List of all functions

struct Geometry{nDim,T}

A struct representing the geometry of a topological object in nDim dimensions.

Arguments

• nDim: The number of dimensions of the topological object.
• T: The type of the elements in the topological object.

cart2ind(A)

Return the linear index of a n-dimensional array corresponding to the cartesian indices I

element(A, element_indices..., cell_indices...)

Return a the element with element_indices of the Cell with cell_indices of the CellArray A.

Arguments

• element_indices::Int|NTuple{N,Int}: the element_indices that designate the field in accordance with A's cell type.
• cell_indices::Int|NTuple{N,Int}: the cell_indices that designate the cell in accordance with A's cell type.

setelement!(A, x, element_indices..., cell_indices...)

Store the given value x at the given element with element_indices of the cell with the indices cell_indices

Arguments

• x::Number: value to be stored in the index element_indices of the cell with cell_indices.
• element_indices::Int|NTuple{N,Int}: the element_indices that designate the field in accordance with A's cell type.
• cell_indices::Int|NTuple{N,Int}: the cell_indices that designate the cell in accordance with A's cell type.

velocity_grids(xci, xvi, di::NTuple{N,T}) where {N,T}

Compute the velocity grids for N dimensionional problems.

Arguments

• xci: The x-coordinate of the cell centers.
• xvi: The x-coordinate of the cell vertices.
• di: A tuple containing the cell dimensions.

WENO5{T, N, A, M} <: AbstractWENO

The WENO5 is a structure representing the Weighted Essentially Non-Oscillatory (WENO) scheme of order 5 for the solution of hyperbolic partial differential equations.

Fields

• d0L, d1L, d2L: Upwind constants.
• d0R, d1R, d2R: Downwind constants.
• c1, c2: Constants for betas.
• sc1, sc2, sc3, sc4, sc5: Stencil weights.
• ϵ: Tolerance.
• ni: Grid size.
• ut: Intermediate buffer array.
• fL, fR, fB, fT: Fluxes.
• method: Method (1:JS, 2:Z).

Description

The WENO5 structure contains the parameters and temporary variables used in the WENO scheme. These include the upwind and downwind constants, the constants for betas, the stencil candidate weights, the tolerance, the grid size, the fluxes, and the method.

WENO_advection!(u, Vxi, weno, di, ni, dt)

Perform the advection step of the Weighted Essentially Non-Oscillatory (WENO) scheme for the solution of hyperbolic partial differential equations.

Arguments

• u: field to be advected.
• Vxi: velocity field.
• weno: structure containing the WENO scheme parameters and temporary variables.
• di: grid spacing.
• ni: number of grid points.
• dt: time step.

Description

The function first calculates the fluxes using the WENO scheme. Then it performs three steps of the WENO scheme. Each step involves calculating the right-hand side of the WENO equation and updating the solution u. The updating of the solution u is done using different combinations of the original solution and the temporary solution weno.ut.

heatdiffusion_PT!(thermal, pt_thermal, K, ρCp, dt, di; iterMax, nout, verbose)

Heat diffusion solver using Pseudo-Transient iterations. Both K and ρCp are n-dimensional arrays.

heatdiffusion_PT!(thermal, pt_thermal, rheology, dt, di; iterMax, nout, verbose)

Heat diffusion solver using Pseudo-Transient iterations.

allzero(x::Vararg{T,N}) where {T,N}

Check if all elements in x are zero.

Arguments

• x::Vararg{T,N}: The input array.

Returns

• Bool: true if all elements in x are zero, false otherwise.

assign!(B::AbstractArray{T,N}, A::AbstractArray{T,N}) where {T,N}

Assigns the values of array A to array B in parallel.

Arguments

• B::AbstractArray{T,N}: The destination array.
• A::AbstractArray{T,N}: The source array.

computeP!(P, P0, RP, ∇V, ΔTc, η, rheology::NTuple{N,MaterialParams}, phaseratio::C, dt, r, θ_dτ)

Compute the pressure field P and the residual RP for the compressible case. This function introduces thermal stresses after the implementation of Kiss et al. (2023). The temperature difference ΔTc on the cell center is used to compute this as well as α as the thermal expansivity.

compute_buoyancy(rheology, args, phase_ratios)

Compute the buoyancy forces based on the given rheology, arguments, and phase ratios.

