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2 changes: 2 additions & 0 deletions .typos.toml
Original file line number Diff line number Diff line change
@@ -1,4 +1,6 @@
[default.extend-words]
# Math subscript in LaTeX (m_{iy} = y-component of midpoint m_i) in docs/src/math.md
iy = "iy"
# Julia-specific functions
indexin = "indexin"
findfirst = "findfirst"
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2 changes: 1 addition & 1 deletion docs/make.jl
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Expand Up @@ -28,7 +28,7 @@ if RUN_EXAMPLES
)
return content
end
# We can add the code to the end of each file in its uncommented form programatically.
# We can add the code to the end of each file in its uncommented form programmatically.
function add_just_the_code_section(dir, file)
file_name, file_ext = splitext(file)
file_path = joinpath(dir, file)
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Expand Up @@ -59,7 +59,7 @@ BCs = BoundaryConditions(mesh, bcs, types)
# This is done using `InternalConditions`. First,
# we need to find all the vertices that lie on
# the line $\{x = 1/2, 0 \leq y \leq 2/5\}$. We could
# compute these manually, but let's find them programatically
# compute these manually, but let's find them programmatically
# instead for the sake of demonstration.
function find_all_points_on_line(tri)
vertices = Int[]
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@@ -1,6 +1,6 @@
using DisplayAs #hide
tc = DisplayAs.withcontext(:displaysize => (15, 80), :limit => true); #hide
# # Piecewise Linear and Natural Neighbour Inteprolation for an Advection-Diffusion Equation
# # Piecewise Linear and Natural Neighbour Interpolation for an Advection-Diffusion Equation
# In this tutorial, we have three aims:
#
# 1. Demonstrate how to solve an advection-diffusion equation.
Expand Down Expand Up @@ -243,7 +243,7 @@ fig
) fig #src

# ## Natural neighbour interpolation
# Since the solution is defined over a triangulation, the most natural form of inteprolation to use,
# Since the solution is defined over a triangulation, the most natural form of interpolation to use,
# other than piecewise linear interpolation, is natural neighbour interpolation. We can use
# [NaturalNeighbours.jl](https://github.com/DanielVandH/NaturalNeighbours.jl) for this;
# NaturalNeighbours.jl also provides the same piecewise linear interpolant above via its
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Expand Up @@ -38,7 +38,7 @@ tc = DisplayAs.withcontext(:displaysize => (15, 80), :limit => true); #hide
# \end{equation}
# ```
# where $c_{\min} = \sqrt{\lambda/(2D)}$, $c = \sqrt{D\lambda/2}$, and $z = x-ct$ is the
# travelling wave coordinates. This travelling wave would mathc our problem exactly
# travelling wave coordinates. This travelling wave would match our problem exactly
# if the rectangle were instead $[0, a] \times \mathbb R$, but by choosing $b$ large
# enough we can at least emulate the travelling wave behaviour closely; the
# homogeneous Neumann conditions are to ensure no energy is lost, thus allowing the travelling
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2 changes: 1 addition & 1 deletion docs/src/literate_wyos/diffusion_equations.jl
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Expand Up @@ -176,7 +176,7 @@ function boundary_edge_contributions!(
end

# Now that we have the parts for handling the main flux contributions, we need to consider
# the boundary conditions. Note that in the code above we have alredy taken not to update
# the boundary conditions. Note that in the code above we have already taken not to update
# $\vb A$ or $\vb b$ if there a boundary condition at the associated node, so we do not
# need to worry about e.g. zeroing out rows of $\vb A$ for a node with a boundary condition.
function apply_dirichlet_conditions!(initial_condition, mesh, conditions)
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Expand Up @@ -14,7 +14,7 @@ tc = DisplayAs.withcontext(:displaysize => (15, 80), :limit => true); #hide
# ```
# We want to turn this into an equation of the form $\mathrm d\vb u/\mathrm dt = \vb A\vb u + \vb b$
# as usual. This takes the same form as our [diffusion equation example](diffusion_equations.md),
# except with the extra $f(\vb x)u$ term, which just adds an exta $f(\vb x)$ term
# except with the extra $f(\vb x)u$ term, which just adds an extra $f(\vb x)$ term
# to the diagonal of $\vb A$. See the previois sections for further mathematical details.

