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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
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dc.contributor.advisor | 王偉仲(Weichung Wang) | |
dc.contributor.author | Huan-Ting Yen | en |
dc.contributor.author | 顏煥庭 | zh_TW |
dc.date.accessioned | 2021-06-08T05:24:06Z | - |
dc.date.copyright | 2011-08-18 | |
dc.date.issued | 2011 | |
dc.date.submitted | 2011-07-28 | |
dc.identifier.citation | [1] P. Arbenz. A comparison of factorization-free eigensolvers with application to cavity resonators. Computational ScienceICCS 2002, pages 295–304, 2009.
[2] J. Baglama, D. Calvetti, G.H. Golub, and L. Reichel. Adaptively preconditioned gmres algorithms. SIAM Journal on Scientific Computing, 20(1):243–269, 1999. [3] Z. Bai. Templates for the solution of algebraic eigenvalue problems, volume 11. Society for Industrial Mathematics, 2000. [4] S. Balay, K. Buschelman, W.D. Gropp, D. Kaushik, M.G. Knepley, L.C. McInnes, B.F. Smith, and H. Zhang. Petsc webpage, 2010. [5] A. Bossavit and J.C. Verite. A mixed fem-biem method to solve 3-d eddy- current problems. Magnetics, IEEE Transactions on, 18(2):431–435, 1982. [6] W.J. Chang. Preconditioning effects in numerical simulations of three- dimensional photonic crystals. 2010. [7] A. Chatterjee, JM Jin, and JL Volakis. Computation of cavity resonances using edge-based finite elements. Microwave Theory and Techniques, IEEE Transactions on, 40(11):2106–2108, 1992. [8] Z. Chen, Q. Du, and J. Zou. Finite element methods with matching and non- matching meshes for maxwell equations with discontinuous coefficients. SIAM Journal on Numerical Analysis, 37(5):1542–1570, 2000. [9] RL Chern, C.C. Chang, C.C. Chang, and RR Hwang. Numerical study of three- dimensional photonic crystals with large band gaps. JOURNAL-PHYSICAL SOCIETY OF JAPAN, 73(3):727–737, 2004. [10] E.T. Chung, Q. Du, and J. Zou. Convergence analysis of a finite volume method for maxwell’s equations in nonhomogeneous media. SIAM journal on numerical analysis, pages 37–63, 2004. [11] T.S. Chung and J. Zou. A finite volume method for maxwell’s equations with discontinuous physical coefficients. International Journal of Applied Mathemat- ics, 7(2):201–224, 2001. [12] Intel Corporation. The Flagship High Performance Computing Math Library for Linux* OS User’s Guide. 2009. [13] W. Gropp and E. Lusk. Users guide for mpich, a portable implementation of mpi, 1996. [14] W. Gropp, E. Lusk, N. Doss, and A. Skjellum. A high-performance, portable implementation of the mpi message passing interface standard. Parallel com- puting, 22(6):789–828, 1996. [15] W. Gropp, E. Lusk, and A. Skjellum. Using mpi: portable parallel programming with the message passing interface. 1999. [16] M. Hano. Finite-element analysis of dielectric-loaded waveguides. Microwave Theory and Techniques, IEEE Transactions on, 32(10):1275–1279, 1984. [17] V. Herna ́ndez, J.E. Rom ́an, A. Toma ́s, and V. Vidal. Slepc users manual. Scal- able Library for Eigenvalue Problem Computations, Departmento de Sistemas Informaticos y Computacion, Valencia, Spain, February, 2009. [18] V. Hernandez, J.E. Roman, and V. Vidal. Slepc: A scalable and flexible toolkit for the solution of eigenvalue problems. ACM Transactions on Mathematical Software (TOMS), 31(3):351–362, 2005. [19] T.M. Huang, W.J. Chang, Y.L. Huang, W.W. Lin, W.C. Wang, and W. Wang. Preconditioning bandgap eigenvalue problems in three dimensional photonic crystals simulations. Journal of Computational Physics, 2010. [20] T.M. Huang, YL Huang, WW Lin, and WC Wang. A null space free jacobi- davidson iteration for maxwells operator. NCTS Preprints in Mathematics (2009-7-004), National Tsing Hua University, Hsinchu, Taiwan. [21] T.M. Hwang, W.W. Lin, W.C. Wang, and W. Wang. Numerical simulation of three dimensional pyramid quantum dot. Journal of computational physics, 196(1):208–232, 2004. [22] T.M. Hwang, W.C. Wang, and W. Wang. Numerical schemes for three- dimensional irregular shape quantum dots over curvilinear coordinate systems. Journal of Computational Physics, 226(1):754–773, 2007. [23] J. Jin, J. Jin, and J.M. Jin. The finite element method in electromagnetics. Wiley New York, 1993. [24] C. Kittel and P. McEuen. Introduction to solid state physics. 