Write 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. Use a starting solution of zero.

(a) Test your matrix using your Choleski decomposition program that you wrote for Question 1 of Assignment 1 to ensure 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 using the Choleski decomposition program from Assignment 1,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), using the Choleski decomposition and the conjugate gradient programs, and how do they it compare with the value you computed in Question 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) Suggest how you could compute the capacitance per unit length of the system from the finite difference solution.

Posted Date: 2/15/2013 4:37:12 AM | Location : United States

Ask an Expert

Related Discussions:- Program implementing the conjugate gradient method, Assignment Help, Ask Question on Program implementing the conjugate gradient method, Get Answer, Expert's Help, Program implementing the conjugate gradient method Discussions

Write discussion on Program implementing the conjugate gradient method
Your posts are moderated

Write your message here..

Related Questions

Compute the terminal voltage and current of each generator, Q. Three dc gen... Q. Three dc generators are operating in parallel with excitations such that their external characteristics are almost straight lines over the working range with the following pairs

What do you mean by addressing and numbering, Q. What do you mean by addres... Q. What do you mean by addressing and numbering? Numbering and Addressing: In data and telephone networks, end equipment are more often single units than multiple devices uni

For the circuit obtain z- and y-parameters, Q. For the circuit shown in Fig... Q. For the circuit shown in Figure, obtain: (a) z-and y-parameters; (b) Transfer function I 2 /I 1 when V 2 = 0.

Bcd to excess 3 code converter, What are the industrial applications of the... What are the industrial applications of the project bcd to excess 3 code converter?

Explain nodes analysis, Nodes analysis Analysis using KCL to solve for ... Nodes analysis Analysis using KCL to solve for voltages at every common node of the network and as determines the currents by and voltages across every elements of the network.

ADC and DAC design, I''m trying to design ADC using MAX1198 and DAC using I... I''m trying to design ADC using MAX1198 and DAC using IDAC in Multisim 12 but none of them are working. I need some help in this regard

Robust, what''s robust? what''s robust?

Draw and explain the block diagram of dma controller, Draw and explain the ... Draw and explain the block diagram of DMA controller. The fundamental idea of DMA is to transfer blocks of data directly between peripherals and memory. The data don't suffer t

Salient features of nep, Salient Features of NEP: Access to electrici... Salient Features of NEP: Access to electricity: The policy not only envisages access to electricity for all but it also emphasizes in which all consumers, particularly t

Registers - microprocessors architecture , Registers Various  register... Registers Various  registers  shown in figure  are discussed  below  in detail.