# LinearSolvers

There are five examples in the `ExampleCodes/LinearSolvers`

directory.

`ABecLaplacian_C`

demonstrates how to solve with cell-centered data in a C++ framework.
This example shows how to use either hypre or PETSc as a bottom-solver (or to solve
the equation at the finest level if you set the “max coarsening level” to 0.

Step-by-step instructions for configuring AMReX to use HYPRE for this example are available here.

`ABecLaplacian_F`

demonstrates how to solve with cell-centered data using the Fortran interfaces.

`NodalPoisson`

demonstrates how to set up and solve a variable coefficient Poisson equation
with the rhs and solution data on nodes.

`MultiComponent`

demonstrates how to solve using a multi-component operator with nodal data.
The operator is of the form \(D(\mathbf{\phi})_i = \alpha_{ij}\nabla^2\phi_j\), where \(\mathbf{\phi}\) is the multi-component solution variable and \(\alpha_{ij}\) is a matrix of coefficients.
The operator (`MCNodalLinOp`

) is implemented using the “reflux-free” method.

`NodeTensorLap`

solves the equation \(\nabla \cdot ( \sigma \nabla \phi ) = \text{RHS}\), where
\(\phi\) and \(\text{RHS}\) are nodal MultiFabs and \(\sigma\) is a tensor constant. It is
assumed that the tensor is symmetric with rank equal to `AMREX_SPACEDIM`

.