fc2d_hps: ForestClaw2D Hierarchical Poincaré-Steklov Implementation

Overview

This repo contains the ongoing implementation of the Hierarchical Poincaré-Steklov (HPS) Method into ForestClaw.

The HPS method is a direct solver for elliptic PDEs.

NOTE: This is not currently meant to be a stand-alone code; it is meant to be cloned into a ForestClaw instance under ${FORESTCLAW_ROOT}/src/solvers.

Features

Current implementation includes a serial, uniform implementation on a p4est grid.

Current patch solvers include FISHPACK90 for solving Poisson's equation on a rectangular domain.

Future implementations include adaptive and parallel implementations of the HPS method, both on CPUs and GPUs using PETSc and Kokkos.

Future patch solvers include a variable coefficient Poisson solver and dispersive Shallow Water Equations (Serre-Green-Naghdi model) for 2D simulations.

Installation

As mentioned above, this is meant to be included as part of a ForestClaw installation. There are uses of ForestClaw functions throughout the HPS functions. A stand-alone version is in the works as well.

To install, first clone ForestClaw: ForestClaw on Github. Then, switch to the develop branch; all fc2d_hps work is being done in tandem to the develop branch of ForestClaw:

git clone https://github.com/ForestClaw/forestclaw
git checkout develop

After cloning ForestClaw but before configuration and compiling, clone this repo into the solvers directory in ForestClaw:

cd ${FORESTCLAW_ROOT}/src/solvers
git clone https://github.com/ForestClaw/fc2d_hps

Once fc2d_hps is a directory in the ForestClaw solvers directory, navigate back to ${FORESTCLAW_ROOT} and configure with cmake. To use fc2d_hps with ForestClaw, you need specific flags set when configuring cmake, namely:

-Dclawpatch=on
-Dmpi=on
-Dhps=on

See the ForestClaw documentation on other installation configuration. When I configure, I use the following script in a build directory parallel to the ForestClaw source directory:

FCLAW=../forestclaw-source

cmake configure \
	-DCMAKE_Fortran_COMPILER=gfortran \
	-DCMAKE_C_COMPILER=mpicc \
	-DCMAKE_CXX_COMPILER=mpic++ \
	-Dclawpatch=on \
	-Dmpi=on \
  	-Dhps=on \
	${FCLAW}

Once configured properly, use make to compile:

make -j

You can run all unit tests via make as well:

make -j test

Usage

Currently, there are two executables to work with, hello and simple. They are found under ${FORESTCLAW_ROOT}/src/solvers/fc2d_hps/examples/

hello

The hello program simply imports all necessary headers and prints out a welcoming message to check for all libraries.

simple

The simple program solves a Poisson equation on a 2D rectangular domain. All options are found in the fclaw_options.ini file. To run:

./simple fclaw_options.ini