p4est 2020 HCM Summer School: Tuesday
Author: Carsten Burstedde

We are organizing a `p4est` summer school sponsored by the Hausdorff Center for Mathematics at the University of Bonn, Germany. Please see also the school's home page and application forms.

## Slot 21: Introduction to Cartesian grid AMR and ForestClaw

DC
  Donna Calhoun (speaker)

In this lecture, I introduce the concept of "adaptive mesh refinement" (AMR) for Cartesian grid solvers from the perspective of early developers interested in solving problems in shock hydrodynamics, through to modern developments using tree-based meshing. In the last part of the talk, I will describe ForestClaw, a parallel, adaptive finite volume solver for Cartesian grids based on p4est.

ForestClaw uses `p4est` for all mesh handling and MPI communication. It leverages the scalability of `p4est` for dynamic adaptive regridding and fast, effective load balancing. ForestClaw is used and adopted by various third-party simuation efforts. This is the first lecture out of three on the topic (slides).

## Slot 22: `p4est` theory (video)

CB
  Carsten Burstedde (local chair, organizer, speaker)

`p4est` is a particular lean implementation of linear octree storage, based on a flexible forest of octrees logical structure (see the connectivity tutorial for the precise encoding conventions). The theory behind all algorithms is based on the mathematical equivalence of a tree refinement and a space filling curve. All operations are reduced to a one-dimensional total order between the elements. This allows to store local and ghost elements in simple arrays and to index ranges of them with offset and length information. Pointers are not needed for single-element access.

`p4est` provides several high-level algorithms that are implemented using a large collection of small functions, most of them working on one or two elements, and some others executing various variants of binary searches. In this session we will discuss the fundamental logic and how it can be exploited to realize several interesting and useful AMR algorithms.

## Slot 23: `p4est` and deal.II, part I

TiH
  Timo Heister (speaker)

The examples and instructions are available at the deal.II and p4est repository.

Timo is one of the maintainers and developers of the deal.II finite element software. Since roughly 2010, deal.II interfaces to `p4est` for scalable mesh storage and modification. The link to `p4est` is well hidden to the user of the library. Thus, this connection is a minimally invasive example to upgrade the mesh storage of an adaptive simulation software without touching the discretization and solver code at all. This is the first out of three lectures on this topic.