Relevant bibliographies by topics / Tridiagonal Matrix Algoritm

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  2. Dissertations / Theses
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  5. Conference papers

Academic literature on the topic 'Tridiagonal Matrix Algoritm'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Tridiagonal Matrix Algoritm"

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Zgirouski, A. A., and N. A. Likhoded. "Modified method of parallel matrix sweep." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 55, no. 4 (January 7, 2020): 425–34. http://dx.doi.org/10.29235/1561-2430-2019-55-4-425-434.

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The topic of this paper refers to efficient parallel solvers of block-tridiagonal linear systems of equations. Such systems occur in numerous modeling problems and require usage of high-performance multicore computation systems. One of the widely used methods for solving block-tridiagonal linear systems in parallel is the original block-tridiagonal sweep method. We consider the algorithm based on the partitioning idea. Firstly, the initial matrix is split into parts and transformations are applied to each part independently to obtain equations of a reduced block-tridiagonal system. Secondly, the reduced system is solved sequentially using the classic Thomas algorithm. Finally, all the parts are solved in parallel using the solutions of a reduced system. We propose a modification of this method. It was justified that if known stability conditions for the matrix sweep method are satisfied, then the proposed modification is stable as well.
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Ran, Rui-sheng, Ting-zhu Huang, Xing-ping Liu, and Tong-xiang Gu. "An inversion algorithm for general tridiagonal matrix." Applied Mathematics and Mechanics 30, no. 2 (February 2009): 247–53. http://dx.doi.org/10.1007/s10483-009-0212-x.

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Mattor, Nathan, Timothy J. Williams, and Dennis W. Hewett. "Algorithm for solving tridiagonal matrix problems in parallel." Parallel Computing 21, no. 11 (November 1995): 1769–82. http://dx.doi.org/10.1016/0167-8191(95)00033-0.

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Takahira, S., T. Sogabe, and T. S. Usuda. "Bidiagonalization of (k, k + 1)-tridiagonal matrices." Special Matrices 7, no. 1 (January 1, 2019): 20–26. http://dx.doi.org/10.1515/spma-2019-0002.

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Abstract In this paper,we present the bidiagonalization of n-by-n (k, k+1)-tridiagonal matriceswhen n < 2k. Moreover,we show that the determinant of an n-by-n (k, k+1)-tridiagonal matrix is the product of the diagonal elements and the eigenvalues of the matrix are the diagonal elements. This paper is related to the fast block diagonalization algorithm using the permutation matrix from [T. Sogabe and M. El-Mikkawy, Appl. Math. Comput., 218, (2011), 2740-2743] and [A. Ohashi, T. Sogabe, and T. S. Usuda, Int. J. Pure and App. Math., 106, (2016), 513-523].
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Chathalingath, Anishchandran, and Arun Manoharan. "Performance Optimization of Tridiagonal Matrix Algorithm [TDMA] on Multicore Architectures." International Journal of Grid and High Performance Computing 11, no. 4 (October 2019): 1–12. http://dx.doi.org/10.4018/ijghpc.2019100101.

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Fast and efficient tridiagonal solvers are highly appreciated in scientific and engineering domain, but challenging optimization task for computer engineers. The state-of-the-art developments in multi-core computing paves the way to meet this challenge to an extent. The technical advances in multi-core computing provide opportunities to exploit lower levels of parallelism and concurrency for inherently sequential algorithms. In this article, the authors present an optimal performance pipelined parallel variant of the conventional Tridiagonal Matrix Algorithm (TDMA), aka the Thomas algorithm, on a multi-core CPU platform. The implementation, analysis and performance comparison of the proposed pipelined parallel TDMA and the conventional version are performed on an Intel SIMD multi-core architecture. The results are compared in terms of elapsed time, speedup, cache miss rate. For a system of ‘n' linear equations where n = 2^36 in presented pipelined parallel TDMA achieves speedup of 1.294X with a parallel efficiency of 43% initially and inclines towards linear speed up as the system grows.
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Duan, Zhi Jian. "Parallel Algorithm for Solving Block-Tridiagonal Linear Systems." Applied Mechanics and Materials 427-429 (September 2013): 2420–23. http://dx.doi.org/10.4028/www.scientific.net/amm.427-429.2420.

