Seed design edges by their persistent names with a count or a size, a bias
and a constraint; one undo step each, saved with the model. Seeds on edges a
reopened design lacks are reported as stale.
Part of #230.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
A reference field (a material, set, step…) with no items was a free-text box; it is now a greyed
drop-down ("No materials yet") with a button that opens the command making one (the
collection's requirement provider). That form comes back to this one on OK, with the new item
picked, or as it was on Cancel. A required reference with one candidate, or with the browser's
selection of its kind, starts picked when the form opens, so the fields and the JSON view agree.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
The mesh tool runs mesh.cells (method cells) and mesh.mirror (method mirror).
The server instructions and docs/mcp.md list the partition, per-cell, mirror
and symmetry commands and point to the crank-mirror sample.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
file.sample crank-mirror partitions the crank arm on its symmetry plane, sweeps
one half all-hex (hex20) and mirrors it into one conforming mesh, then defines
the crank-arm model. Samples may now run preparing commands (datums,
partitions) before their script sees the bodies. Its test checks the halves
alike and joined, every element valid and the sets on both halves; the heavy
test solves it: sigma_xx at the root -62.43 / +62.43 MPa against M/Z = 62.5.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
A symmetry condition (zero normal displacement, zero rotation about the
in-plane axes) on a datum plane normal to X, Y or Z, with its set given or made
of the open design's faces on the plane (a partition's cut faces), so half a
symmetric part is solved as a half. Half a 40 mm bar cut at its mid-width, with
the condition and half the load, bends as the whole bar to 2e-12 with half the
reaction. Inclined planes are refused as not supported yet.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
The bodies' elements are reflected across a datum plane (or a point and
normal) with fieldcraft_mesh::mirror and joined on it. The image is tagged as
the design's body at the reflected place (found by volume and centroid, or
named in `as`), its faces with that body's faces under them, so sets by face
name reach both halves. Half a bar meshed hex8 or hex20 and mirrored has the
whole bar's node and element counts and volume, and its bending deflection to
1e-12; tet4 and tet10 mirror valid and conforming.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
Each cell (a body of the open design) gets its own method: structured hex where
one fits (auto falls back to tet and says why), or tet. All go into one mesh.
Cells on either side of a partition are joined: where their element faces
match node for node the nodes are merged; otherwise (hex next to tet, or
different divisions) the two partition faces get a set each and a dual mortar
tie, the reported hex-tet transition. A 40 mm bar cut in half, one half hex,
the other tet, stretches F L / (E A) to 1e-6.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
Datum planes by principal plane and offset, three points, or point and
normal; datum axes by principal axis, two points, or point and direction.
geometry.partition cuts the open design by a datum plane and keeps the
partition in the model, so geometry.open, file.open and undo cut the design
again. Requirements, forms and the Prepare entries are wired; features.md
lists them as ready.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
Datums are named planes (point, unit normal) and axes (point, unit direction);
a partition names the datum plane that cuts and, optionally, the bodies. A
datum a partition uses cannot be deleted or turned into an axis. Both are
stored in model.json, partitions in the order they cut.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
The ribbon buttons, drop-down rows, command search and the title bar's Solve read
Session::availability: greyed, with what is missing (and where to get it) in the tooltip.
Starting such an entry opens no form; the status bar names what is missing. ui.toolbar
reports each entry's `enabled` and `unavailable`, ui.inspect the Solve button's.
Fixes#220
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
CommandSpec gains `requires: &[Requirement]` (crates/engine/src/requirement.rs): an open
design, geometry, nodes, a mesh, something to analyse, materials and sections for the
elements, sets, the definition an edit or delete acts on, a step, a result. Session::execute
checks them before running, so a command missing one fails at once with no partial work,
naming each missing piece and the toolbar entry that provides it ("Needs a material —
Properties › Material"). Requirements are real prerequisites (the model's own reference
checks and model.check's rules), never a workflow order. engine.commands / list_commands
list them.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
Opening (File > Open, a drop, the recent list) a design that has none of the
bodies the model's mesh and sets are on now asks, like the unsaved-changes
prompt: Start a new model with this design (default, Enter), Keep the
current model (the status names what no longer resolves), or Cancel. The
opened session waits for the answer; the same design opens without asking.
