95 research outputs found
Drift-diffusion models for innovative semiconductor devices and their numerical solution
We present charge transport models for novel semiconductor devices which may include ionic species as well as their thermodynamically consistent finite volume discretization
Tetrahedral mesh improvement using moving mesh smoothing, lazy searching flips, and RBF surface reconstruction
Given a tetrahedral mesh and objective functionals measuring the mesh quality
which take into account the shape, size, and orientation of the mesh elements,
our aim is to improve the mesh quality as much as possible. In this paper, we
combine the moving mesh smoothing, based on the integration of an ordinary
differential equation coming from a given functional, with the lazy flip
technique, a reversible edge removal algorithm to modify the mesh connectivity.
Moreover, we utilize radial basis function (RBF) surface reconstruction to
improve tetrahedral meshes with curved boundary surfaces. Numerical tests show
that the combination of these techniques into a mesh improvement framework
achieves results which are comparable and even better than the previously
reported ones.Comment: Revised and improved versio
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Block preconditioners for linear systems arising from multiscale collocation with compactly supported RBFs
Symmetric collocation methods with radial basis functions allow
approximation of the solution of a partial differential equation, even if the
right-hand side is only known at scattered data points, without needing to
generate a grid. However, the benefit of a guaranteed symmetric positive
definite block system comes at a high computational cost. This cost can be
alleviated somewhat by considering compactly supported radial basis functions
and a multiscale technique. But the condition number and sparsity will still
deteriorate with the number of data points. Therefore, we study certain block
diagonal and triangular preconditioners. We investigate ideal preconditioners
and determine the spectra of the preconditioned matrices before proposing
more practical preconditioners based on a restricted additive Schwarz method
with coarse grid correction (ARASM). Numerical results verify the
effectiveness of the preconditioners
Uniform second order convergence of a complete flux scheme on unstructured 1D grids for a singularly perturbed advection-diffusion equation and some multidimensional extensions
The accurate and efficient discretization of singularly perturbed advection-diffusion equations on arbitrary 2D and 3D domains remains an open problem. An interesting approach to tackle this problem is the complete flux scheme (CFS) proposed by G. D. Thiart and further investigated by J. ten Thije Boonkkamp. For the CFS, uniform second order convergence has been proven on structured grids. We extend a version of the CFS to unstructured grids for a steady singularly perturbed advection-diffusion equation. By construction, the novel finite volume scheme is nodally exact in 1D for piecewise constant source terms. This property allows to use elegant continuous arguments in order to prove uniform second order convergence on unstructured one-dimensional grids. Numerical results verify the predicted bounds and suggest that by aligning the finite volume grid along the velocity field uniform second order convergence can be obtained in higher space dimensions as well
Multilevel interpolation of divergence-free vector fields
We introduce a multilevel technique for interpolating scattered data of divergence-free vector fields with the help of matrix-valued compactly supported kernels. The support radius at a given level is linked to the mesh norm of the data set at that level. There are at least three advantages of this method: no grid structure is necessary for the implementation, the multilevel approach is computationally cheaper than solving a large one-shot system and the interpolant is guaranteed to be analytically divergence-free. Furthermore, though we will not pursue this here, our multiscale approach is able to represent multiple scales in the data if present. We will prove convergence of the scheme, stability estimates and give a numerical example
A novel surface remeshing scheme via higher dimensional embedding and radial basis functions
Many applications heavily rely on piecewise triangular meshes to describe complex surface geometries. High-quality meshes significantly improve numerical simulations. In practice, however, one often has to deal with several challenges. Some regions in the initial mesh may be overrefined, others too coarse. Additionally, the triangles may be too thin or not properly oriented. We present a novel mesh adaptation procedure which greatly improves the problematic input mesh and overcomes all of these drawbacks. By coupling surface reconstruction via radial basis functions with the higher dimensional embedding surface remeshing technique, we can automatically generate anisotropic meshes. Moreover, we are not only able to fill or coarsen certain mesh regions but also align the triangles according to the curvature of the reconstructed surface. This yields an acceptable trade-off between computational complexity and accuracy
an anisoptropic surface remeshing strategy combining higher dimensional embedding with radial basis functions
Abstract Many applications heavily rely on piecewise triangular meshes to describe complex surface geometries. High-quality meshes significantly improve numerical simulations. In practice, however, one often has to deal with several challenges. Some regions in the initial mesh may be overrefined, others too coarse. Additionally, the triangles may be too thin or not properly oriented. We present a novel mesh adaptation procedure which greatly improves the problematic input mesh and overcomes all of these drawbacks. By coupling surface reconstruction via radial basis functions with the higher dimensional embedding surface remeshing technique, we can automatically generate anisotropic meshes. Moreover, we are not only able to fill or coarsen certain mesh regions but also align the triangles according to the curvature of the reconstructed surface. This yields an acceptable trade-off between computational complexity and accuracy
Modeling and simulation of the lateral photovoltage scanning method
The fast, cheap and nondestructive lateral photovoltage scanning (LPS) method detects inhomogeneities in semiconductors crystals. The goal of this paper is to model and simulate this technique for a given doping profile. Our model is based on the semiconductor device equations combined with a nonlinear boundary condition, modelling a volt meter. To validate our 2D and 3D finite volume simulations, we use theory developed by Tauc [21] to derive three analytical predictions which our simulation results corroborate, even for anisotropic 2D and 3D meshes. Our code runs about two orders of magnitudes faster than earlier implementations based on commercial software [15]. It also performs well for small doping concentrations which previously could not be simulated at all due to numerical instabilities. Our simulations provide experimentalists with reference laser powers for which meaningful voltages can still be measured. For higher laser power the screening effect does not allow this anymore
What company does my news article refer to? Tackling multiclass problems with topic modeling
While it is technically trivial to search for the company name to predict the company a new article refers to,
it often leads to incorrect results. In this article, we compare the two approaches bag-of-words
with k-nearest neighbors and Latent Dirichlet Allocation with k-nearest neighbor by
assessing their applicability for predicting the S\&P 500 company which is mentioned in a
business news article or press release. Both approaches are evaluated on a corpus of 13k documents
containing 84\% news articles and 16\% press releases. While the bag-of-words
approach yields accurate predictions, it is highly inefficient due to its gigantic feature space.
The Latent Dirichlet Allocation approach, on the other hand, manages to achieve roughly the same
prediction accuracy (0.58 instead of 0.62) but reduces the feature space by a factor of seven
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