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Efficient parallel iterative algorithm is investigated for solving block-tridiagonal linear systems on distributed-memory multi-computers. Based on Galerkin theory, the communication only need twice between the adjacent processors per iteration step. Furthermore, the condition for convergence is given when the coefficient matrix A is a symmetric positive definite matrix. Numerical experiments implemented on the cluster verify that our algorithm parallel acceleration rates and efficiency are higher than the multisplitting one, and has the advantages over the multisplitting method of high efficiency and low memory space.
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El-Mikkawy, Moawwad, and Faiz Atlan. "A novel algorithm for inverting a generalk-tridiagonal matrix." Applied Mathematics Letters 32 (June 2014): 41–47. http://dx.doi.org/10.1016/j.aml.2014.02.015.

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Fujiwara, Yasuhiro, Sekitoshi Kanai, Yasutoshi Ida, Atsutoshi Kumagai, and Naonori Ueda. "Fast algorithm for anchor graph hashing." Proceedings of the VLDB Endowment 14, no. 6 (February 2021): 916–28. http://dx.doi.org/10.14778/3447689.3447696.

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Anchor graph hashing is used in many applications such as cancer detection, web page classification, and drug discovery. It computes the hash codes from the eigenvectors of the matrix representing the similarities between data points and anchor points; anchors refer to the points representing the data distribution. In performing an approximate nearest neighbor search, the hash codes of a query data point are determined by identifying its closest anchor points. Anchor graph hashing, however, incurs high computation cost since (1) the computation cost of obtaining the eigenvectors is quadratic to the number of anchor points, and (2) the similarities of the query data point to all the anchor points must be computed. Our proposal, Tridiagonal hashing , increases the efficiency of anchor graph hashing because of its two advances: (1) we apply a graph clustering algorithm to compute the eigenvectors from the tridiagonal matrix obtained from the similarities between data points and anchor points, and (2) we detect anchor points closest to the query data point by using a dimensionality reduction approach. Experiments show that our approach is several orders of magnitude faster than the previous approaches. Besides, it yields high search accuracy than the original anchor graph hashing approach.
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Kumar, Surendra, Shashi, and Árpad Pethö. "An algorithm for the numerical inversion of a tridiagonal matrix." Communications in Numerical Methods in Engineering 9, no. 4 (April 1993): 353–59. http://dx.doi.org/10.1002/cnm.1640090409.

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MILOVANOVIĆ, E. I., M. D. MIHAJLOVIĆ, I. Ž. MILOVANOVIĆ, and M. K. STOJČEV. "SOLVING TRIDIAGONAL LINEAR SYSTEMS ON MIMD COMPUTERS." Parallel Processing Letters 04, no. 01n02 (June 1994): 53–64. http://dx.doi.org/10.1142/s0129626494000077.

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A partitioning algorithm for solving tridiagonal system of linear equations which is suitable for implementation on multiprocessor systems with small to moderate number of processors is described in this paper. The method is based on decomposing a matrix of order n×n into p partitions of size n×k, where n=pk. The fundamental idea of the proposed algorithm is that the elimination is performed using alternatively superdiagonal and subdiagonal elements, contrary to the Gaussian elimination which uses main diagonal elements. Performance results obtained when the proposed algorithm is implemented on the p-processor orthogonal and linear arrays, both of MIMD type, are presented.
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Dissertations / Theses on the topic "Tridiagonal Matrix Algoritm"

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Ziad, Abderrahmane. "Contributions au calcul numérique des valeurs propres des matrices normales." Saint-Etienne, 1996. http://www.theses.fr/1996STET4001.

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Première partie: la convergence globale de l'algorithme QR avec le shift de Rayleigh appliquée à une matrice normale Hessenberg supérieure irréductible est démontrée. Ensuite nous avons proposé un shift avec lequel la convergence est cubique, lorsque la matrice est symétrique tridiagonale irréductible. Deuxième partie: nous avons proposé une méthode pour le calcul d'une valeur propre de rang donné d'une matrice symétrique tridiagonale irréductible, cette méthode est un procédé d'initialisation de la méthode dite d'itération inverse de Rayleigh
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Huang, Yuguang. "Algorithm design for structured matrix computations." Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.325925.