ui.inspect shows the prompt as {"design": path}; ui.prompt answers it.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
A Markdown table sizes its columns by the captions, so the pictures came out
at different sizes; an HTML table with a third of the width per cell keeps
them even. The crank-arm picture is scaled to 1400x860 like the others, and
flow-past (no picture yet) moves to the end.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
cargo-deb and cargo-generate-rpm (pinned) package the same stripped binaries and files as the
tar.gz under /usr. The release job compares the file lists, runs lintian, and installs both
packages in Ubuntu 22.04 and Fedora containers.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
Plane strain, plane stress and axisymmetric models take contact pairs and
general (self) contact on the linear edges of tri3 and quad4 elements:
edges oriented out of their elements, the edge mortar of fem with the
thickness or 2 pi r in the weights, the element's area over the edge's
length as the thickness under it, and the in-plane rows of the tangent
blocks. Verified by the contact patch test in plane strain and
axisymmetric (to 1e-9 small sliding, 1e-4 finite), Hertz's line contact
on quad4 edges (Johnson 1985, 4.3; equal to the hex8 model's to 1e-5),
and a hybrid rubber C-ring closing on itself that moves node for node as
the one-layer solid ring.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
One constant pressure per element (mean dilatation, Nagtegaal, Parks &
Rice 1974; the hoop strain in the divergence) for quad4, quad8 and tri6:
the linear stiffness, stresses and thermal load, and the finite- and
small-strain forms of nonlinear steps with their consistent tangent. The
linear triangle and plane stress are refused by name.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
file.sample crank-arm: a 170 mm 6061-T6 crank built in SolidCraft
(crates/engine/samples/crank-arm.json), swept along z by mesh.hex.generate
as 7274 hex20 elements of 3 mm (scaled Jacobian min 0.17). The hex variant
drops the pocket floor fillet and boss chamfers, and its root arcs meet the
bosses 20 degrees off tangent so the arm's top face has no zero-angle cusp.
The square bore is fixed and 1500 N acts on the pedal hole; the faces are
picked by their surfaces, not their names. Its heavy test matches the root
bending stress to M/Z = 62.6 MPa within 3 % (0.3 % in practice).
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
file.sample bracket-hex: the corpus bracket split into 30 SolidCraft cells,
meshed by mesh.hex.blocks as one conforming hex20 mesh of 3 mm, clamped at
the upright and loaded at the foot. The sample's script finds the clamp and
load faces in every cell that has them. Its test matches the tip deflection
of a fine tet10 solution within 1 % and checks the clamp carries the load.
Closes#166
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
file.sample heated-bracket: the corpus filleted bracket in steel, tet10, its
hole bores clamped, the upright's end held at 120 C and the rest cooled by
still air; one coupled temperature-displacement step. Its test checks the
temperatures against the heater and the air, then warms the bracket evenly,
clamps one hole, and matches the free thermal expansion alpha dT times the
distance from the hole along x.
Closes#165
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
file.sample flow-past: air at 25 mm/s past the upright L-bracket in a box of
2.5 mm lattice cells (Re 83), inlet, outlet, a no-slip floor and slip walls;
the fluid step reports the force on each named face. Its test holds the
drag coefficient on the upright's frontal area between 1 and 3.5 (2.3) and
the lattice's mass change under 1 %. No picture: the viewport does not draw
flow results yet (M12).
Part of #164 (its streamlines wait for a flow display in the viewport)
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
file.sample rubber-seal: a gasket ring of hybrid hex8 elements in four
mapped quarter blocks, squeezed 2.5 mm between plates bonded to it
(nonlinear static, Mooney-Rivlin rubber). Its test frees the plates and
matches the closed form for incompressible uniaxial compression within 3 %,
and bounds the bonded ring's extra stiffness. The plates are prescribed
displacements until implicit contact (#161) can press it into a groove.
Closes#163
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
file.sample drop-test: an L-bracket standing on its foot (a SolidCraft script
in sample.rs) swept into hex8, falling 2 m onto a rigid floor tilted 15 deg;
explicit dynamics for 1 ms with gravity and plasticity. Its test checks the
mass against rho V, the impact speed sqrt(2 g h) and kinetic energy, the
energy balance and the momentum the floor takes. docs/examples.md starts
with it, and its picture is docs/media/examples/drop-test.png.
