Monge.. - SFU Wiki

16 JEAN-DAVID BENAMOU, BRITTANY D. FROESE, AND ADAM M. OBERMAN(a)fig:sol_ball(b)fig:err_ball(c)fig:its_ball(d)fig:time_ballFigure 8. Results for u(x, y) = − √ 2 − x 2 − y 2 on an N ×N grid.(a) Surface plot of the solution. (b) Error versus N. (c) Numberof iterations. (d) Total CPU time.fig:balltable:ballN Iterations CPU Time (sec)(M1) (M2) (M1) (M2)21 1009 67 .2 .241 3833 79 1.9 1.061 8343 89 8.5 2.781 14480 99 26.3 5.2101 22189 106 60.2 10.0121 31445 113 120.1 15.0141 42202 119 218.3 21.3Table 9. Computation times when u = − √ 2 − x 2 − y 2 on anN × N grid.For the cone u(x, y) = √ x 2 + y 2 , the convergence rate decreases to O(h .8 ), andthe solution time is about one order of magnitude slower for (M2).Another example is the absolute value function u(x, y) = |x| in §6.2. Here thecomputation time for (M1) is two orders of magnitude faster than for (M2). Sincethe solution is piecewise linear, the discretisation error is zero. However, the rate