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SILVA, JUNIOR Aluizio Freire da. "Desenvolvimento de ferramentas numéricas e computacionais para a descrição de transferência de massa em corpos cilíndricos: aplicação em desidratação osmótica e secagem complementar de banana." Universidade Federal de Campina Grande, 2015. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/779.

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O presente trabalho tem como objetivo desenvolver ferramentas numéricas e computacionais tendo vista descrever processos difusivos em sólidos com formas cilíndricas. Para isto a equação de difusão, considerando os casos de um cilindro infinito e de um cilindro finito, foi discretizada via método dos volumes finitos com uma formulação totalmente implícita, admitindo uma condição de contorno do terceiro tipo. Para as soluções numéricas obtidas pelas discretizações, foram desenvolvidos softwares na plataforma Windows, utilizando a linguagem de programação Fortran. As soluções desenvolvidas foram validadas pela comparação com resultados fornecidos por soluções analíticas. Os testes realizados indicaram coerência nos resultados fornecidos pelas soluções numéricas. Além disso, a fim de obter os parâmetros físicos dos processos de transferência de massa, um otimizador foi desenvolvido e acoplado às soluções numéricas. Foram realizados testes com o otimizador desenvolvido tendo em vista analisar a capacidade deste em encontrar os valores ótimos de um processo de transferência de massa. Os testes indicaram que o otimizador tem capacidade para obter os parâmetros necessários ao estudo deste trabalho, conseguindo chegar a região que contém os valores ótimos para os parâmetros, mesmo quando considerados valores iniciais distantes destes valores ótimos. A partir dos dados obtidos em experimentos de desidratação osmótica de banana (cortada em pedaços de 10 mm) realizados em combinações de 40 e 70°C de temperatura e 40 e 60 °Brix de concentração, foram realizadas otimizações a fim de obter expressões para descrição das difusividades efetivas de água e sacarose e valores para o coeficiente de transferência convectiva de massa. Os resultados obtidos para as difusividades de água e sacarose estão de acordo com a literatura. Os valores fornecidos pelo otimizador para o coeficiente de transferência convectiva de massa indicaram uma condição de contorno do primeiro tipo. Foram realizadas otimizações a partir dos dados da secagem complementar das amostras osmoticamente desidratadas, e os resultados obtidos para a difusividade de água foram compatíveis com os encontrados na literatura. Foi concluído pelas otimizações que as altas concentrações da desidratação osmótica influenciaram a condição de contorno da secagem complementar.
This study aims to develop numerical and computational tools to describe diffusion processes in solids with cylindrical shapes. For this the diffusion equation, considering the case of an infinite cylinder and a finite cylinder, was discretized via finite volume method with a fully implicit formulation, assuming a boundary condition of the third kind. For the numerical solutions obtained by discretization, software has been developed on the Windows platform using the Fortran programming language. The solutions developed were validated by comparison with results provided by analytical solutions. The tests showed consistency in the results provided by the numerical solutions. Furthermore, in order to obtain the physical parameters of the mass transfer process, was developed an optimizer which was coupled with numerical solutions. Tests were performed with the optimizer developed in order to analyze the capacity of finding the optimal values of a mass transfer process. The tests indicated that the optimizer is able to obtain the parameters necessary for the study of this work, reaching the region containing the optimal values for the parameters, even when initial values were considered far from the optimal values. From the data obtained in banana (cut into pieces of 10 mm) osmotic dehydration experiments performed by combining temperature of 40 and 70 ° C and concentration of 40 and 60 ° Brix, optimizations were carried out to obtain expressions for describing the effective diffusivity of water and sucrose and values for convective mass transfer coefficient. The results obtained for the diffusivities of water and sucrose are in agreement with the literature. The values supplied by the optimizer for the mass convective transfer coefficient indicated a boundary condition of the first kind. Optimizations were carried out from the complementary drying data of osmotically dehydrated samples, and the results obtained for the diffusivity of water were consistent with those found in the literature. It was concluded by the optimizations that high concentrations of osmotic dehydration influenced the boundary condition of the complementary drying.
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Miranda, Wilson Domingos Sidinei Alves. "Algoritmo paralelo para determinação de autovalores de matrizes hermitianas." reponame:Repositório Institucional da UnB, 2015. http://repositorio.unb.br/handle/10482/20642.

