| 三维热传导型半导体问题的交替方向有限元方法 |
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| 引用本文： | 刘蕴贤.三维热传导型半导体问题的交替方向有限元方法[J].高等学校计算数学学报,2002,24(1):1-10. |
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| 作者姓名： | 刘蕴贤 |
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| 作者单位： | 山东大学数学学院,济南,250100 |
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| 基金项目： | 国家自然科学基金 ( 1 9972 0 39)，数学天元基金 ( Tr1 0 1 2 6 0 2 9)资助项目 |
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| 摘 要： | 1 引 言三维热传导型半导体器件瞬态问题的数学模型由四个非线性偏微分方程描述1 ,2 ] ,记 Ω为 Ω=0 ,1 ] 3的边界 ,三维问题-Δψ =α( p -e+ N( x) ) , ( x,t)∈Ω× 0 ,T] ,( 1 .1 ) e t= . ( De( x) e-μe( x) e ψ) -R( e,p,T) , ( x,t)∈Ω× ( 0 ,T] ,( 1 .2 ) p t= . ( Dp( x) p +μp( x) p ψ) -R( e,p,T) , ( x,t)∈Ω× ( 0 ,T] ,( 1 .3 )ρ( x) T t-ΔT =( Dp( x) p +μp( x) p ψ) -( De( x) e-μe( x) e ψ) ] . ψ, ( x,t)∈Ω× ( 0 ,T] . ( 1 .4 )ψ( x,t) =e( x,t) =p( …
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| 关 键 词： | 三维热传导型半导体 交替方向 有限元方法 瞬态问题 非线性偏微分方程 收敛性 |
GALERKIN ALTERNATING-DIRECTION METHODS AND ANALYSES FOR THE THREE-DIMENSIONAL SEMICONDUCTOR PROBLEM WITH HEAT-CONDUCTION |
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| Liu Yunxian.GALERKIN ALTERNATING-DIRECTION METHODS AND ANALYSES FOR THE THREE-DIMENSIONAL SEMICONDUCTOR PROBLEM WITH HEAT-CONDUCTION[J].Numerical Mathematics A Journal of Chinese Universities,2002,24(1):1-10. |
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| Authors: | Liu Yunxian |
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| Abstract: | Galerkin alternating direction methods are introduced and analyzed for approximating the solutions of three dimensional transient behavior of semiconductor with heat conduction, whose mathematical models are initial and boundary problems of nonlinear partial differential equation system. Electric potential equation is approximated by mixed finite element method, concentration and heat conduction equations are approximated by Galerkin alternating direction methods. Optimal order error estimates in L 2 are demonstrated. |
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| Keywords: | transient behavior of semiconductor heat conduction mixed finite element alternating direction |
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