Skip to content

README.md

Latest commit

 

History

History
124 lines (100 loc) · 3.45 KB

README.md

File metadata and controls

124 lines (100 loc) · 3.45 KB

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, nearroot (./build/test_solid_angle_r128 nearroot)

Parameters: order=16, nq=16, nvr=768, ntri=768, ratio=1.0

=== test_solid_angle_r128 (quad precision) ===
order=16  nq=16  nvr=768  ntri=768  ratio= 1.0
use_nearroot = T
Mesh built in    4.31 s

--- Part A: solid angle sum ---
far exterior  (1.5,0,0): |omega_sum| =   2.789740E-32
near exterior (1.001,0,0): |omega_sum| =   1.224617E-31
near exterior (1.000001,0,0): |omega_sum| =   4.902802E-30
near exterior (1.000000001,0,0): |omega_sum| =   3.646596E-27

--- Part B: DLP accuracy (direct sum + near correction) ---
N_src = 589824
ntarget = 834 exterior points
Direct DLP sum ...
  done in   50.28 s
Near-field correction ...
  done in   16.45 s

--- Result: DLP(1) = 0 outside ---
max |u|  =   2.173480E-32
rms |u|  =   3.423790E-33
argmax: i=630  tx=  5.555555555555555E-02  2.000000000000000E+00  6.944444444444444E-01
u(imax)        =  -2.173480294783766E-32
K_corr(imax)   =  -4.615084860876367E-33

Double precision, nearroot (./build/test_solid_angle nearroot)

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

=== test_solid_angle ===
order=14  mp=np=8  ntri=768  ratio= 1.0
use_nearroot = T
Mesh built in    0.01 s

--- Part A: solid angle sum ---
far exterior  (1.5,0,0): |omega_sum| =  8.428E-14
near exterior (1.1,0,0): |omega_sum| =  2.639E-13

--- Part B: DLP accuracy (direct sum + near correction) ---
N_src = 80640
ntarget = 6598 exterior points
Direct DLP sum ...
  done in    0.17 s
Near-field correction ...
  done in    0.01 s

--- Result: DLP(1) = 0 outside ---
max |u|  =  3.419E-14
rms |u|  =  1.260E-15