DMK Matlab

Matlab implementation of the Dual-space Multilevel Kernel-splitting (DMK) method for Stokes and Laplace potentials.

Companion code to the preprint Fast summation of Stokes potentials using a new kernel-splitting in the DMK framework by Ludvig af Klinteberg, Leslie Greengard, Shidong Jiang, and Anna-Karin Tornberg.

This is a prototype implementation of the DMK algorithm, designed to aid in understanding the algorithm and in the design of new kernels or other modifications. It is not a fast HPC code. For that, please refer to the official implementation hosted by the Flatiron Institute at https://github.com/flatironinstitute/dmk

Setup

To initialize submodules, run

git submodule update --init --recursive

Usage

• Start Matlab in root directory
• init initializes paths
• runtests runs the test suite
• demo_dmk runs DMK and compares it to a direct summation. Showcases use for all kernels and free space / periodic.
• demo_scaling shows linear scaling
• Scripts in experiments/ reproduce results from paper.

Code structure

• dev_scripts/: bits and pieces of code used when developing functionality
• external/: third-party packages in the form of Git submodules
• src/: all routines needed for DMK
• src/+kernels/: kernel splittings
• src/+approx/ is a package with the routines for approximation using Chebyshev functions and tensor product grids. Holds its own tests in tests.m
• test/: unit tests