# Ginkgo Integrations

[Ginkgo](https://ginkgo-project.github.io/) is a high-performance numerical
linear algebra library for many-core systems, with a focus on the solution of
sparse linear systems. It is implemented using modern C++ with GPU kernels for
NVIDIA (CUDA), AMD (HIP), and Intel (SYCL) GPUs. The library core contains
architecture-agnostic algorithms -- iterative solvers, preconditioners, and
matrix formats -- while runtime polymorphism selects the right
architecture-optimized kernel depending on the target hardware.

```{image} /docs/_static/ginkgo-arch.png
:alt: Ginkgo architecture
:align: center
:width: 70%
```

---

This site collects **self-contained integration examples** that demonstrate how
Ginkgo can be used as a solver backend inside established scientific computing
frameworks. Each example ships with its own build system, source code, and
documentation so you can study the approach, build it locally, and adapt it to
your own project.

---

## Browse by library

::::{grid} 2
:gutter: 3

:::{grid-item-card} deal.II
:link: /deal.ii/poisson/doc
:link-type: doc

Finite-element library for adaptive meshes.

- {doc}`Poisson </deal.ii/poisson/doc>` -- standard elliptic PDE
- {doc}`Adaptive Refinement </deal.ii/adaptive-refinement/doc>` -- AMR with Ginkgo solvers
:::

:::{grid-item-card} MFEM
:link: /mfem/poisson/doc
:link-type: doc

Scalable finite-element library with high-order support.

- {doc}`Poisson </mfem/poisson/doc>` -- basic diffusion problem
- {doc}`High-Order Diffusion </mfem/high-order/doc>` -- high-order elements
:::

:::{grid-item-card} NekRS
:link: /nekrs/poisson/doc
:link-type: doc

GPU-accelerated spectral-element CFD solver.

- {doc}`Poisson </nekrs/poisson/doc>` -- pressure-like solve
- {doc}`Turbulent Channel </nekrs/turbulent-channel/doc>` -- turbulent flow simulation
:::

:::{grid-item-card} SUNDIALS
:link: /sundials/poisson/doc
:link-type: doc

Suite of nonlinear and differential/algebraic equation solvers.

- {doc}`Poisson (KINSOL) </sundials/poisson/doc>` -- nonlinear system with Ginkgo linear solver
- {doc}`Stiff ODE (CVODE) </sundials/ode-system/doc>` -- stiff initial-value problem
:::

::::

---

## Compare by problem

### Poisson equation

The Poisson equation appears in nearly every scientific domain. Compare how
each framework formulates the same problem and uses Ginkgo to solve the
resulting linear system:

| Framework | Example | Approach |
|-----------|---------|----------|
| deal.II   | {doc}`Poisson </deal.ii/poisson/doc>` | Continuous Galerkin FEM on adaptive meshes |
| MFEM      | {doc}`Poisson </mfem/poisson/doc>` | High-performance FEM with flexible backends |
| NekRS     | {doc}`Poisson </nekrs/poisson/doc>` | Spectral-element discretization on GPUs |
| SUNDIALS  | {doc}`Poisson </sundials/poisson/doc>` | Nonlinear solve (KINSOL) with Ginkgo preconditioner |

---

```{toctree}
:hidden:

Integration Strategies </docs/strategies>
deal.II </deal.ii/index>
MFEM </mfem/index>
NekRS </nekrs/index>
SUNDIALS </sundials/index>
```