Arguments

• rheology: The rheology used to compute the buoyancy forces.
• args: Additional arguments required by the rheology.
• phase_ratios: The ratios of the different phases.

compute_buoyancy(rheology, args)

Compute the buoyancy forces based on the given rheology and arguments.

Arguments

• rheology: The rheology used to compute the buoyancy forces.
• args: Additional arguments required for the computation.

compute_buoyancy(rheology::MaterialParams, args, phase_ratios)

Compute the buoyancy forces for a given set of material parameters, arguments, and phase ratios.

Arguments

• rheology: The material parameters.
• args: The arguments.
• phase_ratios: The phase ratios.

compute_buoyancy(rheology::MaterialParams, args)

Compute the buoyancy forces based on the given rheology parameters and arguments.

Arguments

• rheology::MaterialParams: The material parameters for the rheology.
• args: The arguments for the computation.

compute_dt(S::JustRelax.StokesArrays, args...)

Compute the time step dt for the simulation.

maxloc!(B, A; window)

Compute the maximum value of A in the window = (width_x, width_y, width_z) and store the result in B.

compute_ρg!(ρg, rheology, args)

Calculate the buoyance forces ρg for the given GeoParams.jl rheology object and correspondent arguments args.

compute_ρg!(ρg, phase_ratios, rheology, args)

Calculate the buoyance forces ρg for the given GeoParams.jl rheology object and correspondent arguments args. The phase_ratios are used to compute the density of the composite rheology.

continuation_log(x_new, x_old, ν)

Do a continuation step exp((1-ν)*log(x_old) + ν*log(x_new)) with damping parameter ν

flow_bcs!(stokes, bcs::VelocityBoundaryConditions)

Apply the prescribed flow boundary conditions bc on the stokes

flow_bcs!(stokes, bcs::DisplacementBoundaryConditions)

Apply the prescribed flow boundary conditions bc on the stokes

fn_ratio(fn::F, rheology::NTuple{N, AbstractMaterialParamsStruct}, ratio) where {N, F}

Average the function fn over the material phases in rheology using the phase ratios ratio.

interp_Vx_on_Vy!(Vx_on_Vy, Vx)

Interpolates the values of Vx onto the grid points of Vy.

Arguments

• Vx_on_Vy::AbstractArray: Vx at Vy grid points.
• Vx::AbstractArray: Vx at its staggered grid points.

nphases(x::JustRelax.PhaseRatio)

Return the number of phases in x::JustRelax.PhaseRatio.

Jaumann derivative

τijo += vk * ∂τijo/∂xk - ωij * ∂τkjo + ∂τkjo * ωij

take(fldr::String)

Create folder fldr if it does not exist.

tensor_invariant!(A::JustRelax.SymmetricTensor)

Compute the tensor invariant of the given symmetric tensor A.

Arguments

• A::JustRelax.SymmetricTensor: The input symmetric tensor.

thermal_bcs!(T, bcs::TemperatureBoundaryConditions)

Apply the prescribed heat boundary conditions bc on the T

velocity2vertex!(Vx_v, Vy_v, Vz_v, Vx, Vy, Vz)

In-place interpolation of the velocity field Vx, Vy, Vz from a staggered grid with ghost nodes onto the pre-allocated Vx_d, Vy_d, Vz_d 3D arrays located at the grid vertices.

velocity2vertex(Vx, Vy, Vz)

Interpolate the velocity field Vx, Vy, Vz from a staggered grid with ghost nodes onto the grid vertices.

@add(I, args...)

Add I to the scalars in args

copy(B, A)

convenience macro to copy data from the array A into array B

@displacement(U)

Unpacks the displacement arrays U from the StokesArrays A.

@idx(args...)

Make a linear range from 1 to args[i], with i ∈ [1, ..., n]

@normal(A)

Unpacks the normal components of the symmetric tensor A, where its components are defined in the staggered grid. Shear components are unpack following Voigt's notation.

