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Dirichlet-to-Neumann Map for a Hyperbolic Equation
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作者 Fagueye Ndiaye Mouhamadou Ngom Diaraf Seck 《Journal of Applied Mathematics and Physics》 2023年第8期2231-2251,共21页
In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann op... In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann operators corresponding to a potential radial have the same properties for hyperbolic differential equations as for elliptic differential equations. We numerically implement the coefficients of the explicit formulas. Moreover, a Lipschitz type stability is established near the edge of the domain by an estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neumann map in the inverse problem for a hyperbolic differential equation. 展开更多
关键词 Hyperbolic Differential Equation Calderón’s Problem Schrödinger Operator POTENTIAL Inverse Potential Problem dirichlet-to-neumann map Numerical Simulations Lipschitz Stability
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Bandgap calculation for mixed in-plane waves in 2D phononic crystals based on Dirichlet-to-Neumann map 被引量:7
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作者 Ni Zhen Feng-Lian Li +1 位作者 Yue-Sheng Wang Chuan-Zeng Zhang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2012年第4期1143-1153,共11页
In this paper, a method based on the Dirichlet- to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses... In this paper, a method based on the Dirichlet- to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses the scattered fields in a unit cell as the cylindrical wave expansions and imposes the Bloch condition on the boundary of the unit cell. The Dirichlet-to-Neumann (DtN) map is applied to obtain a linear eigenvalue equation, from which the Bloch wave vectors along the irreducible Brillouin zone are calculated for a given frequency. Compared with other methods, the present method is memory-saving and time-saving. It can yield accurate results with fast convergence for various material combinations including those with large acoustic mismatch without extra computational cost. The method is also efficient for mixed fluid-solid systems because it considers the different wave modes in the fluid and solid as well as the proper fluid-solid interface condition. 展开更多
关键词 Phononic crystal Band structure Cylindrical wave expansion dirichlet-to-neumann (dtn map Bloch theorem
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基于Dirichlet-to-Neumann映射分析计算旋电光子晶体波导结构
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作者 李峥 胡真 《南京师大学报(自然科学版)》 CAS 北大核心 2023年第3期12-19,共8页
拓展了Dirichlet-to-Neumann(DtN)映射方法,将其应用于分析二维旋电光子晶体波导结构.首先基于旋电光子晶体单元晶格的DtN映射,构造出波导结构超级晶格的DtN映射,然后在超级晶格的边界上建立起线性特征值问题进行求解.由于该方法只需要... 拓展了Dirichlet-to-Neumann(DtN)映射方法,将其应用于分析二维旋电光子晶体波导结构.首先基于旋电光子晶体单元晶格的DtN映射,构造出波导结构超级晶格的DtN映射,然后在超级晶格的边界上建立起线性特征值问题进行求解.由于该方法只需要在晶格的边界上进行离散,避免了在计算区域内部的离散,故所涉及的矩阵规模相对较小,极大地提高了计算速度.文章最后用数值算例验证了该方法的有效性. 展开更多
关键词 旋电光子晶体波导结构 数值方法 特征值问题 dirichlet-to-neumann(dtn)映射
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Wave Radiation by a Floating Body in Water of Finite Depth Using an Exact DtN Boundary Condition
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作者 RIM Un-Ryong 《Journal of Ocean University of China》 SCIE CAS CSCD 2023年第6期1497-1504,共8页
