LineQuaaadrature

Line-quadrature reference code (Fortran + MATLAB MEX on Mac).

Context

This code was written by Codex and Claude Code as a testbed to reproduce parts of:

• Shidong Jiang and Hai Zhu, Recursive reduction quadrature for the evaluation of Laplace layer potentials in three dimensions, arXiv:2411.08342 (2024).
  https://arxiv.org/abs/2411.08342
• John S. Asvestas, Line integrals and physical optics. Part I. The transformation of the solid-angle surface integral to a line integral, Journal of the Optical Society of America A, 2(6): 891-895 (1985).
  https://doi.org/10.1364/JOSAA.2.000891

The main purpose is to provide extended-precision solid-angle integral tests, to debug whether machine-precision singular / near-singular quadrature is achievable.

Layout

• src/ Fortran source modules
• matlab/ mwrap interface (LineQuaaadrature.mw) and generated MEX wrappers
• test/ Fortran test programs
• build/ compiled artifacts

Build

From this folder:

cd /LineQuaaadrature
make

This builds:

• static library: build/libLineQuaaadrature.a
• MATLAB MEX: matlab/LineQuaaadrature_mex.mexmaca64 (on Apple Silicon macOS)

Run Fortran Tests

Real64 test

make test
./build/test_solid_angle adaptive
./build/test_solid_angle nearroot

make test
./build/test_solid_angle false
./build/test_solid_angle true

Real128 test (extended precision)

make test_r128
./build/test_solid_angle_r128

Optional thread control:

OMP_NUM_THREADS=8 OPENBLAS_NUM_THREADS=1 ./build/test_solid_angle_r128

Clean

make clean

Notes

• Compiler settings are in Makefile (currently gfortran-15, gcc-15).
• MEX wrappers are generated from matlab/LineQuaaadrature.mw using mwrap.

Reference Results

The following reference outputs were recorded on local runs.

Extended precision (./build/test_solid_angle_r128)

Parameters: order=14, nq=12, nvr=432, ntri=768, ratio=1.0

=== test_solid_angle_r128 (quad precision) ===
order=14  nq=12  nvr=432  ntri=768  ratio= 1.0
Mesh built in    2.32 s

--- Part A: solid angle sum ---
far exterior  (1.5,0,0): |omega_sum| =   7.080390E-31
near exterior (1.1,0,0): |omega_sum| =   9.781399E-31

--- Part B: DLP accuracy (direct sum + near correction) ---
N_src = 331776
ntarget = 834 exterior points
Direct DLP sum ...
  done in   23.57 s
Near-field correction ...
  done in   33.85 s

--- Result: DLP(1) = 0 outside ---
max |u|  =   2.751315E-28
rms |u|  =   4.642503E-29

Double precision (./build/test_solid_angle)

Parameters: order=14, mp=np=8, ntri=768, ratio=1.0

=== test_solid_angle ===
order=14  mp=np=8  ntri=768  ratio= 1.0
Mesh built in    0.02 s

--- Part A: solid angle sum ---
far exterior  (1.5,0,0): |omega_sum| =  4.846E-14
near exterior (1.1,0,0): |omega_sum| =  1.312E-14

--- Part B: DLP accuracy (direct sum + near correction) ---
N_src = 80640
ntarget = 6598 exterior points
Direct DLP sum ...
  done in    0.13 s
Near-field correction ...
  done in    0.02 s

--- Result: DLP(1) = 0 outside ---
max |u|  =  3.508E-14
rms |u|  =  1.267E-15