@plastic_strain(A)

Unpacks the plastic strain rate tensor ε_pl from the StokesArrays A, where its components are defined in the staggered grid. Shear components are unpack following Voigt's notation.

@qT(V)

Unpacks the flux arrays qT_i from the ThermalArrays A.

@qT2(V)

Unpacks the flux arrays qT2_i from the ThermalArrays A.

@residuals(A)

Unpacks the momentum residuals from A.

@shear(A)

Unpacks the shear components of the symmetric tensor A, where its components are defined in the staggered grid. Shear components are unpack following Voigt's notation.

@strain(A)

Unpacks the strain rate tensor ε from the StokesArrays A, where its components are defined in the staggered grid. Shear components are unpack following Voigt's notation.

@strain_center(A)

Unpacks the strain rate tensor ε from the StokesArrays A, where its components are defined in the center of the grid cells. Shear components are unpack following Voigt's notation.

@stress(A)

Unpacks the deviatoric stress tensor τ from the StokesArrays A, where its components are defined in the staggered grid. Shear components are unpack following Voigt's notation.

@stress_center(A)

Unpacks the deviatoric stress tensor τ from the StokesArrays A, where its components are defined in the center of the grid cells. Shear components are unpack following Voigt's notation.

@tensor(A)

Unpacks the symmetric tensor A, where its components are defined in the staggered grid. Shear components are unpack following Voigt's notation.

@tensor_center(A)

Unpacks the symmetric tensor A, where its components are defined in the center of the grid cells. Shear components are unpack following Voigt's notation.

@velocity(V)

Unpacks the velocity arrays V from the StokesArrays A.

WENO5{T, N, A, M} <: AbstractWENO

The WENO5 is a structure representing the Weighted Essentially Non-Oscillatory (WENO) scheme of order 5 for the solution of hyperbolic partial differential equations.

Fields

• d0L, d1L, d2L: Upwind constants.
• d0R, d1R, d2R: Downwind constants.
• c1, c2: Constants for betas.
• sc1, sc2, sc3, sc4, sc5: Stencil weights.
• ϵ: Tolerance.
• ni: Grid size.
• ut: Intermediate buffer array.
• fL, fR, fB, fT: Fluxes.
• method: Method (1:JS, 2:Z).

Description

The WENO5 structure contains the parameters and temporary variables used in the WENO scheme. These include the upwind and downwind constants, the constants for betas, the stencil candidate weights, the tolerance, the grid size, the fluxes, and the method.

WENO_advection!(u, Vxi, weno, di, ni, dt)

Perform the advection step of the Weighted Essentially Non-Oscillatory (WENO) scheme for the solution of hyperbolic partial differential equations.

Arguments

• u: field to be advected.
• Vxi: velocity field.
• weno: structure containing the WENO scheme parameters and temporary variables.
• di: grid spacing.
• ni: number of grid points.
• dt: time step.

Description

The function first calculates the fluxes using the WENO scheme. Then it performs three steps of the WENO scheme. Each step involves calculating the right-hand side of the WENO equation and updating the solution u. The updating of the solution u is done using different combinations of the original solution and the temporary solution weno.ut.

heatdiffusion_PT!(thermal, pt_thermal, K, ρCp, dt, di; iterMax, nout, verbose)

Heat diffusion solver using Pseudo-Transient iterations. Both K and ρCp are n-dimensional arrays.

heatdiffusion_PT!(thermal, pt_thermal, rheology, dt, di; iterMax, nout, verbose)

Heat diffusion solver using Pseudo-Transient iterations.

allzero(x::Vararg{T,N}) where {T,N}

Check if all elements in x are zero.

Arguments

• x::Vararg{T,N}: The input array.

Returns

• Bool: true if all elements in x are zero, false otherwise.

assign!(B::AbstractArray{T,N}, A::AbstractArray{T,N}) where {T,N}

Assigns the values of array A to array B in parallel.

