Numerical Methods for PDEs Integral Equation Methods, Lecture 6 Discretization and Quadrature Notes by Suvranu De and J. White May12,2003
Outline Everything is Galerkin Reminder of 1-D and 3-D 2nd Kind Collocation is Galerkin Single Point Quadrature Qualocation Nystrom is Galerkin N point quadrature Multidimensional Quadrature SMA-HPC⊙2003MT First and Second Kind 1
Equation 1-D Examples Volume" Integral equations First Kind 业(x)=G(x,)o(a)dm∈-1,1 Second Kind 业(x)=0(x)+/G(a,)o()dt∈[-1,1 SMA-HPC⊙2003MT First and Second Kind 2
Equation 3-D Examples Surface"3-D Potential Integral Equations First Kind 1 ar()= o(x)drx∈r Second Kind ur(2) 2To()+ o()dr"∈r 0m→ r Onallc-it'll SMA-HPC⊙2003MT First and Second Kind 3
2nd Kind Discretization Collocation Introduce a Basis Representation )=∑omp(a) Make Residual Zero at collocation Points a ()=∑omp()-/,C(a,a)∑o(ad SMA-HPC⊙2003MT First and Second Kind