Summation-by-parts--simultaneous approximation term finite difference approximation of the Laplacian on curvilinear multiblock grids

Publications that use this code

1. Almquist, M., Dunham, E. M, Non-stiff narrow-stencil finite difference approximations of the Laplacian on curvilinear multi-block grids (submitted).

Introduction

This MATLAB code demonstrates the advantages of a newly developed summation-by-parts--simultaneous approximation term (SBP-SAT) finite difference discretization of the Laplacian on curvilinear multiblock grids. The code reproduces all figures in the manuscript Almquist, M., Dunham, E. M, Non-stiff boundary and interface penalties for narrow-stencil finite difference approximations of the Laplacian on curvilinear multiblock grids. J. Comput. Phys, 2020. doi: 10.1016/j.jcp.2020.109294. The code is based on the sbplib repository.

Overview

The code is organized into five subfolders:

1. comparison: Compares the new discretization with the previous state-of-the-art method by Virta and Mattsson, 2014.
2. lemma1: Creates figures that show positivity properties of the SBP operators and are used in the proof of Lemma 1 in the manuscript.
3. marmousi: Example simulations inspired by marine seismic exploration with the Marmousi2 velocity model.
4. villarrica: Example simulations inspired by infrasund monitoring of the Villarrica volcano.
5. schematics: Creates a schematic that illustrates the curvilinear coordinate transformation.

Running the code

1. Clone the laplace-curvilinear repository: hg clone http://hg.code.sf.net/p/laplace-curvilinear/code laplace-curvilinear-code
2. Start MATLAB and navigate to the repository.
3. To run all computations, run the script runAllSimulations. Results from the computations will be stored in .mat-files. WARNING! The Villarrica simulations take approximately 24 hours in total and will store 6 Gb of data.
4. To generate all figures, run the script generateAllFigures (after running runAllSimulations). The figures will appear in a folder named paperFigures.
5. To run a subset of the simulations, for example the Marmousi simulations, run addSubpaths; cd marmousi; generateData(); generateFigures(); cd ..; removeSubpaths;