This contains some research codes for high-order accurate 3D Nystrom BIE for scalar elliptic PDEs with constant coefficients inside or outside of a surface. In more detail, it has: global double periodic trapezoid rule and quad-panel based surface quadratures for kernels that have on-surface weak singularities no more singular than 1/r. For the torus and its modulation via a general smooth radius function it has on-surface quadratures only for uniform arbitrary-order quad patches, for the Laplace (an elliptic BVP) and wave-equation (hyperbolic BVP) kernels. For smooth deformations of the sphere, it has global QFS quadratures for the Laplace kernel, built on global spectral interpolations. It also hosts an old self-contained doubly-periodic Laplace dipole summation code.

Author: Alex Barnett

Contributions: Tom Hagstrom - f90 modules for interpolation from time grid.

Version: 20230317 (tested on MATLAB R2022a)

MATLAB. Codes have not been tested on MATLAB versions prior to R2012a.

For timedomainwaveeqn:

• Fortran compiler to build Hagstrom time interpolation and MEX interface.
• Some driver scripts need you to have the MATLAB/Octave tool memorygraph
• Optionally: fsparse from stenglib, compiled with make('openmp',true), for fast multithreaded sparse matrix assembly.

Download using git or as a zip (see green button above).

Open MATLAB in the top level (BIE3D) directory, and run bie3dsetup to add all needed directories to your path.

Test by running testall which currently tests Laplace quadratures on a torus, and should produce lots of error outputs close to machine precision, convergent sequences of numbers, and some plots, taking around 30-60 secs total.

kernels : Laplace evaluation, including on-surface (self-eval)
surfaces : smooth surface generators
singquad : special surface quadratures for weakly singular kernels
utils : general numerical and plot utilities
test : test codes (other than built-in self-tests)
timedomainwaveeqn : time-domain integral-equations for acoustics codes (see movie)
doublyperiodic : an old self-contained code for doubly-periodic Laplace dipoles in 3D