### 博碩士論文 972201016 完整後設資料紀錄

 DC 欄位 值 語言 DC.contributor 數學系 zh_TW DC.creator 沈廉智 zh_TW DC.creator Lien-Chih Shen en_US dc.date.accessioned 2012-7-9T07:39:07Z dc.date.available 2012-7-9T07:39:07Z dc.date.issued 2012 dc.identifier.uri http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=972201016 dc.contributor.department 數學系 zh_TW DC.description 國立中央大學 zh_TW DC.description National Central University en_US dc.description.abstract 在本論文中,我們將有系統的調查兩種用於解決二次特徵值問題(QEPs)的eigenpackage, 包含：the Scalable Library for Eigenvalue Problem Computations(SLEPc)與Parallel Jacobi-Davidson Package(PJDPack)這兩個建構在Portable, Extensible Toolkit for Scientific Computation(PETSc)的Package. 對於這兩個eigenpackage最主要的差別在於SLEPc是使用linearization approach並且有多種不同的eigensolver去解決generalized後的特徵值問題. 而另一方面, PJDPack只有使用PJD演算法並且對於二次特徵值問題是使用直接解法. 為了能夠進行接下來的討論, 我們使用一個Matlab-based的工具, a collection of nonlinear eigenvalue problem (NLEVP)來製作大量具有差異性值的矩陣來做一些數值實驗並且用robustness, accuracy和efficiency來評估效率問題. zh_TW dc.description.abstract In this thesis, we systematically investigate the numerical performance of two eigenpackages for solving quadratic eigenvalue problems (QEPs), namely Scalable Library for Eigenvalue Problem Computations (SLEPc) and Parallel Jacobi-Davidson Package (PJDPack) are both in common built-on-top of Portable, Extensible, Toolkits for Scientific computation (PETSc) [3]. The major differeces between these two eigenpackages is that SLEPc adopts the linearization approach and provides several linear eigensolvers to solve the resulting companion GEPs. On the other hand, the PJD algorithm is the only kernel solver of PJDPack that targets directly the QEP. To draw the concrete conclusions, we generate a large number of test cases using a Matlab-based toolbox, a collection of nonlinear eigenvalue problem (NLEVP) with a diversity of matrix properties and conduct intense numerical experiments to evaluate the performance in terms of robustness, accuracy and efficiency. en_US DC.subject 二次特徵值問題 zh_TW DC.subject SLEPc zh_TW DC.subject PETSc zh_TW DC.subject PJDPack zh_TW DC.subject Quadratic Eigenvalue Problems en_US DC.subject Quadratic PDE Problems en_US DC.subject PJDPack en_US DC.subject SLEPc en_US DC.subject Performance Comparison en_US DC.subject PETSc en_US DC.title Performance Comparison of Two PETSc-based Eigensolvers for Quadratic PDE Problems zh_TW dc.language.iso zh-TW zh-TW DC.title Performance Comparison of Two PETSc-based Eigensolvers for Quadratic PDE Problems en_US DC.type 博碩士論文 zh_TW DC.type thesis en_US DC.publisher National Central University en_US