Helmholtz open-arc Dirichlet solver via Bruno-Lintner formulation#178
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Helmholtz open-arc Dirichlet solver via Bruno-Lintner formulation#178danfortunato wants to merge 2 commits into
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Builds on PRs #172, #174, #175, #176, #177. Adds support for the Bruno-Lintner integral representation of the Helmholtz Dirichlet problem on open curves (or chunkgraphs with corners). The formulation uses a 2x2 block kernel K = [ 0 c*S ; c*T 0 ] solved as (K + I) sigma = [u_bdry; 0]. The system is solved via chunkermat with opts.rcip=true, opts.open_arc_eye=true, and field evaluation via chunkerkerneval with opts.rcipsav and opts.forcewlchs in struct/layout form (selecting the S column of K_eval = [0 c*S] against the recovered fine-mesh density). What's included: * New 'sc' (= c1*S' + c2*S) Helmholtz kernel mode in: chnk.helm2d.kern -- evaluation chnk.helm2d.fmm -- FMM dispatch @kernel.helm2d -- kernel constructor The 'sc' kernel is used for impedance / Neumann boundaries (e.g. photonics K_imp = 2*S' + 2*eta*S). * chunkermat opts.open_arc_eye = true + opts.open_arc_eye_subdim override the (1,1) sub-block of each per-chunker diagonal block with -I before RCIP, so that (sysmat + eye(N)) yields the [0, c*S; c*T, I] system Bruno-Lintner requires. Default subdim=1 (helmos opdims=[2,2]); subdim=2 reserved for the open-arc Stokes mobility (4x4 block kernel) extension. Test: devtools/test/chunkermat_helmopensurface_dirichletTest.m solves the Dirichlet open-arc Helmholtz problem on a chunkgraph with two corner vertices and a smooth boundary data, then evaluates the field at an interior target via the rcipsav + forcewlchs (struct form) path. Relative error vs an adaptive-quadrature reference is ~4e-13. Original implementation contributed by sj90101 <sj90101@gmail.com>. Co-authored-by: sj90101 <sj90101@gmail.com>
Adds the helmos() user-facing open-arc Helmholtz solver and supporting
geometry/planewave/fieldplot helpers, plus a demo, in chunkie/demo/;
plus three test scripts under devtools/test/.
chunkie/demo/:
helmos.m -- geometry-agnostic open-arc Helmholtz solver.
Caller passes a chunkgraph (with all corners/
junctions as vertices), boundary data, and
targets; helmos sets up RCIP with
opts.open_arc_eye + rcipsav field eval.
Dirichlet ('d') is full-accuracy; Neumann ('n')
is formulation-complete but limited by
chunkie's hypersingular 'dp' quadrature.
helmos_planewave_rhs -- Bruno-Lintner-compatible Dirichlet/Neumann
RHS for an incident planewave.
helmos_fieldplot -- regular-grid abs/real/log10err plot.
geo_linesegment -- single open segment chunkgraph builder.
geo_spiral -- log spiral with one free endpoint.
geo_corners -- polygonal chunkgraph with N corner vertices.
helmos_demo -- end-to-end demo: build geometry, solve,
plot scattered field.
devtools/test/:
helmos_smoke.m -- lo/hi self-convergence on 4 geometries
(linesegment, spiral, corners1, corners3);
reports far+near max diffs ~1e-12.
helmos_self_convergence.m -- self-convergence on polygonal corner
+ planewave cases (~1e-14 lo-hi diffs).
forcewlchs_userapi_test.m -- bare chunker + chunkgraph (rcipsav)
forcewlchs API smoke tests, asserts
expected accuracy at d=1e-6 from a corner.
Tests that need helmos.m / geo_* from chunkie/demo/ add that to the
MATLAB path at the top via mfilename('fullpath').
Co-authored-by: sj90101 <sj90101@gmail.com>
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Summary
Builds on #172, #174, #175, #176, #177. Adds support for the Bruno-Lintner integral representation of the Helmholtz Dirichlet problem on open curves (or chunkgraphs with corners).
The formulation uses a 2x2 block kernel
solved as
(K + I) sigma = [u_bdry; 0]. The system is solved viachunkermatwithopts.rcip=true+opts.open_arc_eye=true; field evaluation useschunkerkernevalwithopts.rcipsav+opts.forcewlchsin struct/layout form.What's included
sc(= c1·S' + c2·S) Helmholtz kernel mode in:chnk.helm2d.kern(evaluation)chnk.helm2d.fmm(FMM dispatch)@kernel.helm2d(kernel constructor)Used for impedance / Neumann boundaries (e.g. photonics
K_imp = 2*S' + 2*eta*S).chunkermatopen-arc options:opts.open_arc_eye = true— overwrite the (1,1) sub-block of each per-chunker diagonal block with-Ibefore RCIP, so thatsysmat + eye(N)yields the[0, c*S; c*T, I]system Bruno-Lintner requires.opts.open_arc_eye_subdim— default 1 (helmos opdims=[2,2]); 2 reserved for the open-arc Stokes mobility 4x4 block kernel extension.Test plan
devtools/test/chunkermat_helmopensurface_dirichletTest.m(new) — solves the Dirichlet open-arc Helmholtz problem on a chunkgraph with two corner vertices, evaluates the field at an interior target via the rcipsav + forcewlchs (struct form) path. Relative error vs adaptive-quadrature reference is ~4e-13.Notes