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Fast algorithms for the accurate evaluation of some singular integral operators that arise in the context of solving certain partial diierential equations within the unit circle in the complex plane are presented. These algorithms are generalizations and extensions of a fast algorithm of Daripa (SIAM J. They are based on some recursive relations in Fourier… (More)

- Prabir Daripa
- 2006

Standard perturbation methods are applied to Euler's equations of motion governing the capillary-gravity shallow water waves to derive a general higher-order Boussinesq equation involving the small-amplitude parameter, α = a/ h 0 , and long-wavelength parameter, β = (h 0 /l) 2 , where a and l are the actual amplitude and wavelength of the surface wave, and… (More)

The pulsatile blood flow in an eccentric catheterized artery is studied numerically by making use of an extended version of the fast algorithm of Borges and Daripa [Jour. Comput. Phys., 2001]. The mathematical model involves the usual assumptions that the arterial segment is straight, the arterial wall is rigid and impermeable, blood is an incompressible… (More)

A numerical method for quasiconformal mapping of doubly connected domains onto annuli is presented. The ratio R of the radii of the annulus is not known a priori and is determined as part of the solution procedure. The numerical method presented in this paper requires solving iteratively a sequence of inhomogeneous Beltrami equations, each for a diierent R.… (More)

A parallel algorithm for solving the Poisson equation with either Dirichlet or Neumann conditions is presented. The solver follows some of the principles introduced in a previous fast algorithm for evaluating singular integral transforms by Daripa et. al. [8, 2]. Here we present recursive relations in Fourier space together with fast Fourier transforms… (More)

We propose a domain embedding method to solve second order elliptic problems in arbitrary two-dimensional domains. This method can be easily extended to three-dimensional problems. The method is based on formulating the problem as an optimal distributed control problem inside a rectangle in which the arbitrary domain is embedded. A periodic solution of the… (More)

In this paper, we extend the work of Daripa et al. [14–16,7] to a larger class of ellip-tic problems in a variety of domains. In particular, analysis-based fast algorithms to solve inhomogeneous elliptic equations of three different types in three different two-dimensional domains are derived. Dirichlet, Neumann and mixed boundary value problems are treated… (More)

The mathematical foundation of an algorithm for fast and accurate evaluation of singular integral transforms was given by Daripa [9,10,12]. By construction, the algorithm offers good parallelization opportunities and a lower computational complexity when compared with methods based on quadrature rules. In this paper we develop a parallel version of the fast… (More)

We consider an illposed Boussinesq equation which arises in shallow water waves and nonlinear lattices. This equation has growing and decaying modes in the linear as well as nonlinear regimes and its linearized growth rate for short-waves of wavenumber k is given by k 2. Previous numerical studies have addressed numerical diiculties and construction of… (More)