1st Kind Example 1-D Reminder Numerical results 25 n=40 15 10 n 0 n=20 15 20 Answers Are Getting Worse!!! 0.5 0.5 SMA+HPC⊙2003M First and Second Kind 5
SMA-HPC ©2002 MIT
2nd Kind Example 1-D Reminder Second Kind Equation (a)=0(2)+门1-a()dsy∈[-1,1 The potential is given The density must be computed 平(x)=x3-x o(x is unknown 03 3 SMA+HPC⊙2003M First and Second Kind 6
SMA-HPC ©2002 MIT
2nd Kind Example 1-D Reminder Discretization 业(x)=0(x)+/1|e-xa(a)dsm∈[-1,1 Centroid Collocated Piecewise Constant Scheme Ro 业(x)=mi+∑=10nm312-ds SMA+HPC⊙2003M First and Second Kind 7
SMA-HPC ©2002 MIT
2nd Kind Example 1-D Reminder 1+x.-xdS x dS xds 14[x-x1dS′ SMA+HPC⊙2003M First and Second Kind 8
SMA-HPC ©2002 MIT
2nd Kind Example 1-D Reminder Numerical results x并半木 n=40 n=10 n=20 0.5 0.5 Answers Are Improving!!! SMA-HPC⊙2003MT First and Second Kind 9
SMA-HPC ©2002 MIT