OBLIG 1, due by Monday 15 February at 13:00 hours

Oblig 1 is given as 2.6.1 Exercise on p. 10 in Lecture notes posted in schedule, lectures, on 11 January. 

TASKS: 

1. Make discretisation of a) a circle with radius R0, b) and ellipse of major half axis a0 and minor half axis b0, and c) a square of side 2a0. Use a Matlab of Python-script for the purpose. 

2. Calculate the coefficients of the integral equation on discrete form given in eq. (26) on p. 10 in the Lecture notes. Solve the integral equation for the circle and compare to the analytical solution in (19). Investigate convergence as function of N (hint: use N=100, 200, 400.)

3. Calculate the added mass coefficient a11 of the circle. Compare to the analytical result m11= rho pi R0^2. 

4. Do the same for the ellipse with b0/a0=0.5 and b0/a0=0.1. Solve the discrete integral equation (26). Investigate convergence as function of the number of segments N. Calculate the added mass coefficients for the ellipse and compare to exact results: m11=rho pi b0^2, m22=rho pi a0^2, m66=(1/8) rho pi (a0^2-b0^2)^2. 

5. Do the same for the square. Solve the discrete integral equation (26). Investigate convergence. Calculate the added mass coefficients and compare to the exact result: m11/rho=4.754 a0=^2, m22/rho=4.754 a0^2, m66/rho=0.725 a0^4.

6. Write a short conclusion (10 lines) of i. what you have done, and ii. what you have found. 

Note: Oblig may be prepared by numerical results and graphs presented by print outs. Text / discussion may be prepared as handwritten on white paper.