59,122 research outputs found
Planewave density interpolation methods for 3D Helmholtz boundary integral equations
This paper introduces planewave density interpolation methods for the
regularization of weakly singular, strongly singular, hypersingular and nearly
singular integral kernels present in 3D Helmholtz surface layer potentials and
associated integral operators. Relying on Green's third identity and pointwise
interpolation of density functions in the form of planewaves, these methods
allow layer potentials and integral operators to be expressed in terms of
integrand functions that remain smooth (at least bounded) regardless the
location of the target point relative to the surface sources. Common
challenging integrals that arise in both Nystr\"om and boundary element
discretization of boundary integral equation, can then be numerically evaluated
by standard quadrature rules that are irrespective of the kernel singularity.
Closed-form and purely numerical planewave density interpolation procedures are
presented in this paper, which are used in conjunction with Chebyshev-based
Nystr\"om and Galerkin boundary element methods. A variety of numerical
examples---including problems of acoustic scattering involving multiple
touching and even intersecting obstacles, demonstrate the capabilities of the
proposed technique
Extracting spacetimes using the AdS/CFT conjecture
We present analytic methods for extracting a class of bulk geometries given
information of certain physical quantities in the boundary CFT. More
specifically we look at singular correlators and entanglement entropy in the
CFT to provide information of null and spacelike geodesics repectively in the
bulk. We show that static spherically symmetric, asymptotically AdS spacetimes
which do not admit null circular orbits can be fully recovered, and that any
spacetime can be recovered up to the local maximum of the potential. We provide
analytical and numerical examples to verify the methods used.Comment: 18 pages, 7 figure
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On the block wavelet transform applied to the boundary element method
This paper follows an earlier work by Bucher et al. [1] on the application of wavelet transforms to the boundary element method, which shows how to reuse models stored in compressed form to solve new models with the same geometry but arbitrary load cases - the so-called virtual assembly technique. The extension presented in this paper involves a new computational procedure created to perform the required two-dimensional wavelet transforms by blocks, theoretically allowing the compression of matrices of arbitrary size. Details of the computer implementation that allows the use of this methodology for very large models or at high compression ratios are given. A numerical application shows a standard PC being used to solve a 131,072 DOF model, previously compressed, for 100 distinct load cases in less than 1 hour – or 33 seconds for each load case
Numerical analysis of nanostructures for enhanced light extraction from OLEDs
Nanostructures, like periodic arrays of scatters or low-index gratings, are
used to improve the light outcoupling from organic light-emitting diodes
(OLED). In order to optimize geometrical and material properties of such
structures, simulations of the outcoupling process are very helpful. The finite
element method is best suited for an accurate discretization of the geometry
and the singular-like field profile within the structured layer and the
emitting layer. However, a finite element simulation of the overall OLED stack
is often beyond available computer resources. The main focus of this paper is
the simulation of a single dipole source embedded into a twofold infinitely
periodic OLED structure. To overcome the numerical burden we apply the Floquet
transform, so that the computational domain reduces to the unit cell. The
relevant outcoupling data are then gained by inverse Flouqet transforming. This
step requires a careful numerical treatment as reported in this paper
Eigenmode-based capacitance calculations with applications in passivation layer design
The design of high-speed metallic interconnects such as microstrips requires the correct characterization of both the conductors and the surrounding dielectric environment, in order to accurately predict their propagation characteristics. A fast boundary integral equation approach is obtained by modeling all materials as equivalent surface charge densities in free space. The capacitive behavior of a finite dielectric environment can then be determined by means of a transformation matrix, relating these charge densities to the boundary value of the electric potential. In this paper, a new calculation method is presented for the important case that the dielectric environment is composed of homogeneous rectangles. The method, based on a surface charge expansion in terms of the Robin eigenfunctions of the considered rectangles, is not only more efficient than traditional methods, but is also more accurate, as shown in some numerical experiments. As an application, the design and behavior of a microstrip passivation layer is treated in some detail
Automated Netlist Generation for 3D Electrothermal and Electromagnetic Field Problems
We present a method for the automatic generation of netlists describing
general three-dimensional electrothermal and electromagnetic field problems.
Using a pair of structured orthogonal grids as spatial discretisation, a
one-to-one correspondence between grid objects and circuit elements is obtained
by employing the finite integration technique. The resulting circuit can then
be solved with any standard available circuit simulator, alleviating the need
for the implementation of a custom time integrator. Additionally, the approach
straightforwardly allows for field-circuit coupling simulations by
appropriately stamping the circuit description of lumped devices. As the
computational domain in wave propagation problems must be finite, stamps
representing absorbing boundary conditions are developed as well.
Representative numerical examples are used to validate the approach. The
results obtained by circuit simulation on the generated netlists are compared
with appropriate reference solutions.Comment: This is a pre-print of an article published in the Journal of
Computational Electronics. The final authenticated version is available
online at: https://dx.doi.org/10.1007/s10825-019-01368-6. All numerical
results can be reproduced by the Matlab code openly available at
https://github.com/tc88/ANTHE
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