PHISPLIT -- phi-functions of Kronecker sums with direction splitting

The PHISPLIT algorithm approximates actions of phi-functions for d-dimensional Kronecker sums of matrices using a mu-mode approach. The technique is based on a direction splitting of the involved matrix functions, which generates an approximation error compatible with an exponential integrator up to second order. For more details, see the reference manuscript

M. Caliari and F. Cassini. Direction splitting of phi-functions in exponential integrators for d-dimensional problems in Kronecker form, arXiv preprint arXiv:2304.02327, 2023

This GitHub repository contains:

• phisplit.m (fully compatible with GNU Octave) which approximates action of phi-functions of Kronecker sums on a tensor
• phiquad.m (fully compatible with GNU Octave) whith computes matrix phi-functions using a quadrature rule
• all the functions and the scripts needed to reproduce the numerical examples contained in the reference manuscript (in the folder examples)

Software

You can directly download the zip archive of the latest complete release here.

Alternatively, since the repository makes use of git submodules, you can obtain all the relevant sources by executing

git clone --recursive https://github.com/caliarim/phisplit

Installing

The software is all consituted by MATLAB scripts. In order use PHISPLIT it is needed to have in path the function tucker.m from the package KronPACK, already available in the repository (see the section Software). In MATLAB/GNU Octave, this can be achieved by running the command

addpath('extern/KronPACK/src')

inside the folder phisplit.

Testing in GNU Octave

PHISPLIT contains several GNU Octave built-in self-tests that can be executed by running the command

test phisplit

For each test, the first argument in the GNU Octave assert command is compared to the second argument, up to the tolerance possibly given in the third argument. Therefore, it is possible to perform the same tests in MATLAB by slightly modifying the syntax of the test.