Accurate, Stable and Efficient Modal Calculations of Photoelectrically Useful Absorption in Lamellar Metallic and Semiconductor Diffraction Gratings
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In the past few years, the level set method has been extensively used for the numerical solution of interface problems in different domains, from free-surface and mean curvature flows to image processing. A crucial ingredient in every implementation of the ...
In this paper we present a method for the numerical solution of elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. The method consists in calculating successive corrections to the solution in patches whose discre ...
Physical systems encompassing a variety of strongly coupled scales pose major computational challenges in terms of analysis modeling and simulation. In this report we first discuss a multiscale modeling approach for the transport of particles such as DNA i ...
In this project we address the numerical approximation of hyperbolic equations and systems using the discontinuous Galerkin (DG) method in combination with higher order polynomial degrees. In short, this is called Spectral Discontinuous Galerkin (SDG) meth ...
The paper presents an original method to determine the 2D magnetic field in a square magnetic circuit. To do it, the method of Schwarz-Christoffel mapping is used. This mapping is a special kind of the conformal mappings, applicable to polygonal 2D configu ...
We propose an extension of secant methods for nonlinear equations using a population of previous iterates. Contrarily to classical secant methods, where exact interpolation is used, we prefer a least squares approach to calibrate the linear model. We propo ...
The comparison of numerical results for implicit-explicit and fully explicit Runge-Kutta time integration methods for a nozzle flow problem shows that filtering can significantly degrade the accuracy of the numerical solution for long-time integration prob ...
Balancing a matrix by a simple and accurate similarity transformation can improve the speed and accuracy of numerical methods for computing eigenvalues. We describe balancing strategies for a large and sparse Hamiltonian matrix H. It is first shown how to ...
We report a novel mode of quasi-static oscillatory crack propagation when a cutting tool is driven through a thin polymer film [6,7]. In our experiments, for tools with a large enough width, the crack tip follows a highly periodic path, leaving behind a st ...
A general semiclassical expression for quantum fidelity (Loschmidt echo) of arbitrary pure and mixed states is derived. It expresses fidelity as an interference sum of dephasing trajectories weighed by the Wigner function of the initial state, and does not ...