1986. [25] R.B. Lehoucq, D.C. Sorensen, and C. Yang. ARPACK users’ guide: solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods. Siam, 1998. [26] N.K. Madsen. Divergence preserving discrete surface integral methods for maxwell’s curl equations using non-orthogonal unstructured grids. Journal of Computational Physics, 119(1):34–45, 1995. [27] P. Monk and E. S ”uli. A convergence analysis of yee’s scheme on nonuniform grids. SIAM journal on numerical analysis, 31(2):393–412, 1994. [28] G. Mur and A. de Hoop. A finite-element method for computing three- dimensional electromagnetic fields in inhomogeneous media. Magnetics, IEEE Transactions on, 21(6):2188–2191, 1985. [29] N. Nigro, M. Storti, S. Idelsohn, and T. Tezduyar. Physics based gmres precon- ditioner for compressible and incompressible navier-stokes equations. Computer methods in applied mechanics and engineering, 154(3-4):203–228, 1998. [30] Y. Saad. A flexible inner-outer preconditioned gmres algorithm. SIAM Journal on Scientific Computing, 14:461–461, 1993. [31] Y. Saad and M.H. Schultz. Gmres: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7(3):856– 869, 1986. [32] D.C. Sorensen. Implicit application of polynomial filters in a k-step arnoldi method. SIAM J. Matrix Anal. Appl, 13(1):357–385, 1992. [33] GW Stewart. A krylov-schur algorithm for large eigenproblems. Institute for Advanced Computer Studies TR, page 21, 2000. [34] GW Stewart. Addendum to” a krylov-schur algorithm for large eigenproblems”. Institute for Advanced Computer Studies TR, page 90, 2001. [35] GW Stewart and A. Mahajan. Matrix algorithms, volume ii: Eigensystems. Applied Mechanics Reviews, 56:B2, 2003. [36] J.L. Volakis, A. Chatterjee, and L.C. Kempel. Finite element method for elec- tromagnetics: antennas, microwave circuits, and scattering applications. Wiley- IEEE Press, 1998. [37] W. Wang, T.M. Hwang, W.W. Lin, and J.L. Liu. Numerical methods for semiconductor heterostructures with band nonparabolicity. Journal of Compu- tational Physics, 190(1):141–158, 2003. [38] K. Yee. Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media. Antennas and Propagation, IEEE Transactions on, 14(3):302–307, 1966. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/24386 | - |
dc.description.abstract | 本論文的主要目地是平行 Krylov-Schur 方法並結合 GMRES 演算法搭配 FFT 預處理解大型稀疏矩陣的廣義特徵值問題。
我們的問題來自三維光子晶體的馬克斯威爾方程,利用 Yee 的離散方法將馬克斯威爾方程離散成廣義特徵值問題來做數值模擬。 利用 Krylov-Schur 方法結合 GMRES 演算法以及搭配 FFT 預處理解廣義特徵值問題的效能非常好,並可加速廣義特徵值問題中線性系統內迭代的收斂速度。 我們的實驗中利用 PETSc, SLEPc, Intel MKL 等數學軟體,平行的數值實驗可執行於多核心電腦以及叢集電腦。 | zh_TW |
dc.description.abstract | This dissertation aims to parallel the Krylov-Schur method with applying generalized minimal residual (GMRES) algorithm, which was combined with the fast Fourier transform (FFT) technique to solve large sparse matrix generalized eigenvalue problem derived from the governing Maxwell equations. The eigenvalue problems will be derived by Yee's scheme, the eigenvalue solver is based on Krylov-Schur method, associated with GMRES algorithm and a fast Fourier transform based preconditioned, which is very e cient and used to accelerate the inner iteration. The code are implemented by using PETSc and MKL. Numerical experiments are performed in multicore CPUs and parallel
clusters. | en |
dc.description.provenance | Made available in DSpace on 2021-06-08T05:24:06Z (GMT). No. of bitstreams: 1 ntu-100-R98221020-1.pdf: 4306399 bytes, checksum: 9124c88b6e720f66b8f357377da86505 (MD5) Previous issue date: 2011 | en |
dc.description.tableofcontents | 1 Introduction....................................................................................1
2 Yee’s Discretization and the model eigenvalue problems................2 3 Eigenvalue solvers..........................................................................6 4 Preconditioning schemes...............................................................10 5 Fast Fourier transform routines of the Intel Math Kernel library.....13 6 Numerical Results.........................................................................17 7 Conclusions..................................................................................22 8 References....................................................................................22 | |
dc.language.iso | zh-TW | |
dc.title | 三維光子晶體的數值模擬之平行計算 | zh_TW |
dc.title | Parallelization in Numerical Simulations of Three Dimensional Photonic Crystals | en |
dc.type | Thesis | |
dc.date.schoolyear | 99-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 黃聰明(Tsung-Ming Huang),李哲榮(Che-Rung Lee) | |
dc.subject.keyword | 三維光子晶體,麥斯威爾方程,廣義特徵值問題,快速傅立葉轉換預處理器, | zh_TW |
dc.subject.keyword | Three-dimensional photonic crystals,Generalized Eigenvalue problems,Fast Fourier Transform preconditioner, | en |
dc.relation.page | 24 | |
dc.rights.note | 未授權 | |
dc.date.accepted | 2011-07-28 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 數學研究所 | zh_TW |
顯示於系所單位: | 數學系 |
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