Triangular IFISS (T-IFISS)

T-IFISS is a MATLAB package for solving (deterministic) steady-state diffusion problems on general two-dimensional domains using finite element methods. It includes Galerkin approximations on triangular grids, a posteriori error estimation, and adaptive algorithms with local mesh refinement. Unstructured meshes are generated using the DistMesh package.
The core version of the package is available from the T-IFISS homepage. The following paper gives an overview of the key features of the package:

A. Bespalov, L. Rocchi and D. Silvester, T-IFISS: a toolbox for adaptive FEM computation, Computers & Mathematics with Applications, Vol. 81 (2021), pp. 373-390.
Link to the paper      Preprint on arXiv

Stochastic T-IFISS

Stochastic T-IFISS extends the core version of T-IFISS to cover stochastic Galerkin approximations of diffusion problems with random coefficients, the associated a posteriori error estimation and adaptive algorithms, including goal-oriented adaptivity and most recently multilevel adaptivity.

The adaptive algorithms for computing single-level stochastic Galerkin approximations are discussed in the following paper:

A. Bespalov and L. Rocchi, Efficient adaptive algorithms for elliptic PDEs with random data, SIAM/ASA Journal on Uncertainty Quantification, Vol. 6 (2018), no. 1, pp. 243-272.
Link to the paper      Download pdf-file

Goal-oriented error estimation strategy and the associated goal-oriented adaptive algorithm are presented in the following paper:

A. Bespalov, D. Praetorius, L. Rocchi and M. Ruggeri, Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs, Computer Methods in Applied Mechanics and Engineering, Vol. 345 (2019), pp. 951-982.
Link to the paper      Preprint on arXiv

An a posteriori error estimator for multilevel stochastic Galerkin approximations and adaptive algorithms for computing multilevel approximations are discussed in this paper:

A. Bespalov, D. Praetorius, and M. Ruggeri, Two-level a posteriori error estimation for adaptive multilevel stochastic Galerkin FEM, SIAM/ASA Journal on Uncertainty Quantification, Vol. 9 (2021), Issue 3, pp. 1184-1216.
Link to the paper      Preprint on arXiv

The complete T-IFISS package, including the stochastic extension, can be downloaded by clicking the button below.

T-IFISS can run on both Windows and MacOS computers. The toolbox has been tested using MATLAB version 9.1 and it is compatible with versions as far back as 6.5.
After you have unpacked the files, start MATLAB in the directory tifiss1.2. Type install_tifiss and follow the on-screen instructions. After installation, type setpath, helpme to get started.
The routines implementing stochastic Galerkin approximations for problems with random coefficients are included in the sub-directory stoch_diffusion.
Licence Information
This library is free software. It can be redistributed and/or modified under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY, and without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. Your use or distribution of T-IFISS or any derivative code implies that you agree to this License.

Copyright © 20172021 by Alex Bespalov, Leonardo Rocchi.