Wave-Based Stochastic Solvers

Overview

This repository consolidates the MATLAB implementations that accompany the thesis Scalable Domain Decomposition Methods for Nonlinear and Time-Dependent Stochastic Systems. The projects cover intrusive and non-intrusive stochastic finite element solvers, domain decomposition strategies, Monte Carlo studies, and reference data for both one-dimensional and two-dimensional acoustic wave problems.

The codebase has been reorganized to keep artifacts in a predictable layout:

.
├── projects
│   ├── 1d
│   │   └── 1dwave
│   └── 2d
│       ├── RV_2Dresults
│       ├── acoustic_DDM_verification
│       ├── acoustic_wave
│       ├── wave_DirectDDM
│       ├── wave_LNP_TwoLevel
│       ├── wave_Lumped
│       ├── wave_MCS_RV
│       ├── wave_NISP_process
│       ├── wave_Neumann
│       ├── wave_RV
│       └── wave_TwoLevel
└── resources
    └── misc

• projects/1d contains the complete one-dimensional solver suite (deterministic, intrusive, Monte Carlo, and NISP variants) plus generated 1D figures/results.
• projects/2d holds the two-dimensional acoustic wave solvers, verification studies, Monte Carlo runs, and post-processing utilities.
• resources/misc stores auxiliary scripts (e.g., Cijk utilities) and analytical comparison figures shared across projects.

Project Highlights

1D suite (projects/1d/1dwave)

Module	Purpose	Notable contents
wave_direct	Baseline deterministic solver for axial bar dynamics.	Ready-to-plot .fig outputs (e.g., dx01deltaT002EA5.fig).
wave_MCS	Monte Carlo sampling with bootstrap studies.	results/ with convergence studies and experiment scripts.
wave_NISP	Non-intrusive spectral projection workflows.	Companion scripts (wave_NISP.m, wave_NISP_newimplementation.m) that reuse stiffness assembly helpers.
wave_Intrusive	Intrusive polynomial chaos implementation.	Assemble_stochastic.m, Cijk030001.mat, and Results/ snapshots.
wave_DDM	Simple 1D domain decomposition demonstrator.	wave_direct.m + acceleration utilities.
1dMCS_gmsh	Helper utilities to build meshes and inputs for Monte Carlo experiments.	axialbar.geo/msh, node/element tables, and extraction scripts.
results	Shared figures/tables cited across subprojects.	PCA figures, mean/SD plots, and convergence diagnostics.

2D suite (projects/2d)

Folder	Focus	Key elements
acoustic_wave	Full pipeline for 2D wave propagation (mesh, data, source, FEniCS verification).	code_verification/, deterministic data/, and source configuration scripts.
acoustic_DDM_verification	Deterministic verification of DDM implementations with Schur-complement diagnostics.	Precomputed interface matrices and figure outputs (e.g., match_01_DDM.fig).
wave_DirectDDM	Direct domain decomposition solver with coarse grid and preconditioner experiments.	A_*.mat, Bt_*, Kt_*, plus solver scripts (DoPCGM_*, GetCoarseGrid.m).
wave_LNP_TwoLevel	Two-level Neumann–Neumann solvers with lognormal parameters.	Hybrid solvers, preconditioners, and results/GaussianPulse_nodamp_233_01/ outputs.
wave_Lumped	Lumped-mass variants storing hundreds of assembled matrices (A_*, M_*).	Dataset for testing mass-lumped preconditioners.
wave_MCS_RV	Monte Carlo solver for random variables with stored result sets (results/2000_sd_1_nodamp, etc.).	Mesh extractions (ExtractGmsh.m) and geometry tables.
wave_NISP_process	Workflow for NISP processing and visualization.	Multiple mindex*.dat files, norm snapshots, and plotting figures.
wave_Neumann	Pure Neumann preconditioner experiments mirroring wave_Lumped data volume.	A_* and M_* archives plus solver scripts.
wave_RV	Random-variable-driven direct solvers with deterministic (AbDet) and stochastic (AbSto) datasets.	Rich results/ directory for Gaussian pulse cases.
wave_TwoLevel	Full two-level hierarchy storing assembled coarse/fine matrices.	Extensive A_*/M_* collections used for parametric sweeps.
RV_2Dresults	Lightweight post-processing scripts and figures that summarize random-variable experiments.	compare_2D.m and exported mean/SD figures.

Shared resources (resources/misc)

Contains helper scripts for constructing Cijk tensors, analytical comparison .fig files, and quick-and-dirty prototyping scripts (e.g., batch_converegence.m). These utilities are intentionally decoupled from the project directories so they can be reused globally.

Getting Started

1. Clone or download this repository and ensure MATLAB R2019b (or newer) is available.
2. Choose a study from projects/1d or projects/2d, open the relevant .m driver (for example, projects/1d/1dwave/wave_MCS/wave_MCS.m).
3. Adjust solver parameters in the corresponding script sections (time step, number of samples, stochastic dimension, etc.).
4. Run the script from MATLAB. Outputs are written back into each module’s results/ directory so they stay co-located with the driving code.

Tip: the repository is intentionally data-light. Large .mat artifacts have been removed and should be regenerated by running the appropriate driver scripts.

Reference

Scalable Domain Decomposition Methods for Nonlinear and Time-Dependent Stochastic Systems

Authors: Vasudevan, Padillath and Sharma, Sudhi
Institution: Carleton University (2023)
DOI: 10.22215/etd/2023-15817

Click to expand BibTeX citation

@phdthesis{vasudevan2023scalable,
  title={Scalable Domain Decomposition Methods for Nonlinear and Time-Dependent Stochastic Systems},
  author={Vasudevan, Padillath and Sharma, Sudhi},
  year={2023},
  school={Carleton University},
  doi={10.22215/etd/2023-15817}
}

How to Contribute

• File an issue describing the solver or dataset you want to extend.
• Follow MATLAB best practices (function headers, input validation) when adding new scripts.
• Keep generated .mat files out of version control—store them under results/ locally and add them to .gitignore if needed.

License

If this repository requires a license, add the preferred terms here. Until then, treat the code as all-rights-reserved and contact the authors listed in the reference for reuse permissions.