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Dissertação (mestrado)–Universidade de Brasília, Universidade UnB de Planaltina, Programa de Pós-Graduação em Ciência de Materiais, 2015.
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Um dos principais problemas da álgebra linear computacional é o problema de autovalor, Au = lu, onde A é usualmente uma matriz de ordem grande. A maneira mais efetiva de resolver tal problema consiste em reduzir a matriz A para a forma tridiagonal e usar o método da bissecção ou algoritmo QR para encontrar alguns ou todos os autovalores. Este trabalho apresenta uma implementação em paralelo utilizando uma combinação dos métodos da bissecção, secante e Newton-Raphson para a solução de problemas de autovalores de matrizes hermitianas. A implementação é voltada para unidades de processamentos gráficos (GPUs) visando a utilização em computadores que possuam placas gráficas com arquitetura CUDA. Para comprovar a eficiência e aplicabilidade da implementação, comparamos o tempo gasto entre os algoritmos usando a GPU, a CPU e as rotinas DSTEBZ e DSTEVR da biblioteca LAPACK. O problema foi dividido em três fases, tridiagonalização, isolamento e extração, as duas últimas calculadas na GPU. A tridiagonalização via DSYTRD da LAPACK, calculada em CPU, mostrou-se mais eficiente do que a realizada em CUDA via DSYRDB. O uso do método zeroinNR na fase de extração em CUDA foi cerca de duas vezes mais rápido que o método da bissecção em CUDA. Então o método híbrido é o mais eficiente para o nosso caso. _______________________________________________________________________________________________ ABSTRACT
One of the main problems in computational linear algebra is the eigenvalue problem Au = lu, where A is usually a matrix of big order. The most effective way to solve this problem is to reduce the matrix A to tridiagonal form and use the method of bisection or QR algorithm to find some or all of the eigenvalues. This work presents a parallel implementation using a combination of methods bisection, secant and Newton-Raphson for solving the eigenvalues problem for Hermitian matrices. Implementation is focused on graphics processing units (GPUs) aimed at use in computers with graphics cards with CUDA architecture. To prove the efficiency and applicability of the implementation, we compare the time spent between the algorithms using the GPU, the CPU and DSTEBZ and DSTEVR routines from LAPACK library. The problem was divided into three phases, tridiagonalization, isolation and extraction, the last two calculated on the GPU. The tridiagonalization by LAPACK’s DSYTRD, calculated on the CPU, proved more efficient than the DSYRDB in CUDA. The use of the method zeroinNR on the extraction phase in CUDA was about two times faster than the bisection method in CUDA. So the hybrid method is more efficient for our case.
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Štrympl, Martin. "Výpočet vlastních čísel a vlastních vektorů hermitovské matice." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2016. http://www.nusl.cz/ntk/nusl-242085.

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This project deals with computation of eigenvalues and eigenvectors of Hermitian positive-semidefinite complex square matrix of order 4. The target is an implementation of computation in language VHDL to field-programmable gate array of type Xilinx Zynq-7000. This master project deals with algorithms used for computation of eigenvalues and eigenvectors of positive-semidefinite symmetric real square and positive-semidefinite complex Hermitian matrix and the analysis of algorithms by AnalyzeAlgorithm program assembled for this purpose. The closing part of this project describes implementation of the computation into field-programmable gate array with use of IP core Xilinx® Floating-Point \linebreak Operator and SVAOptimalizer, SVAInterpreter and SVAToDSPCompiler programs.
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Chen, Yu Chuan, and 陳又權. "Augmented Block Cimmino Distributed Algorithm for solving a tridiagonal Matrix on GPU." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/47971311649912636962.

