Searcharxiv⌕ Search

arXiv subjects

Mohamed M. S. Nasser

Publications and source records attributed to Mohamed M. S. Nasser.

23 records · Page 2Linked to original sources
arXiv2014

Fast computation of the circular map

This paper presents a new numerical implementation of Koebe's iterative method for computing the circular map of bounded and unbounded multiply connected regions of connectivity $m$. The computational cost of the method is $O(mn\ln n)$ where $n$ is the number of nodes in the discretization of each boundary component. The accuracy and efficiency of the presented method are demonstrated by several numerical examples. These examples include regions with high connectivity, regions whose boundaries are closer together, and regions with piecewise smooth boundaries.

math.CV↗
arXiv2014

Fast solution of boundary integral equations with the generalized Neumann kernel

A fast method for solving boundary integral equations with the generalized Neumann kernel and the adjoint generalized Neumann kernel is presented. The method is based on discretizing the integral equations by the Nyström method with the trapezoidal rule to obtain $(m+1)n\times(m+1)n$ linear systems where $m+1$ is the multiplicity of the multiply connected domain and $n$ is the number of nodes in the discretization of each boundary component. The obtained linear systems are solved by the generalized minimal residual (GMRES) method. Each iteration of the GMRES method requires a matrix-vector product which can be computed using the Fast Multipole Method (FMM). The complexity of the presented method is $O((m+1)n\ln n)$ for the integral equation with the generalized Neumann kernel and $O((m+1)n)$ for the integral equation with the adjoint generalized Neumann kernel. The presented numerical results illustrate that the presented method gives accurate results even for domains with high connectivity, domains with piecewise smooth boundaries, and domains with close boundaries.

math.NA↗
arXiv2013

Numerical conformal mapping via a boundary integral equation with the adjoint generalized Neumann kernel

This paper presents a new uniquely solvable boundary integral equation for computing the conformal mapping, its derivative and its inverse from bounded multiply connected regions onto the five classical canonical slit regions. The integral equation is derived by reformulating the conformal mapping as an adjoint Riemann-Hilbert problem. From the adjoint Riemann-Hilbert problem, we derive a boundary integral equation with the adjoint generalized Neumann kernel for the derivative of the boundary correspondence function $θ'$. Only the right-hand side of the integral equation is different from a canonical region to another. The function $θ'$ is integrated to obtain the boundary correspondence function $θ$. The integration constants as well as the parameters of the canonical region are computed using the same uniquely solvable integral equation. A numerical example is presented to illustrate the accuracy of the proposed method.

math.CV↗
arXiv2013

External Potential Flow Around Multiple Aerofoils

This chapter present a fats boundary integral equation method for numerical computing of uniform potential flow past multiple aerofoils. The presented fast multipole-based iterative solution procedure requires only $O(nm\ln n)$ operations where $m$ is the number of aerofoils and $n$ is the number of nodes in the discretization of each aerofoil's boundary. We demonstrate the performance of our methods on several numerical examples.

physics.flu-dyn↗