4,659 research outputs found
Fourier finite element modeling of light emission in waveguides: 2.5-dimensional FEM approach
We present a Fourier finite element modeling of light emission of dipolar
emitters coupled to infinitely long waveguides. Due to the translational
symmetry, the three-dimensional (3D) coupled waveguide-emitter system can be
decomposed into a series of independent 2D problems (2.5D), which reduces the
computational cost. Moreover, the reduced 2D problems can be extremely
accurate, compared to its 3D counterpart. Our method can precisely quantify the
total emission rates, as well as the fraction of emission rates into different
modal channels for waveguides with arbitrary cross-sections. We compare our
method with dyadic Green's function for the light emission in single mode
metallic nanowire, which yields an excellent agreement. This method is applied
in multi-mode waveguides, as well as multi-core waveguides. We further show
that our method has the full capability of including dipole orientations, as
illustrated via a rotating dipole, which leads to unidirectional excitation of
guide modes. The 2.5D Finite Element Method (FEM) approach proposed here can be
applied for various waveguides, thus it is useful to interface single-photon
single-emitter in nano-structures, as well as for other scenarios involving
coupled waveguide-emitters.Comment: 11 pages, 4 figures, Optics Express, 201
Computational complexity and memory usage for multi-frontal direct solvers in structured mesh finite elements
The multi-frontal direct solver is the state-of-the-art algorithm for the
direct solution of sparse linear systems. This paper provides computational
complexity and memory usage estimates for the application of the multi-frontal
direct solver algorithm on linear systems resulting from B-spline-based
isogeometric finite elements, where the mesh is a structured grid. Specifically
we provide the estimates for systems resulting from polynomial
B-spline spaces and compare them to those obtained using spaces.Comment: 8 pages, 2 figure
The cost of continuity: performance of iterative solvers on isogeometric finite elements
In this paper we study how the use of a more continuous set of basis
functions affects the cost of solving systems of linear equations resulting
from a discretized Galerkin weak form. Specifically, we compare performance of
linear solvers when discretizing using B-splines, which span traditional
finite element spaces, and B-splines, which represent maximum
continuity. We provide theoretical estimates for the increase in cost of the
matrix-vector product as well as for the construction and application of
black-box preconditioners. We accompany these estimates with numerical results
and study their sensitivity to various grid parameters such as element size
and polynomial order of approximation . Finally, we present timing results
for a range of preconditioning options for the Laplace problem. We conclude
that the matrix-vector product operation is at most \slfrac{33p^2}{8} times
more expensive for the more continuous space, although for moderately low ,
this number is significantly reduced. Moreover, if static condensation is not
employed, this number further reduces to at most a value of 8, even for high
. Preconditioning options can be up to times more expensive to setup,
although this difference significantly decreases for some popular
preconditioners such as Incomplete LU factorization
Notas acerca del estatuto jurÃdico del judaÃsmo en los paÃses de la Unión Europea
El presente constituye el texto de mi intervención en el "2º Encuentro sobre minorÃas religiosas. El judaÃsmo", que tuvo lugar en la Facultad de Ciencias Sociales y de Humanidades de Cuenca, del 19 al 23 de Febrero de 2001
A summary of my twenty years of research according to Google Scholars
I am David Pardo, a researcher from Spain working mainly on numerical analysis
applied to geophysics. I am 40 years old, and over a decade ago, I realized that my performance as
a researcher was mainly evaluated based on a number called \h-index". This single number contains
simultaneously information about the number of publications and received citations. However, dif-
ferent h-indices associated to my name appeared in di erent webpages. A quick search allowed me
to nd the most convenient (largest) h-index in my case. It corresponded to Google Scholars.
In this work, I naively analyze a few curious facts I found about my Google Scholars and, at
the same time, this manuscript serves as an experiment to see if it may serve to increase my Google
Scholars h-index
A summary of my twenty years of research according to Google Scholars
I am David Pardo, a researcher from Spain working mainly on numerical analysis
applied to geophysics. I am 40 years old, and over a decade ago, I realized that my performance as
a researcher was mainly evaluated based on a number called \h-index". This single number contains
simultaneously information about the number of publications and received citations. However, dif-
ferent h-indices associated to my name appeared in di erent webpages. A quick search allowed me
to nd the most convenient (largest) h-index in my case. It corresponded to Google Scholars.
In this work, I naively analyze a few curious facts I found about my Google Scholars and, at
the same time, this manuscript serves as an experiment to see if it may serve to increase my Google
Scholars h-index
Tilings and the aztec diamond theorem
Tilings over the plane are analysed in this work, making a special focus on the Aztec Diamond Theorem. A review of the most relevant results about monohedral tilings is made to continue later by introducing domino tilings over subsets of R2. Based on previous work made by other mathematicians, a proof of the Aztec Diamond Theorem is presented in full detail by completing the description of a bijection that was not made explicit in the original work
- …