From 964e3cfe31e7416a8e2167f1ef885bb2dde0ad50 Mon Sep 17 00:00:00 2001 From: "Steven G. Johnson" Date: Fri, 23 Jul 2021 13:03:51 -0400 Subject: [PATCH 1/2] minor updates to EM scattering tutorial --- src/emscatter.jl | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/src/emscatter.jl b/src/emscatter.jl index 2199daad..412dfe07 100644 --- a/src/emscatter.jl +++ b/src/emscatter.jl @@ -1,13 +1,13 @@ # In this tutorial, we will learn: # # * How to formulate the weak form for a scalar time-harmonic electromagnetic problem -# * How to implement perfectly matched layers (PML) -# * How does periodic boundary condition work in Gridap -# * How to discretize PDEs with complex-valued solution +# * How to implement a perfectly matched layer (PML) to absorb outgoing waves +# * How to impose periodic boundary conditions in Gridap +# * How to discretize PDEs with complex-valued solutions # # ## Problem statement # -# We are going to solve a scalar electromagnetic wave scattering problem: a plane wave (Hz-polarized $H_{inc}$) scattering of a cylinder dielectric (of radius $R$ and permittivity $\varepsilon$), as illustrated below. The computational cell is of height $H$ and length $L$, and we designate a perfectly matched layer (PML) thickness of $d_{pml}$. +# We are going to solve a scalar electromagnetic wave scattering problem: a plane wave (Hz-polarized $H_{inc}$) scattering of a dielectric cylinder (of radius $R$ and permittivity $\varepsilon$), as illustrated below. The computational cell is of height $H$ and length $L$, and we employ a perfectly matched layer (PML) thickness of $d_{pml}$ to implement outgoing (radiation) boundary conditions for this finite domain. # # ![](../assets/emscatter/Illustration.png) # @@ -312,14 +312,14 @@ Difference=sqrt(sum(∫(abs2(uh_t-uh)*AnalyticalBox)*dΩ)/sum(∫(abs2(uh_t)*Ana @assert Difference < 0.1 # # ## References -# [1] https://en.wikipedia.org/wiki/Electromagnetic_wave_equation +# [1] [Wikipedia: Electromagnetic wave equation](https://en.wikipedia.org/wiki/Electromagnetic_wave_equation) # -# [2] https://en.wikipedia.org/wiki/Perfectly_matched_layer +# [2] [Wikipedia: Perfectly matched layer](https://en.wikipedia.org/wiki/Perfectly_matched_layer) # -# [3] A. Oskooi and S. G. Johnson, “Distinguishing correct from incorrect PML proposals and a corrected unsplit PML for anisotropic, dispersive media,” Journal of Computational Physics, vol. 230, pp. 2369–2377, April 2011. +# [3] A. Oskooi and S. G. Johnson, “[Distinguishing correct from incorrect PML proposals and a corrected unsplit PML for anisotropic, dispersive media](http://math.mit.edu/~stevenj/papers/OskooiJo11.pdf),” Journal of Computational Physics, vol. 230, pp. 2369–2377, April 2011. # # [4] Stratton, J. A. (1941). Electromagnetic Theory. New York: McGraw-Hill. # -# [5] https://en.wikipedia.org/wiki/Jacobi%E2%80%93Anger_expansion +# [5] [Wikipedia: Jacobi–Anger expansion](https://en.wikipedia.org/wiki/Jacobi%E2%80%93Anger_expansion) # -# [6] https://en.wikipedia.org/wiki/Bessel_function \ No newline at end of file +# [6] https://en.wikipedia.org/wiki/Bessel_function From 025a5f5679d7d27a38cf16ac8ee327f4abf86028 Mon Sep 17 00:00:00 2001 From: "Steven G. Johnson" Date: Fri, 23 Jul 2021 13:05:57 -0400 Subject: [PATCH 2/2] link fix --- src/emscatter.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/emscatter.jl b/src/emscatter.jl index 412dfe07..e4b1b95b 100644 --- a/src/emscatter.jl +++ b/src/emscatter.jl @@ -322,4 +322,4 @@ Difference=sqrt(sum(∫(abs2(uh_t-uh)*AnalyticalBox)*dΩ)/sum(∫(abs2(uh_t)*Ana # # [5] [Wikipedia: Jacobi–Anger expansion](https://en.wikipedia.org/wiki/Jacobi%E2%80%93Anger_expansion) # -# [6] https://en.wikipedia.org/wiki/Bessel_function +# [6] [Wikipedia: Bessel function](https://en.wikipedia.org/wiki/Bessel_function)