From 96c3490caa00f9a241b284ca0e1962e10e7d0a8c Mon Sep 17 00:00:00 2001 From: Matthias Maier Date: Thu, 24 Apr 2025 16:02:49 -0500 Subject: [PATCH] Step 81: fix typos in the documentation - The boundary term over \partial\Omega should be tested with \varphi itself and not with \curl\varphi - fix sign mistake in derivation --- examples/step-81/doc/intro.dox | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/examples/step-81/doc/intro.dox b/examples/step-81/doc/intro.dox index 1a165340e7..bd35d15db3 100644 --- a/examples/step-81/doc/intro.dox +++ b/examples/step-81/doc/intro.dox @@ -203,13 +203,13 @@ Accordingly, our rescaled equations are -i\mu_r \hat{\mathbf{H}} + \hat{\nabla} \times \hat{\mathbf{E}} &= -\hat{\mathbf{M}}_a, \\ - \hat{\nabla} \cdot (\mu_r\hat{\mathbf{H}}) &= \frac{1}{i\omega}\hat{\nabla} + \hat{\nabla} \cdot (\mu_r\hat{\mathbf{H}}) &= \frac{1}{i}\hat{\nabla} \cdot \hat{\mathbf{M}}_a, \\ i\varepsilon_r\hat{\mathbf{E}} + \nabla\times(\mu^{-1}\mathbf{H}) &= \mathbf{J}_a, \\ - \nabla\cdot(\varepsilon\mathbf{E}) &= \frac{1}{i\omega}\hat{\nabla} + \nabla\cdot(\varepsilon\mathbf{E}) &= \frac{1}{i}\hat{\nabla} \cdot\hat{\mathbf{J}}_a. @f} @@ -238,7 +238,7 @@ in $\Omega\backslash\Sigma$. - \int_\Omega \varepsilon_r\mathbf{E} \cdot \bar{\varphi}\;\text{d}x - \int_\Sigma [\nu \times (\mu_r^{-1}\nabla\times\mathbf{E} + \mu^{-1}\mathbf{M}_a)]_{\Sigma}\cdot \bar{\varphi}_T\;\text{d}o_x\\ -\qquad - \int_{\partial\Omega} (\nu \times (\mu_r^{-1}\nabla\times\mathbf{E} + +\qquad + \int_{\partial\Omega} (\nu \times (\mu_r^{-1}\nabla\times\mathbf{E} + \mu^{-1}\mathbf{M}_a)) \cdot \bar{\varphi}_T\;\text{d}o_x = i\int_\Omega \mathbf{J}_a \cdot \bar{\varphi}\;\text{d}x - \int_\Omega \mu_r^{-1}\mathbf{M}_a \cdot (\nabla \times \bar{\varphi})\;\text{d}x. @@ -277,7 +277,7 @@ Combining, our weak form is as follows: - \int_\Omega \varepsilon_r\mathbf{E} \cdot \bar{\varphi}\;\text{d}x - i\int_\Sigma (\sigma_r^{\Sigma}\mathbf{E}_T) \cdot \bar{\varphi}_T\;\text{d}o_x\\ \qquad - i\int_{\partial\Omega} (\sqrt{\mu_r^{-1}\varepsilon}\mathbf{E}_T) \cdot -(\nabla\times\bar{\varphi}_T)\;\text{d}o_x.= +\bar{\varphi}_T\;\text{d}o_x = i\int_\Omega \mathbf{J}_a \cdot \bar{\varphi}\;\text{d}x - \int_\Omega \mu_r^{-1}\mathbf{M}_a \cdot (\nabla \times \bar{\varphi})\;\text{d}x. @f] @@ -310,7 +310,7 @@ A(\mathbf{E},\varphi) \dealcoloneq \int_\Omega (\mu_r^{-1}\nabla\times\mathbf{E} - \int_\Omega \varepsilon_r\mathbf{E} \cdot \bar{\varphi}\;\text{d}x - i\int_\Sigma (\sigma_r^{\Sigma}\mathbf{E}_T) \cdot \bar{\varphi}_T\;\text{d}o_x - i\int_{\partial\Omega} (\sqrt{\mu_r^{-1}\varepsilon}\mathbf{E}_T) \cdot -(\nabla\times\bar{\varphi}_T)\;\text{d}o_x.\\ +\bar{\varphi}_T\;\text{d}o_x.\\ F(\varphi) \dealcoloneq i\int_\Omega \mathbf{J}_a \cdot \bar{\varphi}\;\text{d}x - \int_\Omega \mu_r^{-1}\mathbf{M}_a \cdot (\nabla \times \bar{\varphi})\;\text{d}x. @f] @@ -360,7 +360,7 @@ A_{ij} = \int_\Omega (\mu_r^{-1}\nabla \times \varphi_j) \cdot - i\int_\Sigma (\sigma_r^{\Sigma}\varphi_{j_T}) \cdot \bar{\varphi}_{i_T}\;\text{d}o_x - i\int_{\partial\Omega} (\sqrt{\mu_r^{-1}\varepsilon}\varphi_{j_T}) - \cdot (\nabla\times \bar{\varphi}_{i_T})\;\text{d}o_x, + \cdot \bar{\varphi}_{i_T}\;\text{d}o_x, @f] @f[ F_i = i\int_\Omega \mathbf{J}_a \cdot \bar{\varphi_i}\;\text{d}x -- 2.39.5