Merge pull request #162 from goggle/typos01

Fix some typos

Author: amartinhuertas

README.md

@@ -64,7 +64,7 @@ Join to our [gitter](https://gitter.im/Gridap-jl/community) chat to ask question
 
 ## How to cite Gridap
 
-In order to give credit to the `Gridap` contributors, we simply ask you to cite the refence below in any publication in which you have made use of `Gridap` packages:
+In order to give credit to the `Gridap` contributors, we simply ask you to cite the reference below in any publication in which you have made use of `Gridap` packages:
 
 ```
 @article{Badia2020,

src/TopOptEMFocus.jl

@@ -199,7 +199,7 @@ LHp=(L/2, h1+h2)   # Start of PML for x,y > 0
 LHn=(L/2, 0)       # Start of PML for x,y < 0
 phys_params = (; k, n_metal, n_air, μ, R, dpml, LHp, LHn)
 
-# PML coordinate streching functions
+# PML coordinate stretching functions
 function s_PML(x; phys_params)
     σ = -3 / 4 * log(phys_params.R) / phys_params.dpml / phys_params.n_air
     xf = Tuple(x)
@@ -230,7 +230,7 @@ Fields.∇(Λf::Λ) = x -> TensorValue{2, 2, ComplexF64}(-(Λf(x)[1])^2 * ds_PML
 
 # ## Filter and threshold
 # 
-# Here we use the filter and threshold dicussed above. The parameters for the filter and threshold are extracted from Ref [6]. Note that every integral in the filter is only defined on $\Omega_d$
+# Here we use the filter and threshold discussed above. The parameters for the filter and threshold are extracted from Ref [6]. Note that every integral in the filter is only defined on $\Omega_d$
 # 
 
 r = 5/sqrt(3)               # Filter radius
@@ -344,7 +344,7 @@ Dξdpf(pf, n_air, n_metal, β, η)= 2 * (n_air - n_metal) / (n_air + (n_metal -
 DAdpf(u, v, pfh; phys_params, β, η) = ((p -> Dξdpf(p, phys_params.n_air, phys_params.n_metal, β, η)) ∘ pfh) * (∇(v) ⊙ ∇(u))
 
 
-# Then we create a function `gf_pf` that depends directly on $p_f$ and write out the derivate using adjoint method formula. Note that the threshold chainrule is already implemented in the functions above.
+# Then we create a function `gf_pf` that depends directly on $p_f$ and write out the derivative using adjoint method formula. Note that the threshold chainrule is already implemented in the functions above.
 # 
 
 function gf_pf(pf_vec; β, η, phys_params, fem_params)
@@ -440,7 +440,7 @@ g1-g0, grad'*δp
 
 # ## Optimization with  NLopt
 # 
-# Now we use NLopt.jl package to implement the MMA algorithm for optimization. Note that we start with $\beta=8$ and then gradually increase it to $\beta=32$ in consistant with Ref. [6].
+# Now we use NLopt.jl package to implement the MMA algorithm for optimization. Note that we start with $\beta=8$ and then gradually increase it to $\beta=32$ in consistent with Ref. [6].
 # 
 
 using NLopt
@@ -500,7 +500,7 @@ save("shape.png", fig)
 # ![](../assets/TopOptEMFocus/shape.png)
 # 
 
-# For the electric field, recall that $\vert E\vert^2\sim\vert \frac{1}{\epsilon}\nabla H\vert^2$, the factor 2 below comes from the amplitude compared to the incident plane wave. We can see that the optimized shapes are very similiar to the optimized shape in Ref. [6], proving our results. 
+# For the electric field, recall that $\vert E\vert^2\sim\vert \frac{1}{\epsilon}\nabla H\vert^2$, the factor 2 below comes from the amplitude compared to the incident plane wave. We can see that the optimized shapes are very similar to the optimized shape in Ref. [6], proving our results. 
 # 
 
 maxe = 30 # Maximum electric field magnitude compared to the incident plane wave
@@ -529,6 +529,6 @@ save("Field.png", fig)
 # 
 # [5] B. S. Lazarov and O. Sigmund, "[Filters in topology optimization based on Helmholtz-type differential equations](https://en.wikipedia.org/wiki/Jacobi%E2%80%93Anger_expansion)", International Journal for Numerical Methods in Engineering, vol. 86, pp. 765-781, December 2010.
 # 
-# [6] R.E. Christiansen, J. Michon, M. Benzaouia, O. Sigmund, and S.G. Johnson, "[Inverse design of nanoparticles for enhanced Raman scattering](https://opg.optica.org/oe/fulltext.cfm?uri=oe-28-4-4444&id=426514)," Optical Express, vol. 28, pp. 4444-4462, Feburary 2020.
+# [6] R.E. Christiansen, J. Michon, M. Benzaouia, O. Sigmund, and S.G. Johnson, "[Inverse design of nanoparticles for enhanced Raman scattering](https://opg.optica.org/oe/fulltext.cfm?uri=oe-28-4-4444&id=426514)," Optical Express, vol. 28, pp. 4444-4462, February 2020.
 # 
 

src/emscatter.jl

@@ -89,7 +89,7 @@ model = GmshDiscreteModel("../models/geometry.msh")
 
 # ## FE spaces
 # 
-# We use the first-order lagrangian as the finite element function space basis. The dirihlet edges are labeld with `DirichletEdges` in the mesh file. Since our problem involves complex numbers (because of PML), we need to assign the `vector_type` to be `Vector{ComplexF64}`.
+# We use the first-order lagrangian as the finite element function space basis. The Dirichlet edges are labeled with `DirichletEdges` in the mesh file. Since our problem involves complex numbers (because of PML), we need to assign the `vector_type` to be `Vector{ComplexF64}`.
