program, and then the conjugate gradient program written for this assignment.

c) Plot a graph of the infinity norm and the 2-norm of the residual vector versus the number of iterations for the conjugate program.

d) What is the potential at (x,y) = (0.06, 0.04), by using the Choleski decomposition and the conjugate gradient programs, and how do they it compare with the value you find outd in problem 2(b) above. How do they compare with the value at the same (x,y) location and for the same node spacing that you computed in Assignment 1 using SOR.

e) Recommend how you could find out the capacitance per unit length of the system from the finite difference solution.

Electrical & Electronics, Engineering

  • Category:- Electrical & Electronics
  • Reference No.:- M92020

Have any Question?


Related Questions in Electrical & Electronics

Question 1for the ce amplifier in figure 1 given the

Question 1 For the CE amplifier in Figure (1), given the following component parameters: Parameter Value β DC , β AC 150 V BE 0 . 7 V V CC 12 V R C 820 ? R E 1 100 ? R E 2 220 ? R 1 20 k? R 2 5 . 2 k? R L 100 k? C 1 , C ...

Question -i a star-connected three-phase synchronous

Question - (i) A star-connected, three-phase synchronous induction motor takes a current of 10 amps from a 415 volt supply at unity power factor when supplying a steady load. If the synchronous reactance is 5 ohms/phase ...

1 a name the three major groups of contamination and

1. (a) Name the three major groups of contamination and briefly describe their physical characteristics. (b) Where do the above contamination types come from? Give one example of each. 2. Name two processes metrics which ...

Question 1 in the voltage regulator circuit in figure p221

Question 1: In the voltage regulator circuit in Figure P2.21, V 1 = 20 V, V Z = 10 V, R i = 222Ω and P z (max) = 400 mW. (a) Determine I L, I z , and I L , if R L = 380Ω. (b) Determine the value of R L , that will establ ...

Summative assessmentin 2017 sej101 assessment will consist

Summative Assessment In 2017 SEJ101 assessment will consist of nine tasks that will develop a portfolio of your assessed work. Throughout the trimester you will have the opportunity for feedback on all nine tasks before ...

1 a name the three major groups of contamination and

1. (a) Name the three major groups of contamination and briefly describe their physical characteristics. (b) Where do the above contamination types come from? Give one example of each. 2. Name two processes metrics which ...

1 a name the three major groups of contamination and

1. (a) Name the three major groups of contamination and briefly describe their physical characteristics. (b) Where do the above contamination types come from? Give one example of each. 2. Name two processes metrics which ...

Case studythis assignment consists of a written report of

CASE STUDY This assignment consists of a written report of approximately 1000 words and any diagrams in which you are asked to critically compare different process methods used to achieve the same result and show an awar ...

Problem 1 a two-phase servomotor has rated voltage applied

Problem 1: A two-phase servomotor has rated voltage applied to its excitation winding. The torque speed characteristic of the motor with Vc = 220 V, 60 Hz applied to its control phase winding is shown in Fig.1. The momen ...

Electrical engineering questions -q1 two ideal voltage

Electrical Engineering Questions - Q1. Two ideal voltage sources designated as machines 1 and 2 are connected, as shown in the figure below. Given E 1 = 65∠0 o V, E 2 = 65∠30 o V, Z = 3Ω. Determine if Machine 1 is genera ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

Why might a bank avoid the use of interest rate swaps even

Why might a bank avoid the use of interest rate swaps, even when the institution is exposed to significant interest rate

Describe the difference between zero coupon bonds and

Describe the difference between zero coupon bonds and coupon bonds. Under what conditions will a coupon bond sell at a p

Compute the present value of an annuity of 880 per year

Compute the present value of an annuity of $ 880 per year for 16 years, given a discount rate of 6 percent per annum. As

Compute the present value of an 1150 payment made in ten

Compute the present value of an $1,150 payment made in ten years when the discount rate is 12 percent. (Do not round int

Compute the present value of an annuity of 699 per year

Compute the present value of an annuity of $ 699 per year for 19 years, given a discount rate of 6 percent per annum. As