We study gravitational lensing by a generic extended mass distribution. For that, we consider the diffraction of electromagnetic (EM) waves an extended, weakly aspherical, gravitating object. account for static field such lens representing its exterior potential in most form, expressed via infinite set symmetric trace free (STF) tensor multipole moments. This yields general form phase shift, wh...

Many different simulation methods for Stokes flow problems involve a common computationally intense task -- the summation of kernel function over $O(N^2)$ pairs points. One popular technique is Kernel Independent Fast Multipole Method (KIFMM), which constructs spatial adaptive octree all points and places small number equivalent multipole local around each box, completes sum with $O(N)$ cost, u...

Article history: Received 27 January 2012 Received in revised form 3 October 2012 Accepted 16 January 2013 Available online 1 February 2013

A new two-dimensional panel technique has been developed to solve Laplacian flows, which eliminates the edge effect present in traditional panel methods. Such a method is very useful for applications where the velocity induced by the panels is required at arbitrary locations. Particle based flow solvers are a prime example. The method, however, requires considerably more computational effort. I...

Because of its practical significance, many different methods have been developed for the solution of the time-harmonic Maxwell equations in an exterior domain at higher frequency. Often methods with complimentary strengths can be combined to obtain an even better method. In this paper we provide a numerical study of a method for coupling of the Ultra-Weak Variational Formulation (UWVF) of Maxw...