We consider the problem of calculating resonance frequencies and radiative losses of an optical resonator. The optical resonator is in the form of a thin membrane with variable dielectric properties. This work provides two very different approaches for doing such calculations. The first is an asymptotic method which exploits the small thickness and high index of the membrane. We derive a limiti...

Molecular dynamics modeling has provided a powerful tool for simulating and understanding diverse systems – ranging from materials processes to biophysical phenomena. Parallel formulations of these methods have been shown to be among the most scalable scientific computing applications. Many instances of this class of methods rely on a static bond structure for molecules, rendering them infeasib...

(2012) Numerical techniques for the variable order time fractional diffusion equation. NOTICE: this is the author's version of a work that was accepted for publication in Applied Mathematics and Computation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. ...

We examine some techniques and results rrom algebraic geometry, and assess how and to what e'xtent. fhey are oT use in computer-aided-geometric deSi~Gl't Focusing on offset and blending surface construction, we illustrate how to apply and assess algebraic methods_ We also examine some numerical techniques for interrogating offsets and blending surfaces constructed using the algebraic approach.

In the study of long-time correlations extremely long orbits must be calculated. This may be accomplished much more reliably using fixed-point arithmetic. Use of this arithmetic on the Cray–1 computer is illustrated.

The shape-from-shading (SfS) problem is a classic problem in computer vision. The task in SfS is to compute on the basis of the shading variation in a given 2-D image the 3-D depth of the depicted scene. The corresponding mathematical model eventually leads to a boundary value problem for a Hamilton-Jacobi equation. In this paper we evaluate and compare suitable numerical methods. We begin with...

Knowledge of accuracy of numerical integration is important for composing an overall numerical error budget; in orbit determination and propagation for space surveillance, there is frequently a computation time-accuracy tradeoff that must be balanced. There are several techniques to assess the accuracy of a numerical integrator. In this paper we compare some of those techniques: comparison with...

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library We briefly discuss a...