The present paper focuses on the wave radiation by an oscillating body with six degrees of freedom by using the DtN artifi-cial boundary condition.The artificial boundary is usually selected as a circle or spherical s... The present paper focuses on the wave radiation by an oscillating body with six degrees of freedom by using the DtN artifi-cial boundary condition.The artificial boundary is usually selected as a circle or spherical surface to solve various types of fields,such as sound waves or electromagnetic waves,provided that the considered domain is infinite or unbounded in all directions.However,the substantial wave motion is considered in water of finite depth,that is,the fluid domain is bounded vertically but unbounded horizon-tally.Thus,the DtN boundary condition is given on an artificial cylindrical surface,which divides the water domain into an interior and exterior region.The boundary integral equation is adopted to implement the present model.In the case of a floating cylinder,the results of hydrodynamic coefficients of a chamfer box are discussed. 展开更多
关键词 wave radiation boundary element method dirichlet-to-neumann map artificial boundary floating body finite-depth water
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二维水下声辐射问题的改进径向基点插值法研究
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作者 桂强 孙磊 +2 位作者 游翔宇 柴应彬 李威 《计算力学学报》 CAS CSCD 北大核心 2024年第2期344-351,共8页
径向基点插值法是一种典型的无网格数值计算方法,在分析声学问题时,相比于传统有限元法能更好地抑制频散误差,且在相同的节点分布下通常可以得到更精确的数值解。本文提出一种改进的节点选取方案用于构造插值形函数,即改进径向基点插值... 径向基点插值法是一种典型的无网格数值计算方法,在分析声学问题时,相比于传统有限元法能更好地抑制频散误差,且在相同的节点分布下通常可以得到更精确的数值解。本文提出一种改进的节点选取方案用于构造插值形函数,即改进径向基点插值法。该方案采取一个简单而直接的格式,可确保在进行数值积分时同一背景积分单元中的被积函数是连续可微的,从而减小数值积分误差,得到比原始径向基点插值法更精确的数值解。同时,为了处理外声场问题,本文采用DtN映射技术将无限域截断为有界计算域,满足索默菲尔德辐射条件。数值试验表明,相比于传统有限元法和原始径向基点插值法,本文改进方法具有更高的计算精度和计算效率,在研究水下声辐射问题时具有良好的应用前景。 展开更多
关键词 径向基点插值法 水下声辐射 dtn映射 无界域 无网格技术
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映射-编码-分发构架在DTN中的应用
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作者 钱景辉 谢开源 《传感器与微系统》 CSCD 北大核心 2012年第9期146-149,152,共5页
在移动模型不可预知的延迟容忍网络(DTN)中,有效地传输数据是非常困难的。由于连接的频繁断开和缺乏对网络动态结构的了解,传统的传输策略很难发挥效用。通过分析和比较目前DTN中常见的转发机制,提出一种新的映射—编码—分发(MCR)分层... 在移动模型不可预知的延迟容忍网络(DTN)中,有效地传输数据是非常困难的。由于连接的频繁断开和缺乏对网络动态结构的了解,传统的传输策略很难发挥效用。通过分析和比较目前DTN中常见的转发机制,提出一种新的映射—编码—分发(MCR)分层架构。仿真结果表明:其在不同的DTN环境下均具有较好的性能。 展开更多
关键词 映射—编辑—分发 延迟容忍网络 机会网络 路由
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二维光子晶体波导中慢光的Dirichlet-to-Neumann映射方法计算 被引量:1
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作者 朱阿敏 胡真 《云南师范大学学报(自然科学版)》 2017年第4期44-53,共10页
利用Dirichlet-to-Neumann(DtN)映射方法计算了三角形排列的二维单线缺陷光子晶体波导管中的慢光.首先利用六边形单元晶格的(DtN)映射构建三角形排列的超级晶体的DtN映射,然后利用超级晶体的DtN映射把求解Bloch传播模问题转化为求较小... 利用Dirichlet-to-Neumann(DtN)映射方法计算了三角形排列的二维单线缺陷光子晶体波导管中的慢光.首先利用六边形单元晶格的(DtN)映射构建三角形排列的超级晶体的DtN映射,然后利用超级晶体的DtN映射把求解Bloch传播模问题转化为求较小矩阵的线性特征值问题.单元晶格的DtN映射把单元晶格边界上的波动场映射成边界上的法向导数.利用单元晶格的DtN映射避免了在单元晶格内部的离散,只需在边界上计算,减少了未知数个数,得到的矩阵较小,从而大大减少了计算量.不管介质是否是色散的,利用超级晶体的DtN映射建立的特征值问题都是线性的.数值算例表明用DtN映射方法来计算波导管中的慢光是非常有效的. 展开更多
关键词 慢光 dirichlet-to-neumann(dtn)映射 二维单线缺陷光子晶体波导管
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基于Dirichlet-to-Neumann映射计算旋磁光子晶体的带隙结构 被引量:2
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作者 杨华娇 胡真 《云南师范大学学报(自然科学版)》 2020年第3期46-52,共7页
