A second kind integral equation formulation is presented for the Dirichlet problem for the Laplace equation in two dimensions, with the boundary conditions specified on a collection of open curves. The performance of the obtained apparatus is illustrated with several numerical examples. The formulation is a simplification of the equation previously constructed by the authors. 2003 Elsevier Inc....

We summarize a recently developed integral equation approach to tackling the long-time existence problem for smooth solution v(x, t) to the 3-D Navier-Stokes equation in the context of a periodic box problem with smooth time-independent forcing and initial condition v0. Using an inverse Laplace transform of v̂(k, t) − v̂0 in 1/t, we arrive at an integral equation for Û(k, p), where p is inverse-L...

Abstract: In this paper, Laplace decomposition method is developed to solve linear and nonlinear fractional integrodifferential equations. The proposed method is based on the application of Laplace transform to nonlinear fractional integro-differential equation. The nonlinear term can easily be handled with the help of Adomian polynomials. The fractional derivative is described in the Caputo se...

In this paper, we analyze the convergence of the preconditioned GMRESmethod for the first order finite element discretizations of the Helmholtz equation in media with losses. We consider a Laplace preconditioner, an inexact Laplace preconditioner and a two-level preconditioner. Our analysis is based on bounding the field of values of the preconditioned system matrix in the complex plane. The an...

We establish a lower bound for the gradient of the solution to 1-Laplace equation in a strongly star-shaped annulus with capacity type boundary conditions. The proof involves properties of the radial derivative of the solution, so that starshapedness of level sets easily follows. x1. Introduction In this paper we deal with solutions to the 1-Laplace equation 1 u = n X i;j=1 u x i u x j u x i x ...

Many problems in image analysis, digital processing and shape optimization are expressed as variational problems and involve the discritization of laplacians. Indeed, PDEs containing Laplace-Beltrami operator arise in surface fairing, mesh smoothing, mesh parametrization, remeshing, feature extraction, shape matching, etc. The discretization of the laplace-Beltrami operator has been widely stud...