A fictitious domain method is presented for solving elliptic partial differential equations using Galerkin spectral approximation. The fictitious domain approach consists in immersing the original domain into a larger and geometrically simpler one in order to avoid the use of boundary fitted or unstructured meshes. In the present study, boundary constraints are enforced using Lagrange multiplie...

In this article we prove convergence of adaptive finite element methods for second order elliptic eigenvalue problems. We consider Lagrange finite elements of any degree and prove convergence for simple as well as multiple eigenvalues under a minimal refinement of marked elements, for all reasonable marking strategies, and starting from any initial triangulation.

Nonnested multigrid methods are shown to be optimal-order solvers for systems of finite element equations arising from elliptic boundary problems in any space dimension. Results are derived for Lagrange-type elements of arbitrary degree.

We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviors of these variables, the meshes can be independently adapted. The resulting linear systems are usually much smaller, when compared to the usage of a single mesh, and the overall computational run...

AMS Subject Classi cation: 20-04, 05C25, 20C30 Rockmore was supported in part by a National Science Foundation Mathematical Sciences Postdoctoral Fellowship. We study the complexity of performing Fourier analysis for the group SL2(Fq), where Fq is the finite field of q elements. Direct computation of a complete set of Fourier transforms for a complex-valued function f on SL2(Fq) requires q6 ope...

We consider a continuous version of Gabor multipliers: operators consisting of a short-time Fourier transform, followed by multiplication by a distribution on phase space (called the Gabor symbol), followed by an inverse short-time Fourier transform, allowing different localizing windows for the forward and inverse transforms. For a given pair of forward and inverse windows, which linear operat...

Our aim is to develop a microwave antenna whose radiation pattern is electronically controlled. The radiation pattern of regular antennas is determined by the Fourier-transform of the complex illumination function on the antenna aperture. This radiation pattern is mechanically fixed so its alteration is impossible. Therefore we construct an antenna system of several antenna elements. All elemen...

The ESA global astrometry space mission Gaia has been monitoring the position of a billion stars since 2014. analysis such massive dataset is challenging in terms data processing involved. In particular, blind detection and characterization single or multiple companions to (planets, brown dwarfs, stars) using requires highly efficient algorithms. this article, we present set analytical methods ...

An original approach is presented to the timedependent thermal modelling of complex 3-dimensional electronic systems, from metallised power FETs and MMICs, though MCMs, up to circuit board level. This method o ers a powerful alternative to conventional numerical thermal simulation techniques. In contrast to semi-analytical Fourier approaches involving DFT-FFT, the method is based on explicit, f...