扩展了Dirichlet-to-Neumann(DtN)映射方法,构造出了旋磁光子晶体单元晶格的DtN映射,并利用该映射建立特征值问题来计算二维旋磁光子晶体的带隙结构.该方法只需要在边界上进行离散,从而得到的特征值问题矩阵较小,并且该特征值问题以频... 扩展了Dirichlet-to-Neumann(DtN)映射方法,构造出了旋磁光子晶体单元晶格的DtN映射,并利用该映射建立特征值问题来计算二维旋磁光子晶体的带隙结构.该方法只需要在边界上进行离散,从而得到的特征值问题矩阵较小,并且该特征值问题以频率ω为给定的参数,以波数β的函数为特征值,所以无论对于色散介质还是非色散介质,它都是线性特征值问题.最后,分别以正方形、三角形以及蜂巢状周期排列的旋磁光子晶体为例验证了该数值方法的有效性. 展开更多
关键词 dirichlet-to-neumann(dtn)映射 旋磁光子晶体 带隙结构 数值方法
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基于Dirichlet-to-Neumann映射计算波导中缺陷激发的连续谱束缚态
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作者 陆明鑫 胡真 《云南师范大学学报(自然科学版)》 2022年第2期41-46,共6页
利用Dirichlet-to-Neumann(DtN)映射方法分析和计算在光子晶体波导中由点缺陷激发的BIC,通过将整个平面上的特征值问题转化成截断区域内的正方形单元晶格所有边上的特征值问题,避免了对于计算区域内部的计算,缩小了矩阵规模,降低了计算... 利用Dirichlet-to-Neumann(DtN)映射方法分析和计算在光子晶体波导中由点缺陷激发的BIC,通过将整个平面上的特征值问题转化成截断区域内的正方形单元晶格所有边上的特征值问题,避免了对于计算区域内部的计算,缩小了矩阵规模,降低了计算的工作量和难度.基于该方法,确定了几种能够激发波导中BIC的点缺陷的参数范围. 展开更多
关键词 数值方法 连续谱束缚态 特征值问题 dirichlet-to-neumann(dtn)映射
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基于Dirichlet-to-Neumann映射方法计算二维光子晶体在布里渊区中心处的狄拉克点
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作者 张小荣 胡真 《河北师范大学学报(自然科学版)》 CAS 2018年第2期108-116,共9页
光子晶体狄拉克点是光子晶体能带结构在布里渊区上形成具有线性色散关系的双锥形结构的交点.通常狄拉克点出现在布里渊区的边界上,近年来研究发现光子晶体狄拉克点也可以出现在布里渊区的中心处,而此时的光子晶体具有非常独特的性能,可... 光子晶体狄拉克点是光子晶体能带结构在布里渊区上形成具有线性色散关系的双锥形结构的交点.通常狄拉克点出现在布里渊区的边界上,近年来研究发现光子晶体狄拉克点也可以出现在布里渊区的中心处,而此时的光子晶体具有非常独特的性能,可以被制造成零折射率材料.利用Dirichlet-to-Neumann(DtN)映射方法计算二维光子晶体在布里渊区中心处的狄拉克点.固定圆柱的半径,改变圆柱介质的介电常数,通过寻找能带结构在布里渊区中心处的交点,来确定光子晶体在布里渊区中心处的狄拉克点.利用DtN映射方法只需在单元晶格的边界离散,使得在每一步计算中,求解的都是较小矩阵的线性特征值问题.最后数值算例验证了利用DtN映射方法来计算二维光子晶体在布里渊区中心处的狄拉克点是有效的. 展开更多
关键词 光子晶体 狄拉克点 能带结构 零折射率材料 dtn映射
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旋磁光子晶体单向表面模式的高效数值计算 被引量:1
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作者 任莹蓉 胡真 《云南师范大学学报(自然科学版)》 2020年第6期43-49,共7页
应用Dirichlet-to-Neumann(DtN)映射方法计算旋磁光子晶体的单向表面模式,首先以单元晶格的DtN映射为基础构造出超级晶格的DtN映射,然后利用超级晶格的DtN映射建立线性特征值问题并进行求解.由于DtN映射方法只需要在计算区域的边界上进... 应用Dirichlet-to-Neumann(DtN)映射方法计算旋磁光子晶体的单向表面模式,首先以单元晶格的DtN映射为基础构造出超级晶格的DtN映射,然后利用超级晶格的DtN映射建立线性特征值问题并进行求解.由于DtN映射方法只需要在计算区域的边界上进行离散,避免了在计算区域内部的离散,从而极大地减少了未知数的个数,使得求解特征值问题时涉及的矩阵规模非常小,提高了计算速度,最后利用数值算例验证了这一方法的有效性. 展开更多
关键词 数值方法 旋磁光子晶体 特征值问题 dirichlet-to-neumann(dtn)映射
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On the reconstruction of Dirichlet-to-Neumann map in inverse scattering problems with stability estimates 被引量:2
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作者 WANG HaiBing 1,2 & LIU JiJun 1 1 Department of Mathematics,Southeast University,Nanjing 210096,China 2 School of Mathematics and Computational Science,Hunan University of Science and Technology,Xiangtan 411201,China 《Science China Mathematics》 SCIE 2010年第8期2069-2084,共16页
Consider the determination of Dirichlet-to-Neumann(D-to-N) map from the far-field pattern in inverse scattering problems,which is the key step in some recently developed inversion schemes such as probe method.Essentia... Consider the determination of Dirichlet-to-Neumann(D-to-N) map from the far-field pattern in inverse scattering problems,which is the key step in some recently developed inversion schemes such as probe method.Essentially,this problem is related to the reconstruction of the scattered wave from its far-field data.We firstly prove the well-known uniqueness result of