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Level sets of potential functions bisecting unbounded quadrilaterals
(
Springer Nature
, 2022 , Article)
We study the mixed Dirichlet–Neumann problem for the Laplace equation in the complement of a bounded convex polygonal quadrilateral in the extended complex plane. The Dirichlet / Neumann conditions at opposite pairs of ...
Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals
(
Springer Nature
, 2022 , Article)
We study numerical conformal mappings of planar Jordan domains with boundaries consisting of finitely many circular arcs, also called polycircular domains, and compute the moduli of quadrilaterals for these domains. ...
Condenser capacity and hyperbolic perimeterImage 1
(
Elsevier
, 2021 , Article)
We study the conformal capacity by using novel computational algorithms based on implementations of the fast multipole method, and analytic techniques. Especially, we apply domain functionals to study the capacities of ...
Computation of conformal invariants
(
Elsevier
, 2020 , Article)
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies to a wide variety ...
Conformal Invariants in Simply Connected Domains
(
Springer Link
, 2020 , Article)
This paper studies the numerical computation of several conformal invariants of simply connected domains in the complex plane including, the hyperbolic distance, the reduced modulus, the harmonic measure, and the modulus ...
Condenser capacity and hyperbolic diameter
(
Elsevier
, 2021 , Article)
Given a compact connected set E in the unit disk B2, we give a new upper bound for the conformal capacity of the condenser (B2,E) in terms of the hyperbolic diameter t of E. Moreover, for t>0, we construct a set of hyperbolic ...
Isoperimetric properties of condenser capacity
(
Elsevier
, 2021 , Article)
For compact subsets E of the unit disk D we study the capacity of the condenser (D,E) by means of set functionals defined in terms of hyperbolic geometry. In particular, we study experimentally the case of a hyperbolic ...
Numerical computation of Mityuk's function and radius for circular/radial slit domains
(
Elsevier
, 2020 , Article)
We consider Mityuk's function and radius which have been proposed in [15] as generalizations of the reduced modulus and conformal radius to the cases of multiply connected domains. We present a numerical method to compute ...
Numerical computation of the capacity of generalized condensers
(
Elsevier
, 2020 , Article)
We present a boundary integral method for numerical computation of the capacity of generalized condensers. The presented method applies to a wide variety of generalized condenser geometry including the cases when the plates ...