Introduction to Afivo

Table of Contents

• What is Afivo?
• For which problems can Afivo be used?
• What is included?
• What is not included?

What is Afivo?

Afivo is a framework for simulations on adaptively refined quadtree and octree grids. Because Afivo has no built-in support for specific physics applications a user has to write his/her own numerical methods. Some key features/characteristics of the framework are:

• Adaptively refined quadtree and octree grids
• OpenMP parallelization
• Geometric multigrid routines
• Flexible handling of refinement and physical boundaries
• Written in modern Fortran
• Fully open source
• Application-independent
• Silo and VTK unstructured output

The motivation for developing Afivo is discussed in [3]. In summary, the main reason was to provide a relatively simple framework that can easily be modified.

For which problems can Afivo be used?

Afivo can be used to simulate physical systems exhibiting multiscale features, e.g. features that appear at different spatial and temporal scales. Numerical simulations of such systems benefit from Afivo's adaptive mesh refinement (AMR), especially if a high-resolution mesh is only required in a small fraction of the total volume.

What is included?

Afivo provides general functionality for parallel simulations with adaptive mesh refinement:

• It can adjust the refinement according to user-supplied information
• It stores cell-centered and face-centered variables
• It provides routines to perform restriction and prolongation (to convert fine grid values to coarse ones and vice versa)
• It can fill so-called ghost cells, which allow the user to perform computations as on a uniform grid
• It can (help) solve elliptic partial differential equations with the built-in multigrid methods
• It can write output in Silo and VTK format, which can directly be visualized with tools such as Visit

What is not included?

Besides the multigrid methods, there are no built-in solvers. To use Afivo for e.g. hyperbolic problems, a user will have to implement both a spatial and temporal discretization. Some of the included Examples show how this can be done.