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碩士
國立清華大學
資訊工程學系
103
The tridiagonal solver nowadays appears as a fundamental component in scientific and engi-neering problems, such as Alternating Direction Implicit methods (ADI), fluid Simulation, and Poisson’s equation. Due to the particular sparse format of tridiagonal matrix, many algorithms of solving the system are conceived. Previously, the main stream of solving the system is by using Diagonal Pivoting to reduce the accuracy issue. But, Diagonal Pivoting has its limits and will lead to error solution while the condition number increases. Augmented Block Cimmino Distributed (ABCD) algorithm serves as another option when trying to resolve the problem accurately. In this thesis, we study and implement the ABCD algorithm on GPU. Because of the spe-cial structure of tridiagonal matrices, we investigate the boundary padding technique to eliminate the execution branches on GPU for better performance. In addition, our implementation incorpo-rates various performance optimization techniques, such as memory coalesce, to further enhance the performance. In the experiments, we evaluate the accuracy and performance of our GPU im-plementation against CPU implementation, and analyze the effectiveness of each performance op-timization technique. The performance of GPU version is about 15 times faster than that of the CPU version.
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Books on the topic "Tridiagonal Matrix Algoritm"

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Research Institute for Advanced Computer Science (U.S.), ed. An O(logN) parallel algorithm for computing the Eigenvalues of a symmetric tridiagonal matrix. [Moffett Field, Calif.?]: Research Institute for Advanced Computer Science, NASA Ames Research Center, 1989.

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Book chapters on the topic "Tridiagonal Matrix Algoritm"

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Stojčev, M. K., E. I. Milovanović, M. D. Mihajlović, and I. Ž. Milovanović. "Parallel algorithm for inverting tridiagonal matrix on linear processor array." In Parallel Processing: CONPAR 94 — VAPP VI, 229–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-58430-7_21.

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Issakhov, Alibek. "Mathematical Modelling of the Thermal Process in the Aquatic Environment with Considering the Hydrometeorological Condition at the Reservoir-Cooler by Using Parallel Technologies." In Sustaining Power Resources through Energy Optimization and Engineering, 227–43. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-9755-3.ch010.

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This paper presents the mathematical model of the thermal power plant in reservoir under different hydrometeorological conditions, which is solved by three dimensional Navier - Stokes and temperature equations for an incompressible fluid in a stratified medium. A numerical method based on the projection method, which divides the problem into four stages. At the first stage it is assumed that the transfer of momentum occurs only by convection and diffusion. Intermediate velocity field is solved by fractional steps method. At the second stage, three-dimensional Poisson equation is solved by the Fourier method in combination with tridiagonal matrix method (Thomas algorithm). At the third stage it is expected that the transfer is only due to the pressure gradient. Finally stage equation for temperature solved like momentum equation with fractional step method. To increase the order of approximation compact scheme was used. Then qualitatively and quantitatively approximate the basic laws of the hydrothermal processes depending on different hydrometeorological conditions are determined.
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Conference papers on the topic "Tridiagonal Matrix Algoritm"

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Huang, Jingpin, Liman Chen, and Cong Shen. "Inverse arnoldi algorithm for construction of tridiagonal quaternion matrix." In 2018 Chinese Control And Decision Conference (CCDC). IEEE, 2018. http://dx.doi.org/10.1109/ccdc.2018.8407567.

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Iannelli, G. S., and A. J. Baker. "Accuracy and Efficiency Assessments for a Weak Statement CFD Algorithm for High-Speed Aerodynamics." In ASME 1992 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/92-gt-433.

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A bilinear finite element, implicit Runge-Kutta space-time discretization has been established for an aerodynamics weak statement CFD algorithm. The algorithm admits real-gas effects simulation, for reliable hypersonic flow characterization, via an equilibrium reacting air model. The terminal algebraic system is solved using an efficient block-tridiagonal quasi-Newton linear algebra procedure that employs tensor matrix product factorizations within a lexicographic mesh-sweeping protocol. A block solution-adaptive remeshing, for totally arbitrary convex elements, is also utilized to facilitate accurate shock and/or boundary layer flow resolution. Numerical validations are presented for representative benchmark supersonic-hypersonic aerodynamics problem statements.
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Zhang, Wei, and Timothy S. Fisher. "Simulation of Phonon Interfacial Transport in Strained Silicon-Germanium Heterostructures." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-80053.