 # 
 
 # ### Test and trial finite element function space
@@ -100,7 +100,7 @@ U = V # mathematically equivalent to TrialFESpace(V,0)
 
 # ## Numerical integration
 # 
-# We generate the triangulation and a second-order Gaussian quadrature for the numerial integration. Note that we create a boundary triangulation from a `Source` tag for the line excitation. Generally, we do not need such additional mesh tags for the source, we can use a delta function to approximate such line source excitation. However, by generating a line mesh, we can increase the accuracy of this source excitation.
+# We generate the triangulation and a second-order Gaussian quadrature for the numerical integration. Note that we create a boundary triangulation from a `Source` tag for the line excitation. Generally, we do not need such additional mesh tags for the source, we can use a delta function to approximate such line source excitation. However, by generating a line mesh, we can increase the accuracy of this source excitation.
 # 
 
 # ### Generate triangulation and quadrature from model 
@@ -118,11 +118,11 @@ dΓ = Measure(Γ,degree)
 # 
 
 # ### PML parameters
-Rpml = 1e-12      # Tolerence for PML reflection 
+Rpml = 1e-12      # Tolerance for PML reflection 
 σ = -3/4*log(Rpml)/d_pml # σ_0
 LH = (L,H) # Size of the PML inner boundary (a rectangular centere at (0,0))
 
-# ### PML coordinate streching functions
+# ### PML coordinate stretching functions
 function s_PML(x,σ,k,LH,d_pml)
     u = abs.(Tuple(x)).-LH./2  # get the depth into PML
     return @. ifelse(u > 0,  1+(1im*σ/k)*(u/d_pml)^2, $(1.0+0im))
@@ -196,7 +196,7 @@ uh = solve(op)
 # H_0=\sum_m i^mJ_m(kr)e^{im\theta},
 # ```
 #
-# where $m=0,\pm 1,\pm 2,\dots$ and $J_m(z)$ is the Bessel function of the fisrt kind. 
+# where $m=0,\pm 1,\pm 2,\dots$ and $J_m(z)$ is the Bessel function of the first kind. 
 # 
 # For simplicity, we start with only the $m$-th component and take it as the incident part: 
 #

src/fsi_tutorial.jl

@@ -288,7 +288,7 @@ a_f((u,p),(v,q)) = ∫( ε(v) ⊙ (σ_dev_f ∘ ε(u)) - (∇⋅v)*p + q*(∇⋅
 a_fs((us,uf,p),(vs,vf,q)) = ∫( α*(jump_Γ(vf,vs)⋅jump_Γ(uf,us)) +
                                jump_Γ(vf,vs)⋅t_Γfs(1,p,uf,n_Γfs) +
                                t_Γfs(χ,q,vf,n_Γfs)⋅jump_Γ(uf,us) )dΓ_fs
-# Where $\chi$ is a parameter that can take values $1.0$ or $-1.0$ and it is used to define the symmetric or antisymmetric version of the method, respectively. To difine this form we used the well known Nitsche's method, which enforces the continuity of fluid and solid velocities as well as the continuity of the normal stresses, see for instance [2].
+# Where $\chi$ is a parameter that can take values $1.0$ or $-1.0$ and it is used to define the symmetric or antisymmetric version of the method, respectively. To define this form we used the well known Nitsche's method, which enforces the continuity of fluid and solid velocities as well as the continuity of the normal stresses, see for instance [2].
 const γ = 1.0
 const χ = -1.0
 jump_Γ(wf,ws) = wf.⁺-ws.⁻

src/poisson_transient.jl

@@ -6,7 +6,7 @@
 
 # ## Problem statement
 
-# We solve the heat equation in a 2-dimensional domain $\Omega$, the unit square, with Homogenous Dirichlet boundaries on the whole boundary $\partial \Omega$. We consider a time-dependent conductivity $\kappa(t)=1.0 + 0.95\sin(2\pi t)$, a time-dependent volumetric forcing term $f(t) = \sin(\pi t)$ and a constant Homogenous boundary condition $g = 0.0$. The initial solution is $u(x,0) = u_0 = 0$. With these definitions, the strong form of the problem reads:
+# We solve the heat equation in a 2-dimensional domain $\Omega$, the unit square, with Homogeneous Dirichlet boundaries on the whole boundary $\partial \Omega$. We consider a time-dependent conductivity $\kappa(t)=1.0 + 0.95\sin(2\pi t)$, a time-dependent volumetric forcing term $f(t) = \sin(\pi t)$ and a constant Homogeneous boundary condition $g = 0.0$. The initial solution is $u(x,0) = u_0 = 0$. With these definitions, the strong form of the problem reads:
 
 # ```math
 # \left\lbrace
@@ -54,7 +54,7 @@ refFE = ReferenceFE(lagrangian,Float64,1)
 # The space of test functions is constant in time and is defined in steady problems:
 V = TestFESpace(𝒯,refFE,dirichlet_tags="boundary")
 
-# The trial space is now a `TransientTrialFESpace`, wich is constructed from a `TestFESpace` and a function (or vector of functions) for the Dirichlet boundary condition/s. In that case, the boundary condition function is a time-independent constant, but it could also be a time-dependent field depending on the coordinates $x$ and time $t$.
+# The trial space is now a `TransientTrialFESpace`, which is constructed from a `TestFESpace` and a function (or vector of functions) for the Dirichlet boundary condition/s. In that case, the boundary condition function is a time-independent constant, but it could also be a time-dependent field depending on the coordinates $x$ and time $t$.
 g(x,t::Real) = 0.0
 g(t::Real) = x -> g(x,t)
 U = TransientTrialFESpace(V,g)