the D-to-N map from the far-field pattern using a new scheme based on the mixed reciprocity principle.The advantage of this new proof scheme is that it provides an efficient algorithm for computing the D-to-N map,avoiding the numerical differentiation for the scattered wave.Then combining with the classical potential theory,a simple and feasible regularizing reconstruction scheme for the D-to-N map is proposed.Finally the stability estimate for the reconstruction with noisy input data is rigorously analyzed. 展开更多
关键词 INVERSE scattering dirichlet-to-neumann map REGULARIZATION mixed RECIPROCITY PRINCIPLE stability
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Dirichlet-to-Neumann Map Method with Boundary Cells for Photonic Crystals Devices
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作者 Jianhua Yuan Ya Yan Lu 《Communications in Computational Physics》 SCIE 2011年第1期113-128,共16页
In a two-dimensional(2D)photonic crystal(PhC)composed of circular cylinders(dielectric rods or air holes)on a square or triangular lattice,various PhC devices can be created by removing or modifying some cylinders.Mos... In a two-dimensional(2D)photonic crystal(PhC)composed of circular cylinders(dielectric rods or air holes)on a square or triangular lattice,various PhC devices can be created by removing or modifying some cylinders.Most existing numerical methods for PhC devices give rise to large sparse or smaller but dense linear systems,all of which are expensive to solve if the device is large.In a previous work[Z.Hu et al.,Optics Express,16(2008),17383-17399],an efficient Dirichlet-to-Neumann(DtN)map method was developed for general 2D PhC devices with an infinite background PhC to take full advantage of the underlying lattice structure.The DtN map of a unit cell is an operator that maps the wave field to its normal derivative on the cell boundary and it allows one to avoid computing the wave field in the interior of the unit cell.In this paper,we extend the DtN map method to PhC devices with a finite background PhC.Since there is no bandgap effect to confine the light in a finite PhC,a different technique for truncating the domain is needed.We enclose the finite structure with a layer of empty boundary and corner unit cells,and approximate the DtN maps of these cells based on expanding the scattered wave in outgoing plane waves.Our method gives rise to a relatively small and sparse linear systems that are particularly easy to solve. 展开更多
关键词 Photonic crystal dirichlet-to-neumann map numerical simulation
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Dirichlet-to-Neumann Mapping for the Characteristic Elliptic Equations with Symmetric Periodic Coefficients
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作者 Jingsu Kang Meirong Zhang Chunxiong Zheng 《Communications in Computational Physics》 SCIE 2014年第9期1102-1115,共14页
Based on the numerical evidences,an analytical expression of the Dirichletto-Neumann mapping in the form of infinite product was first conjectured for the onedimensional characteristic Schrodinger equation with a sinu... Based on the numerical evidences,an analytical expression of the Dirichletto-Neumann mapping in the form of infinite product was first conjectured for the onedimensional characteristic Schrodinger equation with a sinusoidal potential in[Commun.Comput.Phys.,3(3):641-658,2008].It was later extended for the general secondorder characteristic elliptic equations with symmetric periodic coefficients in[J.Comp.Phys.,227:6877-6894,2008].In this paper,we present a proof for this Dirichlet-toNeumann mapping. 展开更多
