Browsing by Author "Li, ZL"

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Fast solvers for 3D Poisson equations involving interfaces in a finite or the infinite domain
(2006-06-15)
Lai, MC
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Li, ZL
;
Lin, XB
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應用數學系
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Department of Applied Mathematics
In this paper, numerical methods are proposed for Poisson equations defined in a finite or infinite domain in three dimensions. In the domain, there can exists an interface across which the source term, the flux, and therefore the solution may be discontinuous. The existence and uniqueness of the solution are also discussed. To deal with the discontinuity in the source term and in the flux, the original problem is transformed to a new one with a smooth solution. Such a transformation can be carried out easily through an extension of the jumps along the normal direction if the interface is expressed as the zero level set of a three-dimensional function. An auxiliary sphere is used to separate the infinite region into an interior and exterior domain. The Kelvin's inversion is used to map the exterior domain into an interior domain. The two Poisson equations defined in the interior and the exterior written in spherical coordinates are solved simultaneously. By choosing the mesh size carefully and exploiting the fast Fourier transform, the resulting finite difference equations can be solved efficiently. The approach in dealing with the interface has also been used with the artificial boundary condition technique which truncates the infinite domain. Numerical results demonstrate second order accuracy of our algorithms. (c) 2005 Elsevier B.V. All rights reserved.
New formulations for interface problems in polar coordinates
(2003)
Li, ZL
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Wang, WC
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Chern, IL
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Lai, MC
;
應用數學系
In this paper, numerical methods are proposed for some interface problems in polar or Cartesian coordinates. The new methods are based on a formulation that transforms the interface problem with a nonsmooth or discontinuous solution into a problem with a smooth solution. The new formulation leads to a simple second order finite difference scheme for the partial differential equation and a new interpolation scheme for the normal derivative of the solution. In conjunction with the fast immersed interface method, a fast solver has been developed for the interface problems with a piecewise constant but a discontinuous coefficient using the new formulation in a polar coordinate system.
Strong red emission in heterojunctions of conjugated polymer blends
(2004-06-14)
Li, ZL
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Meng, HF
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Horng, SF
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Hsu, CS
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Chen, LC
We demonstrate strong red electroluminescence in bilayer polymer light-emitting diodes with poly(3-hexylthiophene) and polyfluorene copolymers. The emission spectrum of the diode, peaked at 612 nm, is different from either of the two polymer layers, and is attributed to the exciplex state existing only at the heterojunction. The efficiency of this junction emission is very high for red polymer light-emitting diodes. Peak luminance of 3500 cd/m(2) with yield 1.3 cd/A is achieved. The emission color can be made more saturated by blending red-emitting polymers into the polyfluorene to eliminate the small residual green emission. (C) 2004 American Institute of Physics.