Michael Medvinsky

North Carolina State University | NCSU · Department of Mathematics

We propose an algorithm based on the Method of Difference Potentials (MDP) for the numerical solution of multiple scattering problems in three space dimensions. The propagation of waves is assumed time-harmonic and governed by the Helmholtz equation. The latter is approximated with 6th order accuracy on a Cartesian grid by means of a compact finite...

Numerical approximations and computational modeling of problems from Biology and Materials Science often deal with partial differential equations with varying coefficients and domains with irregular geometry. The challenge here is to design an efficient and accurate numerical method that can resolve properties of solutions in different domains/subd...

The method of difference potentials was originally proposed by Ryaben’kii, and is a generalized discrete version of the method of Calderon’s operators. It handles non-conforming curvilinear boundaries, variable coefficients, and non-standard boundary conditions while keeping the complexity of the solver at the level of a finite-difference scheme on...

Numerical approximations and computational modeling of problems from Biology and Materials Science often deal with partial differential equations with varying coefficients and domains with irregular geometry. The challenge here is to design an efficient and accurate numerical method that can resolve properties of solutions in different domains/subd...

Designing numerical methods with high-order accuracy for problems in irregular domains and/or with interfaces is crucial for the accurate solution of many problems with physical and biological applications. The major challenge here is to design an efficient and accurate numerical method that can capture certain properties of analytical solutions in...

The method of difference potentials generalizes the method of Calderon’s operators from PDEs to arbitrary difference equations and systems. It offers several key advantages, such as the capability of handling boundaries/interfaces that are not aligned with the discretization grid, variable coefficients, and nonstandard boundary conditions. In doing...

Image charge approximations are developed for electric potentials in the Poisson-Boltzmann theory in inhomogeneous media consisting of dielectrics or electrolyte solutions such as the layered structure in a membrane or cylindrical ion-channels. The image ...

The method of difference potentials was originally proposed by Ryaben’kii and can be interpreted as a generalized discrete version of the method of Calderon’s operators in the theory of partial differential equations. It has a number of important advantages; it easily handles curvilinear boundaries, variable coefficients, and non-standard boundary...

An improved connectivity to radio access point is enabled by a server that includes a database storing data about various radio access points, and an evaluation module evaluating the quality of connection to each of the access points. Clients receive updates about relevant access points from the server and use the information to connect to the pref...

We compare several On Surface Radiation Boundary Conditions in two dimensions, for solving the Helmholtz equation exterior to an ellipse. We also introduce a new boundary condition for an ellipse based on a modal expansion in Mathieu functions. We compare the OSRC to a finite difference method.

We compare several local absorbing boundary conditions for solving the Helmholtz equation, by a finite difference or finite element method, exterior to a general scatterer. These boundary conditions are imposed on an artificial elliptical or prolate spheroid outer surface. In order to compare the computational solution with an analytical solution,...

Selecting a static IP address is disclosed. A DHCP discover message is sent. A message that includes target network gateway information is received. A static IP address is selected based at least in part on the target network gateway information.

Substituting an address is disclosed. A first packet is received from a first network at a driver in a mobile device. A second packet is received from a second network at the driver in the mobile device after previously receiving the first packet. A destination address is substituted in the second packet such that a mobile device application is una...