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JoshuaLampert committed Jul 20, 2024
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2 changes: 1 addition & 1 deletion docs/src/pdes.md
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Expand Up @@ -85,7 +85,7 @@ non-symmetric collocation.

Let us see how this can be implemented in KernelInterpolation.jl by solving the Poisson equation ``-\Delta u = f`` in an L-shaped
domain. We start by defining the equation (thus the differential operator) and the right-hand side. KernelInterpolation.jl already
provides a set of predefined [differential operators](@ref api-diffops) and [equations](@ref api-stateq).
provides a set of predefined [differential operators](@ref api-diffops) and [equations](@ref api-equations).

```@example poisson
using KernelInterpolation
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127 changes: 36 additions & 91 deletions docs/src/ref.md
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CurrentModule = KernelInterpolation
```

```@autodocs
Modules = [KernelInterpolation]
Pages = ["KernelInterpolation.jl"]
```

## [Kernel functions](@id api-kernels)

```@docs
AbstractKernel
get_name
RadialSymmetricKernel
Phi
phi
GaussKernel
MultiquadricKernel
InverseMultiquadricKernel
PolyharmonicSplineKernel
ThinPlateSplineKernel
WendlandKernel
WuKernel
RadialCharacteristicKernel
MaternKernel
Matern12Kernel
Matern32Kernel
Matern52Kernel
Matern72Kernel
RieszKernel
SumKernel
ProductKernel
TransformationKernel
```@autodocs
Modules = [KernelInterpolation]
Pages = [joinpath("kernels", "kernels.jl"), joinpath("kernels", "radialsymmetric.jl"), joinpath("kernels", "special_kernels.jl")]
```

## Node sets

```@docs
NodeSet
empty_nodeset
separation_distance
values_along_dim
distance_matrix
random_hypercube
random_hypercube_boundary
homogeneous_hypercube
homogeneous_hypercube_boundary
random_hypersphere
random_hypersphere_boundary
```@autodocs
Modules = [KernelInterpolation]
Pages = ["nodes.jl"]
```

## Interpolation

```@docs
Interpolation
TemporalInterpolation
interpolate
kernel_inner_product
kernel_norm
dim
interpolation_kernel
nodeset
coefficients
kernel_coefficients
polynomial_coefficients
polynomial_basis
polyvars
order
system_matrix
```@autodocs
Modules = [KernelInterpolation]
Pages = ["interpolation.jl"]
```

## [Differential Operators](@id api-diffops)

```@docs
PartialDerivative
Gradient
Laplacian
EllipticOperator
```

## [Stationary partial differential equations](@id api-stateq)

```@docs
PoissonEquation
EllipticEquation
```@autodocs
Modules = [KernelInterpolation]
Pages = ["differential_operators.jl"]
```

## Time-dependent partial differential equations
## [Partial differential equations](@id api-equations)

```@docs
AdvectionEquation
HeatEquation
AdvectionDiffusionEquation
```@autodocs
Modules = [KernelInterpolation]
Pages = ["equations.jl"]
```

## Discretization

```@docs
SpatialDiscretization
solve_stationary
Semidiscretization
semidiscretize
```@autodocs
Modules = [KernelInterpolation]
Pages = ["discretization.jl"]
```

## Kernel matrices

```@docs
kernel_matrix
polynomial_matrix
pde_matrix
pde_boundary_matrix
operator_matrix
```@autodocs
Modules = [KernelInterpolation]
Pages = ["kernel_matrices.jl"]
```

## [Callbacks](@id api-callbacks)

```@docs
AliveCallback
SummaryCallback
SaveSolutionCallback
```@autodocs
Modules = [KernelInterpolation]
Pages = [joinpath("callbacks_step", "alive.jl"), joinpath("callbacks_step", "summary.jl"), joinpath("callbacks_step", "save_solution.jl")]
```

## Input/Output

```@docs
vtk_read
vtk_save
add_to_pvd
```@autodocs
Modules = [KernelInterpolation]
Pages = ["io.jl"]
```

## Utilities

```@docs
examples_dir
get_examples
default_example
```@autodocs
Modules = [KernelInterpolation]
Pages = ["util.jl"]
```

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