Quadrature Domain Solver

Domain type

Weight

Domain

singular (0 ∈ Ω)

Riemann map φ(z)

Quadrature function h(w)

Preset:

Thesis example:

h(w) =

Degree m_∞: (−1 = no polynomial part)

Map parameters

PQD power α

α =

Riemann map center φ(0)

Centroid of poles

Manual:

Residue q at origin

q =

|q| 0.000

arg 0.000π

Conformal radius c = φ′(∞)

c

searching…

Solver settings

Boundary samples:

Aggressiveness:

Auto-fit view on solve

Advanced solve behaviour

Auto-switch singular ⇄ non-singular PQD when the boundary crosses the origin

Overlays

→ Vector field:

Critical points

Curvature heat-strip

Annotated phenomena

Faber roots

Search options (advanced)

Phases

Direct algebraic

Continuation in t

Multistart, perturbed

Diverse seeds, log-uniform

Deflation (Brown–Gearhart)

Multistart budget

Newton restarts

Diverse seeds

Deflation seeds

Background search chunks

Chunk size

Keep searching (no chunk cap)

Newton & continuation

Newton max iterations

Newton tolerance

Continuation t-start

Continuation grow factor

Deflation

α (strength)

p (exponent)

Also deflate from valid solutions

Acceptance

Univalence samples

Identity tol

Show non-univalent candidates

Show identity-failing candidates

Auto-escalate to exhaustive on failure

RNG

Seed

Status

Idle

solving…

running…

Analytic oracle

Faber polynomials

Order N

All roots up to N Single F_n, n =

Plot roots on domain Show polynomial

Alternate solutions searching…

Direct problem

Schwarz reflection dynamics

Geometric properties

Boundary singularities

Geometry & accuracy