Arguments

• B::AbstractArray{T,N}: The destination array.
• A::AbstractArray{T,N}: The source array.

computeP!(P, P0, RP, ∇V, ΔTc, η, rheology::NTuple{N,MaterialParams}, phaseratio::C, dt, r, θ_dτ)

Compute the pressure field P and the residual RP for the compressible case. This function introduces thermal stresses after the implementation of Kiss et al. (2023). The temperature difference ΔTc on the cell center is used to compute this as well as α as the thermal expansivity.

compute_buoyancy(rheology, args, phase_ratios)

Compute the buoyancy forces based on the given rheology, arguments, and phase ratios.

Arguments

• rheology: The rheology used to compute the buoyancy forces.
• args: Additional arguments required by the rheology.
• phase_ratios: The ratios of the different phases.

compute_buoyancy(rheology, args)

Compute the buoyancy forces based on the given rheology and arguments.

Arguments

• rheology: The rheology used to compute the buoyancy forces.
• args: Additional arguments required for the computation.

compute_buoyancy(rheology::MaterialParams, args, phase_ratios)

Compute the buoyancy forces for a given set of material parameters, arguments, and phase ratios.

Arguments

• rheology: The material parameters.
• args: The arguments.
• phase_ratios: The phase ratios.

compute_buoyancy(rheology::MaterialParams, args)

Compute the buoyancy forces based on the given rheology parameters and arguments.

Arguments

• rheology::MaterialParams: The material parameters for the rheology.
• args: The arguments for the computation.

compute_dt(S::JustRelax.StokesArrays, args...)

Compute the time step dt for the simulation.

maxloc!(B, A; window)

Compute the maximum value of A in the window = (width_x, width_y, width_z) and store the result in B.

compute_ρg!(ρg, rheology, args)

Calculate the buoyance forces ρg for the given GeoParams.jl rheology object and correspondent arguments args.

compute_ρg!(ρg, phase_ratios, rheology, args)

Calculate the buoyance forces ρg for the given GeoParams.jl rheology object and correspondent arguments args. The phase_ratios are used to compute the density of the composite rheology.

continuation_log(x_new, x_old, ν)

Do a continuation step exp((1-ν)*log(x_old) + ν*log(x_new)) with damping parameter ν

flow_bcs!(stokes, bcs::VelocityBoundaryConditions)

Apply the prescribed flow boundary conditions bc on the stokes

flow_bcs!(stokes, bcs::DisplacementBoundaryConditions)

Apply the prescribed flow boundary conditions bc on the stokes

fn_ratio(fn::F, rheology::NTuple{N, AbstractMaterialParamsStruct}, ratio) where {N, F}

Average the function fn over the material phases in rheology using the phase ratios ratio.

interp_Vx_on_Vy!(Vx_on_Vy, Vx)

Interpolates the values of Vx onto the grid points of Vy.

Arguments

• Vx_on_Vy::AbstractArray: Vx at Vy grid points.
• Vx::AbstractArray: Vx at its staggered grid points.

nphases(x::JustRelax.PhaseRatio)

Return the number of phases in x::JustRelax.PhaseRatio.

Jaumann derivative

τijo += vk * ∂τijo/∂xk - ωij * ∂τkjo + ∂τkjo * ωij

take(fldr::String)

Create folder fldr if it does not exist.

tensor_invariant!(A::JustRelax.SymmetricTensor)

Compute the tensor invariant of the given symmetric tensor A.

Arguments

• A::JustRelax.SymmetricTensor: The input symmetric tensor.

thermal_bcs!(T, bcs::TemperatureBoundaryConditions)

Apply the prescribed heat boundary conditions bc on the T

velocity2vertex!(Vx_v, Vy_v, Vz_v, Vx, Vy, Vz)

In-place interpolation of the velocity field Vx, Vy, Vz from a staggered grid with ghost nodes onto the pre-allocated Vx_d, Vy_d, Vz_d 3D arrays located at the grid vertices.

velocity2vertex(Vx, Vy, Vz)

Interpolate the velocity field Vx, Vy, Vz from a staggered grid with ghost nodes onto the grid vertices.

@add(I, args...)

