38 citations · 157 across the 26 of their papers we have counts for
30 papers
Fast computation of analytic capacity
Mohamed M S Nasser, Christopher C. Green, Matti Vuorinen
A boundary integral equation method is presented for fast computation of the analytic capacities of compact sets in the complex plane. The method is based on using the Kerzman--Ste…
Towards computing the harmonic-measure distribution function for the middle-thirds Cantor set
Christopher C. Green, Mohamed M. S. Nasser
This paper is concerned with the numerical computation of the harmonic-measure distribution function, or -function for short, associated with a particular planar domain. This fu…
Mobile disks in hyperbolic space and minimization of conformal capacity
Harri Hakula, Mohamed M. S. Nasser, Matti Vuorinen
Our focus is to study constellations of disjoint disks in the hyperbolic space, the unit disk equipped with the hyperbolic metric. Each constellation corresponds to a set which…
Image augmentation with conformal mappings for a convolutional neural network
Oona Rainio, Mohamed M. S. Nasser, Matti Vuorinen +1
For augmentation of the square-shaped image data of a convolutional neural network (CNN), we introduce a new method, in which the original images are mapped onto a disk with a conf…
Level sets of potential functions bisecting unbounded quadrilaterals
Mohamed M. S. Nasser, Semen Nasyrov, Matti Vuorinen
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\,/\…
Numerical computation of a preimage domain for an infinite strip with rectilinear slits
El Mostafa Kalmoun, Mohamed M. S. Nasser, Matti Vuorinen
Let be the multiply connected domain in the extended complex plane $\overline{\C}$ obtained by removing non-overlapping rectilinear segments from the infinite strip $S=\{z\…
Conformal capacity and polycircular domains
Harri Hakula, Mohamed M. S. Nasser, Matti Vuorinen
We study numerical conformal mapping of multiply connected planar domains with boundaries consisting of unions of finitely many circular arcs, so called polycircular domains. We co…
Computing the logarithmic capacity of compact sets having (infinitely) many components with the Charge Simulation Method
Jörg Liesen, Mohamed M. S. Nasser, Olivier Sète
We apply the Charge Simulation Method (CSM) in order to compute the logarithmic capacity of compact sets consisting of (infinitely) many "small" components. This application allows…
Simulating local fields in carbon nanotube reinforced composites for infinite strip with voids
Mohamed Nasser, El Mostafa Kalmoun, Vladimir Mityushev +1
We consider the steady heat conduction problem within a thermal isotropic and homogeneous infinite strip composite reinforced by uniformly and randomly distributed non-overlapping…
Circular arc polygons, numerical conformal mappings, and moduli of quadrilaterals
Mohamed Nasser, Oona Rainio, Antti Rasila +4
We study numerical conformal mappings of planar Jordan domains with boundaries consisting of finitely many circular arcs and compute the moduli of quadrilaterals for these domains.…
The Riemann-Hilbert problem and the generalized Neumann kernel on unbounded multiply connected regions
Mohamed M. S. Nasser
A Fredholm integral equation of the second kind with the generalized Neumann kernel associated with the Riemann-Hilbert problem on unbounded multiply connected regions will be deri…
Condenser capacity and hyperbolic perimeter
Mohamed M. S. Nasser, Oona Rainio, Matti Vuorinen
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…
Condenser capacity and hyperbolic diameter
Mohamed M. S. Nasser, Oona Rainio, Matti Vuorinen
Given a compact connected set in the unit disk , we give a new upper bound for the conformal capacity of the condenser in terms of the hyp…
Isoperimetric properties of condenser capacity
Mohamed M. S. Nasser, Matti Vuorinen
For compact subsets of the unit disk we study the capacity of the condenser by means of set functionals defined in terms of hyperbolic…
The Motion of a Point Vortex in Multiply Connected Polygonal Domains
El Mostafa Kalmoun, Mohamed M S Nasser, Khalifa A. Hazaa
We study the motion of a single point vortex in simply and multiply connected polygonal domains. In case of multiply connected domains, the polygonal obstacles can be viewed as the…
Conformal Invariants in Simply Connected Domains
Mohamed M S Nasser, Matti Vuorinen
We study numerical computation of several conformal invariants of simply connected domains in the complex plane including, the hyperbolic distance, the reduced modulus, the harmoni…
PlgCirMap: A MATLAB toolbox for computing conformal mappings from polygonal multiply connected domains onto circular domains
Mohamed M. S. Nasser
This paper presents a MATLAB toolbox for computing the conformal mapping from a given polygonal multiply connected domain onto a circular multiply connected domain and its inverse.…
Application of integral equations to simulate local fields in carbon nanotube reinforced composites
Mohamed M S Nasser, El Mostafa Kalmoun
We consider the steady heat conduction problem within a thermal isotropic and homogeneous square ring composite reinforced by non-overlapping and randomly distributed carbon nanotu…
Numerical computation of the capacity of generalized condensers
Mohamed M S Nasser, Matti Vuorinen
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 g…
Computation of conformal invariants
Mohamed M S Nasser, Matti Vuorinen
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.…
Numerical computation of Mityuk's function and radius for circular-radial slit domains
El Mostafa Kalmoun, Mohamed M S Nasser, Matti Vuorinen
We consider Mityuk's function and radius which have been proposed in \cite{Mit} as generalizations of the reduced modulus and conformal radius to the cases of multiply connected do…
A fast numerical method for ideal fluid flow in domains with multiple stirrers
Mohamed M. S. Nasser, Christopher C. Green
A collection of arbitrarily-shaped solid objects, each moving at a constant speed, can be used to mix or stir ideal fluid, and can give rise to interesting flow patterns. Assuming…
A boundary integral method for the general conjugation problem in multiply connected circle domains
Mohamed M S Nasser
We present a boundary integral method for solving a certain class of Riemann-Hilbert problems known as the general conjugation problem. The method is based on a uniquely solvable b…
Fast and accurate computation of the logarithmic capacity of compact sets
Jörg Liesen, Olivier Sète, Mohamed M. S. Nasser
We present a numerical method for computing the logarithmic capacity of compact subsets of , which are bounded by Jordan curves and have finitely connected complement.…