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1
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Energy estimates and numerical verification of the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell’s system

100%
Beilina L.
Open Mathematics
|
2013
|
tom 11
|
nr 4
702-733
EN
We rigorously derive energy estimates for the second order vector wave equation with gauge condition for the electric field with non-constant electric permittivity function. This equation is used in the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell’s system. Our numerical experiments illustrate efficiency of the modified hybrid scheme in two and three space dimensions when the method is applied for generation of backscattering data in the reconstruction of the electric permittivity function.
2
Content available remote

Spatially-dependent and nonlinear fluid transport: coupling framework

84%
Geiser J.
Open Mathematics
|
2012
|
tom 10
|
nr 1
116-136
EN
We introduce a solver method for spatially dependent and nonlinear fluid transport. The motivation is from transport processes in porous media (e.g., waste disposal and chemical deposition processes). We analyze the coupled transport-reaction equation with mobile and immobile areas. The main idea is to apply transformation methods to spatial and nonlinear terms to obtain linear or nonlinear ordinary differential equations. Such differential equations can be simply solved with Laplace transformation methods or nonlinear solver methods. The nonlinear methods are based on characteristic methods and can be generalized numerically to higher-order TVD methods [Harten A., High resolution schemes for hyperbolic conservation laws, J. Comput. Phys., 1983, 49(3), 357–393]. In this article we will focus on the derivation of some analytical solutions for spatially dependent and nonlinear problems which can be embedded into finite volume methods. The main contribution is to embed one-dimensional analytical solutions into multi-dimensional finite volume methods with the construction idea of mass transport [Geiser J., Mobile and immobile fluid transport: coupling framework, Internat. J. Numer. Methods Fluids, 2010, 65(8), 877–922]. At the end of the article we present some results of numerical experiments for different benchmark problems.
3
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A note on the rate of convergence for Chebyshev-Lobatto and Radau systems

84%
Berriochoa E., Cachafeiro A., Díaz J., Martínez E.
Open Mathematics
|
2016
|
tom 14
|
nr 1
156-166
EN
This paper is devoted to Hermite interpolation with Chebyshev-Lobatto and Chebyshev-Radau nodal points. The aim of this piece of work is to establish the rate of convergence for some types of smooth functions. Although the rate of convergence is similar to that of Lagrange interpolation, taking into account the asymptotic constants that we obtain, the use of this method is justified and it is very suitable when we dispose of the appropriate information.
4
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Numerical investigation of a new class of waves in an open nonlinear heat-conducting medium

84%
Dimova M., Dimova S., Vasileva D.
Open Mathematics
|
2013
|
tom 11
|
nr 8
1375-1391
EN
The paper contributes to the problem of finding all possible structures and waves, which may arise and preserve themselves in the open nonlinear medium, described by the mathematical model of heat structures. A new class of self-similar blow-up solutions of this model is constructed numerically and their stability is investigated. An effective and reliable numerical approach is developed and implemented for solving the nonlinear elliptic self-similar problem and the parabolic problem. This approach is consistent with the peculiarities of the problems - multiple solutions of the elliptic problem and blow-up solutions of the parabolic one.
5
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Numerical simulation of surface acoustic wave actuated cell sorting

84%
Franke T., Hoppe R., Linsenmann C., Zeleke K.
Open Mathematics
|
2013
|
tom 11
|
nr 4
760-778
EN
We consider the mathematical modeling and numerical simulation of high throughput sorting of two different types of biological cells (type I and type II) by a biomedical micro-electro-mechanical system (BioMEMS) whose operating behavior relies on surface acoustic wave (SAW) manipulated fluid flow in a microchannel. The BioMEMS consists of a separation channel with three inflow channels for injection of the carrier fluid and the cells, two outflow channels for separation, and an interdigital transducer (IDT) close to the lateral wall of the separation channel for generation of the SAWs. The cells can be distinguished by fluorescence. The inflow velocities are tuned so that without SAW actuation a cell of type I leaves the device through a designated outflow channel. However, if a cell of type II is detected, the IDT is switched on and the SAWs modify the fluid flow so that the cell leaves the separation channel through the other outflow boundary. The motion of a cell in the carrier fluid is modeled by the Finite Element Immersed Boundary method (FE-IB). Numerical results are presented that illustrate the feasibility of the surface acoustic wave actuated cell sorting approach.
6
Content available remote

Hybrid fluid-quantum coupling for the simulation of the transport of partially quantized particles in a DG-MOSFET

69%
Jourdana C., Vauchelet N.
Nanoscale Systems: Mathematical Modeling, Theory and Applications
|
2015
|
tom 4
|
nr 1
EN
This paper is devoted to numerical simulations of electronic transport in nanoscale semiconductor devices forwhich charged carriers are extremely confined in one direction. In such devices, like DG-MOSFETs, the subband decomposition method is used to reduce the dimensionality of the problem. In the transversal direction electrons are confined and described by a statistical mixture of eigenstates of the Schrödinger operator. In the longitudinal direction, the device is decomposed into a quantum zone (where quantum effects are expected to be large) and a classical zone (where they are negligible). In the largely doped source and drain regions of a DG-MOSFET, the transport is expected to be highly collisional; then a classical transport equation in diffusive regime coupled with the subband decomposition method is used for the modeling, as proposed in N. Ben Abdallah et al. (2006, Proc. Edind. Math. Soc. [7]). In the quantum region, the purely ballistic model presented in Polizzi et al. (2005, J. Comp. Phys. [25]) is used. This work is devoted to the hybrid coupling between these two regions through connection conditions at the interfaces. These conditions have been obtained in order to verify the continuity of the current. A numerical simulation for a DG-MOSFET, with comparison with the classical and quantum model, is provided to illustrate our approach.
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