Closes#162
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
An oracle case of a block pressed on another and slid with static and kinetic coefficients
(mu_k N carried once slipping), and the docs of the friction formulation; ROADMAP M7 and
parity updated.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
solve.nonlinear counts the slipping nodes, solve.probe gives a secondary node's shear traction
and slip, and the results display draws contact_shear and contact_slip, contact_status coding
stick and slip.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
Two oracle cases: the contact patch test on non-matching meshes in small and finite sliding,
and Hertz's cylinder on a flat under force control (peak pressure, pressure distribution,
subsurface stress). docs/fem.md describes the formulation, the literature survey its papers;
ROADMAP M7 and parity are updated.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
solve.nonlinear summarises each contact (normal force, largest pressure, closed nodes, deepest
penetration, augmentations), solve.probe gives a secondary node's pressure, gap and status per
contact, and the results display draws contact_pressure, contact_gap and contact_status. The
contact commands, the catalogue and the model docs say what nonlinear static steps do with a
pair.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
An explicit step may ask for mass scaling to a target time increment (on
a set, or the whole model): elements whose stable increment is below it
get the density that reaches it, with their lumped masses, frequency
bound and hourglass scales; adiabatic heating keeps the physical
density. The run reports the elements scaled, the added mass in all and
per section with its fraction, a warning, and the added mass's kinetic
energy in the energy account. Verified on a uniform bar scaled to twice
its increment (added mass 3×, increment doubled, a quarter of the
kinetic energy left to the physical mass). ROADMAP and parity note the
hyperelastic materials and mass scaling.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
Neo-Hookean, Mooney–Rivlin and Yeoh materials in explicit dynamics, in
total form from the deformation gradient (objective by construction):
the one-point hex8 takes its mean F over the undeformed element and the
stress τ/J; tet4 takes the isochoric stress of its own F with the
average nodal pressure of the decoupled volumetric energy (Bonet–Burton
at finite strain). Each element's frequency bound follows the tangent's
largest normal stiffness. Small-displacement steps and thermal strain of
hyperelastic elements are refused by name.
Verified by uniaxial strain to λ = 1.5 of all three laws on hex8 and
tet4 against the material point (to rounding), and the oracle case
explicit-neo-hookean-implicit: a quasi-static explicit pull against the
implicit nonlinear solver (lateral contraction to 0.09%, stress to 0.03%).
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
Its values come from abaqus-docs.mit.edu, which returns 403 Forbidden outside MIT's network, so
they are not from a publicly accessible source. The section is kept aside for review.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
A README section tabulates, per benchmark, the reference, the result the
Abaqus 2017 Benchmarks Guide publishes (element, mesh, error) and ours from
the oracle, with a cited source per value and notes where the rows are not
like for like. Linked from docs/verification.md.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
arc-shallow-arch: a sinusoidal arch of 40 × 2 × 1 hex20 under a sinusoidal dead load scaled to
the one-mode closed form's upper limit load: the upper limit point at 0.992 (−0.8 %), the lower
at 0.219 (0.8 % of the peak load) and exactly one negative eigenvalue between them. ROADMAP and
parity updated, docs/oracle.md regenerated.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
NonlinearStatic.arc_length {constraint, max_load_factor, displacement_limit}: Riks–Crisfield
arc-length increments (cylindrical or spherical arc, tangent predictor signed by the angle
criterion, the constraint's quadratic root chosen by the angle with the last iterate), arcs
grown, shrunk and cut back as increments are. The converged state's tangent is factored for the
next predictor (LDLᵀ when indefinite); its negative eigenvalues are recorded per increment and
changes in their count are reported as limit or bifurcation points. Ends at the maximum load
factor, a displacement limit or the increment cap. Abaqus *STATIC, RIKS; LS-DYNA refuses it by
name; forms gain the arc-length group. A shallow arch of hex20 snaps through on the closed-form
path (1.9 %), both limit points found, inertia 0 → 1 → 0 between them.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
NonlinearStatic.imperfection {step, mode, scale}: the buckling step's mode, scaled to a largest
component of `scale`, is added to the node coordinates before the step is solved, with a warning
naming it; Abaqus and LS-DYNA decks refuse it by name. A clamped–free column with its first mode
as imperfection under half its buckling load amplifies it by 1/(1 − α) within 2.8 %.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
buckle-euler-pinned and buckle-euler-cantilever (hex20 columns, −0.18 % from Euler with
Engesser's shear correction) and buckle-plate-square (a simply supported square plate, b/t =
100, −0.39 % from k = 4; the support and thickness choices in its README). ROADMAP and parity
updated, docs/oracle.md regenerated.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
Procedure::Buckle {modes, shift}: the step's loads as a linear preload, K_σ from its stresses,
and (K + λ K_σ) φ = 0 by block Lanczos in the K inner product: K⁻¹(−K_σ) on Cholesky without a
shift, the buckling transformation (K + σ K_σ)⁻¹ K on LDLᵀ with one, whose inertia counts the
load factors below σ (Grimes–Lewis–Simon 1994). Lanczos gains an operand and an eigenvalue map
(defaults keep frequency steps bit for bit) and reports converged negative eigenvalues. Results
are frequency results with a `buckling` part; modes display with their load factor.
solve.buckle (in the Static drop-down); Abaqus *BUCKLE, Nastran SOL 105 and LS-DYNA refuse it by
name. Euler columns of hex20 within 0.18 % of Engesser's load.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
CommandSpec::listing gives id, label, the parameter doc and the schema; MCP
list_commands, the control channel's engine.commands and the new
fieldcraft-cli commands --json use it.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
Segment-to-segment penalty contact between element faces: each secondary
face and each main face facing it are projected onto the secondary face's
plane, split into triangles, clipped (Sutherland–Hodgman) and integrated
with a three-point rule per sub-triangle (Puso–Laursen segmentation, the
penalty at the integration points as Fischer–Wriggers), so a uniform
pressure gives the consistent nodal forces on both meshes and the contact
patch test passes on non-matching meshes. Every contact runs both ways at
half the penalty: pairs with each surface as the secondary, general and
self contact face against face. A bucket grid of face boxes every
increment, faces integrated in parallel and their forces added in face
order: the same numbers on any thread count.