关键词 dirichlet-to-neumann mapping Schrodinger equation symmetric periodic potentials absorbing boundary conditions.
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Localisation Inverse Problem of Absorbing Laplacian Transport
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作者 Ibrahim Baydoun 《Journal of Modern Physics》 2013年第5期572-578,共7页
We study the localisation inverse problem corresponding to Laplacian transport of absorbing cell. Our main goal is to find sufficient Dirichelet-to-Neumann conditions insuring that this inverse problem is uniquely sol... We study the localisation inverse problem corresponding to Laplacian transport of absorbing cell. Our main goal is to find sufficient Dirichelet-to-Neumann conditions insuring that this inverse problem is uniquely soluble. In this paper, we show that the conformal mapping technique is adopted to this type of problem in the two dimensional case. 展开更多
关键词 LAPLACIAN TRANSPORT dirichlet-to-neumann Operators Inverse Problem CONFORMAL mapping
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基于DtN映射和三次样条逼近的二维分段均匀波导的算法
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作者 李建英 黄晋阳 《北京化工大学学报(自然科学版)》 CAS CSCD 北大核心 2014年第2期124-128,共5页
基于DtN映射的双向传播算法是计算具有二维分段均匀结构波导的最有效的算法之一。本文发展了一种新的计算DtN映射的算法,该算法主要利用三次样条函数逼近来计算每一均匀段上的DtN映射。此方法可以直接解析地表出需计算的特征值与特征向... 基于DtN映射的双向传播算法是计算具有二维分段均匀结构波导的最有效的算法之一。本文发展了一种新的计算DtN映射的算法,该算法主要利用三次样条函数逼近来计算每一均匀段上的DtN映射。此方法可以直接解析地表出需计算的特征值与特征向量,直接给出一阶导数的计算公式,减少了近似计算过程,从而减少计算误差。另外,它对解的光滑性要求较低,因此具有更好的适用性。本文给出的Cost 268 modeling task算例表明,这种基于DtN映射的三次样条函数逼近算法是一种高效的算法。 展开更多
关键词 波导结构 数值计算 dtn映射 三次样条函数
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A BIE-BASED DtN-FEM FOR FLUID-SOLID INTERACTION PROBLEMS
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作者 Tao Yin Andreas Rathsfeld J Liwei Xu 《Journal of Computational Mathematics》 SCIE CSCD 2018年第1期47-69,共23页
In this paper, we are concerned with the coupling of finite element methods and bound- ary integral equation methods solving the classical fluid-solid interaction problem in two dimensions. The original transmission p... In this paper, we are concerned with the coupling of finite element methods and bound- ary integral equation methods solving the classical fluid-solid interaction problem in two dimensions. The original transmission problem is reduced to an equivalent nonlocal bound- ary value problem via introducing a Dirichlet-to-Neumann mapping by the direct boundary integral equation method. We show the existence and uniqueness of the solution for the corresponding variational equation. Numerical results based on the finite element method coupled with the standard Galerkin boundary element method, the fast multipole method and the NystrSm method for approximating the DtN mapping are provided to illustrate the efficiency and accuracy of the numerical schemes. 展开更多
关键词 Fluid-solid interaction problem dirichlet-to-neumann mapping Finite element method Fast multipole method NystrSm method.
