Adaptive ML-SCFEM is a MATLAB toolbox for computing and investigating adaptive stochastic collocation finite element approximations for elliptic PDEs with random inputs.
The code in this repository is associated with the following two papers:
-
A. Bespalov, D. Silvester and F. Xu,
Error estimation and adaptivity for stochastic collocation finite elements.
Part I: single-level approximation.
SIAM Journal on Scientific Computing, Vol. 44 (2022), Issue 5, pp. A3393-A3412.
https://doi.org/10.1137/21M1446745
Preprint
http://arxiv.org/abs/2109.07320 -
A. Bespalov and D. Silvester,
Error estimation and adaptivity for stochastic collocation finite elements.
Part II: multilevel approximation.
SIAM Journal on Scientific Computing, Vol. 45 (2023), Issue 2, pp. A781-A797.
https://doi.org/10.1137/22M1479361
Preprint
https://arxiv.org/abs/2202.08902
The driver for generating adaptive single-level SC-FEM approximations is
singlelevelSC.m
The driver for generating adaptive multilevel SC-FEM approximations is
multilevelSC.m
To run the software, download and unpack the file
adaptive_ml-scfem.zip
The default implementation is for a Unix architecture.
On a Windows machine, run the script-file
install_adaptive_scfem.m
before running the above main drivers for the first time.
The diary files included in this repository were generated using MATLAB R2021a running under Windows 10 Enterprise x64 Version 10.0.19042.
The test runs reproducing the numerical results in [1, Section 5] are saved
in the following diary files:
SCtest_sl_tp1.txt
SCtest_sl_tp2a.txt
SCtest_sl_tp2b.txt
SCtest_sl_tp2c.txt
The test runs reproducing the numerical results in [2, Section 4] are saved
in the following diary files:
SCtest_ml_tp1.txt
SCtest_ml_tp2c.txt
SCtest_sl_tp3.txt
SCtest_ml_tp3.txt
The T-IFISS* driver for the SG comparison run is
stoch_adapt_testproblem
The associated diary file is
SGtest_tp1.txt
*Stochastic T-IFISS can be downloaded from
https://github.com/albespalov/Stochastic_T-IFISS