Add I to the scalars in args

copy(B, A)

convenience macro to copy data from the array A into array B

@displacement(U)

Unpacks the displacement arrays U from the StokesArrays A.

@idx(args...)

Make a linear range from 1 to args[i], with i ∈ [1, ..., n]

@normal(A)

Unpacks the normal components of the symmetric tensor A, where its components are defined in the staggered grid. Shear components are unpack following Voigt's notation.

@plastic_strain(A)

Unpacks the plastic strain rate tensor ε_pl from the StokesArrays A, where its components are defined in the staggered grid. Shear components are unpack following Voigt's notation.

@qT(V)

Unpacks the flux arrays qT_i from the ThermalArrays A.

@qT2(V)

Unpacks the flux arrays qT2_i from the ThermalArrays A.

@residuals(A)

Unpacks the momentum residuals from A.

@shear(A)

Unpacks the shear components of the symmetric tensor A, where its components are defined in the staggered grid. Shear components are unpack following Voigt's notation.

@strain(A)

Unpacks the strain rate tensor ε from the StokesArrays A, where its components are defined in the staggered grid. Shear components are unpack following Voigt's notation.

@strain_center(A)

Unpacks the strain rate tensor ε from the StokesArrays A, where its components are defined in the center of the grid cells. Shear components are unpack following Voigt's notation.

@stress(A)

Unpacks the deviatoric stress tensor τ from the StokesArrays A, where its components are defined in the staggered grid. Shear components are unpack following Voigt's notation.

@stress_center(A)

Unpacks the deviatoric stress tensor τ from the StokesArrays A, where its components are defined in the center of the grid cells. Shear components are unpack following Voigt's notation.

@tensor(A)

Unpacks the symmetric tensor A, where its components are defined in the staggered grid. Shear components are unpack following Voigt's notation.

@tensor_center(A)

Unpacks the symmetric tensor A, where its components are defined in the center of the grid cells. Shear components are unpack following Voigt's notation.

@velocity(V)

Unpacks the velocity arrays V from the StokesArrays A.

checkpointing_jld2(dst, stokes, thermal, time, timestep, igg)

Save necessary data in dst as a jld2 file to restart the model from the state at time. If run in parallel, the file will be named after the corresponidng rank e.g. checkpoint0000.jld2 and thus can be loaded by the processor while restarting the simulation. If you want to restart your simulation from the checkpoint you can use load() and specify the MPI rank by providing a dollar sign and the rank number.

Example

```julia
checkpointing_jld2(
    "path/to/dst",
    stokes,
    thermal,
    t,
    igg,
)

```

checkpointing_hdf5(dst, stokes, T, η, time, timestep)

Save necessary data in dst as and HDF5 file to restart the model from the state at time

load_checkpoint_hdf5(file_path)

Load the state of the simulation from an .h5 file.

Arguments

• file_path: The path to the .h5 file.

Returns

• P: The loaded state of the pressure variable.
• T: The loaded state of the temperature variable.
• Vx: The loaded state of the x-component of the velocity variable.
• Vy: The loaded state of the y-component of the velocity variable.
• Vz: The loaded state of the z-component of the velocity variable.
• η: The loaded state of the viscosity variable.
• t: The loaded simulation time.
• dt: The loaded simulation time.

Example

```julia

Define the path to the .h5 file

file_path = "path/to/your/file.h5"

Use the load_checkpoint function to load the variables from the file

P, T, Vx, Vy, Vz, η, t, dt = load_checkpoint(file_path)`

load_checkpoint_jld2(file_path)

Load the state of the simulation from a .jld2 file.

Arguments

• file_path: The path to the .jld2 file.

Returns

• stokes: The loaded state of the stokes variable.
• thermal: The loaded state of the thermal variable.
• time: The loaded simulation time.
• timestep: The loaded time step.

metadata(src, dst, files...)

Copy files..., Manifest.toml, and Project.toml from src to dst

function save_hdf5(dst, fname, data)

Save data as the fname.h5 HDF5 file in the folder dst

function save_hdf5(fname, data)

Save data as the fname.h5 HDF5 file