Single- and Double-Layer Potential Matrices

These files contain precomputed single- and double-layer potential matrices used in the 2D wave scattering examples for the jaxhps package. These matrices are used to discretize a boundary integral equation which simulates the Sommerfeld radiation condition. See https://arxiv.org/abs/2503.17535 for more details.

After unzipping the folder, you will see files with filenames like SD_k{kval}_n{nval}_nside{nsideval}_dom1.mat. Each file contains S and D matrices for a particular discretization and wavenumber. The files are saved in MATLAB file format. The values in these filenames are:

kval is the wavenumber for the Helmholtz problem. The forward scattering example in the jaxhps package uses kval=100, and the inverse scattering example uses kval=20. 

nval corresponds to the order of the Gauss panels used in the HPS discretization. The HPS method uses a quadtree to discretize the spatial domain, and each leaf in the quadtree has an order nval discretization on each side.

nsideval corresponds to the number of leaves along a side of the domain. A quadtree with depth L will have 2^L leaves along each side.

Once downloaded, you can run the 2D wave scattering examples and specify a discretization level and wavenumber; the example scripts will automatically load the correct file.