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A nonequilibrium Green’s function (NEGF) method is used to simulate the phonon transport across a strained thin film between two semi-infinite contacts. The calculation of dynamical matrix, self-energy matrix and transmission function are discussed. Uncoupled Green’s functions are computed numerically using a block tridiagonal algorithm. The numerical role of the broadening constant is investigated. The bulk density of states in a single atomic chain is calculated and compares well with an analytical solution. The transmission function and thermal conductance across the thin film are evaluated for two different configurations (Ge-Si-Ge and Si-Ge-Si) and compared against homogeneous bulk systems (Si only and Ge only), indicating that heterogeneous interfaces reduce thermal conductance significantly.
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Li, Sumei, and Jiteng Jia. "A Cost-Efficient Numerical Algorithm for Evaluating the Determinant of a Quasi-Tridiagonal Matrix." In 2018 5th International Conference on Systems and Informatics (ICSAI). IEEE, 2018. http://dx.doi.org/10.1109/icsai.2018.8599353.

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Sankhavara, C. D., and H. J. Shukla. "Influence of Partition Location on Natural Convection in a Partitioned Enclosure." In ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. ASMEDC, 2005. http://dx.doi.org/10.1115/ht2005-72093.

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In this study, Natural convection heat transfer and fluid flow of square partitioned enclosure with two partitions protruding centrally from the end walls of an enclosure have been analysed numerically using finite element method. The enclosure has opposite isothermal walls at different temperatures. The thickness and length of the partitions is fixed and equal to 1/10 and 1/4 of width of the enclosure respectively. Computation for Rayleigh number in the range of 104 to 106 has been conducted. The influence of different thermal boundary conditions at the end walls and at the partitions is included in the investigation. ‘Standard’ boundary conditions are introduced as more appropriate to simulate situations of practical engineering interest. To solve the relevant governing equations a segregated sequential solution algorithm is used after employing Boussinesq approximation. These equations after discretization were solved by using the tridiagonal matrix algorithm. Results clearly demonstrate that partition location has a significant effect on heat transfer.
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Senkal, Caner, and Shuichi Torii. "Thermal Fluid Flow Transport Characteristics in Confined Channels With Two-Dimensional Dual Jet Impingement." In ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajk2011-03015.

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The flow and heat transfer characteristics of laminar dual circular jet impinging on a heating plate with inclined confinement surface has been investigated numerically. Governing equations in steady state are solved by a control volume based finite-difference method. The simulations have been carried out for Reynolds number (250≤Re≤418), the angle of inclination of the confined upper wall (0 ≤ θ ≤ 10), circular jet to annular jet velocity ratio (0≤VR≤2) and jet to target plate distances between 2D and 8D where D is the outer diameter of dual jet.SIMPLE algorithm was used to obtain velocity and temperature fields. Hybrid difference scheme is adopted for the discretized terms in the governing equations. The discretised equations are solved iteratively using the tridiagonal matrix algorithm line solver. Heat transfer performance along the heated wall is amplified with an increase in the velocity ratio and the Reynolds number. On the contrary, a substantial reduction in the heat transfer rate, for VR = 0.0, occurs in the stagnation zone, because the absence of the inner nozzle injection causes the recirculation in the corresponding region. The heat transfer rate in the stagnation zone is attenuated by increasing the jet nozzle to impinging plate distance. In particular, the effect of the inclination angle in the down-stream region, especially at the vicinity of outlet, is major then other effects Nusselt number distribution on the impingement plate is affected by inclined upper wall because inclination of the wall accelerates the exhaust flow. The streamwise reduction in the heat transfer rate for θ = 0° is suppressed by the presence of the inclined confinement surface and its value is intensified by the inclination angle.
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