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New computational treatment of optical wave propagation in lossy waveguides
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作者 Jian-xin ZHU Guan-jie WANG 《Frontiers of Information Technology & Electronic Engineering》 SCIE EI CSCD 2015年第8期646-653,共8页
In this paper, the optical wave propagation in lossy waveguides is described by the Helmholtz equation with the complex refractive-index, and the Chebyshev pseudospectral method is used to discretize the transverse op... In this paper, the optical wave propagation in lossy waveguides is described by the Helmholtz equation with the complex refractive-index, and the Chebyshev pseudospectral method is used to discretize the transverse operator of the equation. Meanwhile, an operator marching method, a one-way re-formulation based on the Dirichlet- to-Neumann (DtN) map, is improved to solve the equation. NumericM examples show that our treatment is more efficient. 展开更多
关键词 Adjoint operator ORTHOGONAL CHEBYSHEV Pseudospectral method dirichlet-to-neumann map
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A FOURTH ORDER DERIVATIVE-FREE OPERATOR MARCHING METHOD FOR HELMHOLTZ EQUATION IN WAVEGUIDES
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作者 Ya Yan Lu 《Journal of Computational Mathematics》 SCIE CSCD 2007年第6期719-729,共11页
A fourth-order operator marching method for the Helmholtz equation in a waveguide is developed in this paper. It is derived from a new fourth-order exponential integrator for linear evolution equations. The method imp... A fourth-order operator marching method for the Helmholtz equation in a waveguide is developed in this paper. It is derived from a new fourth-order exponential integrator for linear evolution equations. The method improves the second-order accuracy associated with the widely used step-wise coupled mode method where the waveguide is approximated by segments that are uniform in the propagation direction. The Helmholtz equation is solved using a one-way reformulation based on the Dirichlet-to-Neumann map. An alternative version closely related to the coupled mode method is also given. Numerical results clearly indicate that the method is more accurate than the coupled mode method while the required computing effort is nearly the same. 展开更多
关键词 Helmholtz equation WAVEGUIDES dirichlet-to-neumann map Operator marching.
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A numerical local orthogonal transform method forstratified waveguides
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作者 Peng LI Wei-zhou ZHONG +1 位作者 Guo-sheng LI Zhi-hua CHEN 《Journal of Zhejiang University-Science C(Computers and Electronics)》 SCIE EI 2010年第12期998-1008,共11页
Flattening of the interfaces is necessary in computing wave propagation along strati?ed waveguides in large range step sizes while using marching methods. When the supposition that there exists one horizontal straight... Flattening of the interfaces is necessary in computing wave propagation along strati?ed waveguides in large range step sizes while using marching methods. When the supposition that there exists one horizontal straight line in two adjacent interfaces does not hold, the previously suggested local orthogonal transform method with an analytical formulation is not feasible. This paper presents a numerical coordinate transform and an equation transform to perform the transforms numerically for waveguides without satisfying the supposition. The boundary value problem is then reduced to an initial value problem by one-way reformulation based on the Dirichlet-to-Neumann (DtN) map. This method is applicable in solving long-range wave propagation problems in slowly varying waveguides with a multilayered medium structure. 展开更多
关键词 Helmholtz equation Local orthogonal transform dirichlet-to-neumann (dtn) reformulation Marching method Internal interface
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