# ## Implementation
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2 changes: 1 addition & 1 deletion docs/src/literate_wyos/poissons_equation.jl
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Expand Up @@ -312,7 +312,7 @@ E |> tc #hide
# For plotting the electric field, we will show the electric field intensity $\|\vb E\|$,
# and we can also show the arrows. Rather than showing all arrows, we will show them at
# a smaller grid of values, which requires differentiating `itp` so that we can get the
# gradients at arbitary points.
# gradients at arbitrary points.
∂ = differentiate(itp, 1)
x = LinRange(0, 10, 25)
y = LinRange(0, 10, 25)
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Original file line number Diff line number Diff line change
Expand Up @@ -82,7 +82,7 @@ We now need to define the internal conditions.
This is done using `InternalConditions`. First,
we need to find all the vertices that lie on
the line $\{x = 1/2, 0 \leq y \leq 2/5\}$. We could
compute these manually, but let's find them programatically
compute these manually, but let's find them programmatically
instead for the sake of demonstration.

````@example laplaces_equation_with_internal_dirichlet_conditions
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Expand Up @@ -8,7 +8,7 @@ tc = DisplayAs.withcontext(:displaysize => (15, 80), :limit => true); #hide
nothing #hide
````

# Piecewise Linear and Natural Neighbour Inteprolation for an Advection-Diffusion Equation
# Piecewise Linear and Natural Neighbour Interpolation for an Advection-Diffusion Equation

In this tutorial, we have three aims:

Expand Down Expand Up @@ -210,7 +210,7 @@ fig

## Natural neighbour interpolation

Since the solution is defined over a triangulation, the most natural form of inteprolation to use,
Since the solution is defined over a triangulation, the most natural form of interpolation to use,
other than piecewise linear interpolation, is natural neighbour interpolation. We can use
[NaturalNeighbours.jl](https://github.com/DanielVandH/NaturalNeighbours.jl) for this;
NaturalNeighbours.jl also provides the same piecewise linear interpolant above via its
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Original file line number Diff line number Diff line change
Expand Up @@ -53,7 +53,7 @@ u(y, t) = \begin{cases} 1-\mathrm{e}^{c_{\min}z} & z \leq 0, \\ 0 & z > 0, \end{
```

where $c_{\min} = \sqrt{\lambda/(2D)}$, $c = \sqrt{D\lambda/2}$, and $z = x-ct$ is the
travelling wave coordinates. This travelling wave would mathc our problem exactly
travelling wave coordinates. This travelling wave would match our problem exactly
if the rectangle were instead $[0, a] \times \mathbb R$, but by choosing $b$ large
enough we can at least emulate the travelling wave behaviour closely; the
homogeneous Neumann conditions are to ensure no energy is lost, thus allowing the travelling
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2 changes: 1 addition & 1 deletion docs/src/wyos/diffusion_equations.md
Original file line number Diff line number Diff line change
Expand Up @@ -198,7 +198,7 @@ end
````

Now that we have the parts for handling the main flux contributions, we need to consider
the boundary conditions. Note that in the code above we have alredy taken not to update
the boundary conditions. Note that in the code above we have already taken not to update
$\vb A$ or $\vb b$ if there a boundary condition at the associated node, so we do not
need to worry about e.g. zeroing out rows of $\vb A$ for a node with a boundary condition.

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2 changes: 1 addition & 1 deletion docs/src/wyos/linear_reaction_diffusion_equations.md
Original file line number Diff line number Diff line change
Expand Up @@ -27,7 +27,7 @@ To start, let's give the mathematical details. The problems we will be solving t

We want to turn this into an equation of the form $\mathrm d\vb u/\mathrm dt = \vb A\vb u + \vb b$
as usual. This takes the same form as our [diffusion equation example](diffusion_equations.md),
except with the extra $f(\vb x)u$ term, which just adds an exta $f(\vb x)$ term
except with the extra $f(\vb x)u$ term, which just adds an extra $f(\vb x)$ term
to the diagonal of $\vb A$. See the previois sections for further mathematical details.

## Implementation
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2 changes: 1 addition & 1 deletion docs/src/wyos/poissons_equation.md
Original file line number Diff line number Diff line change
Expand Up @@ -356,7 +356,7 @@ E |> tc #hide
For plotting the electric field, we will show the electric field intensity $\|\vb E\|$,
and we can also show the arrows. Rather than showing all arrows, we will show them at
a smaller grid of values, which requires differentiating `itp` so that we can get the
gradients at arbitary points.
gradients at arbitrary points.

````@example poissons_equation
∂ = differentiate(itp, 1)
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2 changes: 1 addition & 1 deletion src/specific_problems/mean_exit_time.jl
Original file line number Diff line number Diff line change
Expand Up @@ -26,7 +26,7 @@ You can solve this problem using [`solve`](@ref solve(::AbstractFVMTemplate, arg
- `ICs::InternalConditions=InternalConditions()`: The [`InternalConditions`](@ref).

The functions for `BCs` and `ICs` are not used. Whenever a [`Neumann`](@ref) condition is encountered,
or a [`Dirichlet`](@ref) condition, it is assumed that the conditon is homogeneous. If any of the
or a [`Dirichlet`](@ref) condition, it is assumed that the condition is homogeneous. If any of the
conditions are [`Dudt`](@ref) or [`Constrained`](@ref) types, then an error is thrown.

## Keyword Arguments
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