The penalty per area ε = s γ min(m/A)/Δt² comes from the lumped masses,
each node's directional area and the stable increment, bounded by
Gershgorin's row sums so contact never shortens the increment. Coulomb
friction with exponential decay by a regularised return map at the
secondary nodes; rigid walls take Coulomb impulses. Contact work and
friction dissipation join the energy balance; each contact reports its
peak force, first and last contact, deepest penetration, friction and the
nodes adjusted at the start (initial penetrations adjusted strain-free or
refused with the node, face and depth); a cap on contact faces.
Verified (crates/explicit/tests/contact.rs, tests/oracle/explicit-*):
colliding bars (2L/c +1.2%, ρcAv₀/2, KE kept to 0.005%, contact energy
back to 8e-5 of it), blocks sliding to a stop on a rigid wall and on a
plate under constant and decaying friction (0.005–0.2%), the patch test
(σ_zz uniform to 0.06%), two spheres colliding against Hertz (peak +2.3%,
duration −0.4%; the oracle case waits for a graded sphere mesher), a free
body untouched by general contact, determinism across threads. Oracle
measures gain `over` (ratios). Existing fixtures do not move.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
Contact definitions on face sets: a pair (each surface's nodes against the
other's faces), general contact on a surface (self contact) or on every
exterior face of the solids; Coulomb friction with static and kinetic
coefficients and an exponential decay, a penalty scale and the choice to
adjust or refuse initially penetrating nodes, validated with caps. Rigid
walls of explicit steps gain friction. The check wants solid faces on
contact surfaces; sets used by a contact cannot be deleted.
fem::contact: the closest point of a triangle (Ericson) or a bilinear
quadrilateral (projected Newton) to a point, and a bucket grid of face
boxes for the global search, deterministic and bounded.
Commands interaction.contact.pair, .general, .edit, .delete and .find
(the touching parts of the mesh, with face sets and pairs made of them);
contacts in the model browser. Abaqus writes *SURFACE INTERACTION with
*FRICTION (exponential decay), *CONTACT PAIR and general *CONTACT; LS-DYNA
*CONTACT_AUTOMATIC_SURFACE_TO_SURFACE and _SINGLE_SURFACE with FS, FD, DC;
Nastran refuses contact by name. The implicit solver refuses contact by
name (M7); the explicit solver refuses it until the next commit.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
nl-hybrid-incompressible: 27 hybrid hex8 at ν = 0.4999 pulled to λ = 2 by a prescribed
displacement, against the compressible neo-Hookean closed form (1.4·10⁻⁹); its first
iterations need the LDLᵀ factorization. ROADMAP and parity updated, docs/oracle.md regenerated.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
A tangent that is not positive definite is factored by LDLᵀ (Cholesky first, one symbolic
factorization) instead of cutting the increment back; each iteration records the tangent's
negative eigenvalues and the summary warns when a converged state keeps some. A model that can
move freely is still an error at its first tangent, located by the undeformed Cholesky factor;
a singular tangent later is a cutback. Nearly incompressible hybrid hex8, hex20 and tet10 at
ν = 0.4999 under prescribed displacement now converge to the closed form.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
A supernodal LDLᵀ on the Cholesky factor's symbolic factorization (ordering, supernodes, fill,
cap and parallel subtree tasks shared through a Symbolic and a generic driver; the Cholesky
numerics are unchanged bit for bit). Pivots by the bounded Bunch–Kaufman (rook) search of
Ashcraft, Grimes & Lewis among each supernode's columns (Schenk & Gärtner's supernode
Bunch–Kaufman), 1 × 1 and 2 × 2, right-looking panels whose trailing update reuses the tiled
Cholesky kernels with L D formed on the fly. Reports the inertia; a column without a pivot above
round-off is a located Singular error; NaN is refused. Symmetric::new picks Cholesky, LDLᵀ, or
Cholesky with an LDLᵀ fallback; solve_refined adds iterative refinement. 1.1–1.2× the Cholesky
time on a 140 000-equation hex8 pattern.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
