In [7, 8], they proposed a new singular function(NSF) method to compute singular solutions of Poisson equations on a polygonal domain with re-entrant angles. Singularities are eliminated and only the regular part of the solution that is in H is computed. The stress intensity factor and the solution can be computed as a post processing step. This method was extended to the interface problem and ...

................................................................................V DECLARATION OF ORIGINALITY ........................................... VII ACKNOWLEDGEMENTS........................................................... IX TABLE OF CONTENTS.............................................................. XI TABLE OF FIGURES.................................................................

This project’s aim seeks to study the acceleration of numerical algorithms used to solve the Helmholtz equation with Dirichlet boundary conditions. The Helmholtz equation arises naturally in physical problems modeled by partial differential equations in space and time as a time-independent wave equation when applying the technique of separation of variables. Using Dirichlet boundary conditions ...

The majority of natural sources (black-bodies, fluorescent bulbs, etc) generate completely un-polarized light; the majority of detectors (eyes, photo-cameras, photomultipliers, etc) are polarization-insensitive. To reflect this, we attempt to describe approximately electromagnetic waves without polarization. Corresponding scalar equations are non-trivial modifications of standard d’Alembert and...

This paper analyzes the effect of large wave numbers on the wavelet method for integral equations arising in electromagnetic applications. It is shown that the compression of the stiffness matrix deteriorates with increasing wave number, a characteristic that has been reported before in the literature. Here, however, the exact dependence on the wave number is calculated analytically for the two...

The (p, q)-growth of entire function solutions of Helmholtz equations in R has been studied. We obtain some lower bounds on order and type through function theoretic formulae related to those of associate. Our results extends and improve the results studied by McCoy [10].

An analysis of discretizations of the Helmholtz equation in L 2 and in negative norms (extended version) Flatness of semilinear parabolic PDEs-A generalized Chauchy-Kowalevski approach 27/2012 R. Donninger and B. Schörkhuber Stable blow up dynamics for energy supercritical wave equations 26/2012 P.

An efficient domain decomposition method is developed for discretized Helmholtz equations resulting from acoustical geological survey problems. A Schwarz-type multiplicative preconditioner is constructed using a fast direct method in subdomains by embedding them to rectangular domains. The GMRES iterations are reduced to a subspace corresponding to interfaces. Numerical experiments with several...

If a quantum mechanical particle is scattered by a potential well, the wave function of the particle can propagate with negative phase time. Because of the analogy of the Schrödinger and Helmholtz equations this phenomenon is expected to be observable for electromagnetic wave propagation. Experimental data for electromagnetic wells realized by waveguides filled with different dielectrics now co...