### How to sum over basis functions

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Hello,

I am currently trying to implement 2D electromagnetic scattering from an infinite metallic cylinder (such as in Section 9.2.3 of Jianming Jin's book). On the surface of the metallic cylinder,

$E^{scattered}=-E^{in}$

where $E^{scattered}$

$b_i=\sum_j^{ND}E_j^{in}\int_{\Omega}\nabla u_i\cdot\nabla v_j^D-k^2_0u_i\cdot v_j^Dd\Omega$

Where ND is the number of basis functions on the surface of the cylinder, and $u_i$

My question is this: is it possible to implement a sum over basis functions such as in the equation above?

Thanks!

I am currently trying to implement 2D electromagnetic scattering from an infinite metallic cylinder (such as in Section 9.2.3 of Jianming Jin's book). On the surface of the metallic cylinder,

$E^{scattered}=-E^{in}$

`E`^{scattered}=−`E`^{in}where $E^{scattered}$

`E`^{scattered}is what I am solving for and $E^{in}$`E`^{in}in my known source term. This results in a right-hand side expression of:$b_i=\sum_j^{ND}E_j^{in}\int_{\Omega}\nabla u_i\cdot\nabla v_j^D-k^2_0u_i\cdot v_j^Dd\Omega$

`b`_{i}=∑_{j}^{ND}`E`_{j}^{in}∫_{Ω}∇`u`_{i}·∇`v`_{j}^{D}−`k`^{2}_{0}`u`_{i}·`v`_{j}^{D}`d`ΩWhere ND is the number of basis functions on the surface of the cylinder, and $u_i$

`u`_{i}are my testing functions, and $v_j^D$`v`_{j}^{D}are my basis functions on the surface of the metallic cylinder.My question is this: is it possible to implement a sum over basis functions such as in the equation above?

Thanks!

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