پديد آورنده :
درمغان، شادي
عنوان :
يك خوش‌حالت ساز تكراري بر اساس جداسازي حاصل از حاصل‌ضرب كرونكر
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي (آناليز عددي)
محل تحصيل :
اصفهان : دانشگاه صنعتي اصفهان
صفحه شمار :
ده، 67ص. : مصور، جدول، نمودار
استاد راهنما :
مهدي تاتاري
توصيفگر ها :
خوش‌حالت ساز , معادلات ديفرانسيل معمولي , معادلات ديفرانسيل جزيي , خوش‌حالت سازي , روش‌هاي تكراري
استاد داور :
امير هاشمي، رضا مزروعي
تاريخ ورود اطلاعات :
1399/08/19
تاريخ ويرايش اطلاعات :
1399/08/24
چكيده انگليسي :
An iterative preconditioner based on a splitting resulted from kronecker product Shadi Dormaghan September 18 2020 Master of Science Thesis Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Mehdi Tatari Advisor Dr Majid Gazor 2000 MSC 65F10 65L06 65N22Keywords Preconditioner Ordinary differential equations Partial differential equations Preconditioning Abstract The solution of large sparse linear systems of the form 1 Ax b where A aij is an n n matrix and b a given right hand side vector is central to many numerical simulationsin science and engineering and is often the most time consuming part of a computation and linearization of partialdifferential equations PDEs of elliptic and parabolic type large and sparse linear systems also arise in applicationsnot governed by PDEs These include the design and computer analysis of circuits power system networks chemicalengineering processes economics models and queueing systems The classification of the solution methods is both direct and iterative Direct methods based on the factorization of thecoefficient matrix A into easily invertible matrices are widely used and are the solver of choice in many industrialcodes especially where reliability is the primary concern Indeed direct solvers are very robust and they tend torequire a predictable amount of resources in terms of time and storage Unfortunately direct methods scale poorlywith problem size in terms of operation counts and memory requirements especially on problems arising from thediscretization of PDEs in three space dimensions in order to solve this problem iterative methods is a better choice While iterative methods require fewer storage and often require fewer operations than direct methods they do not havethe reliability of direct methods In some applications iterative methods often fail and preconditioning is necessary though not always sufficient to attain convergence in a reasonable amount of time It is widely recognized that preconditioning is the most critical ingredient in the development of efficient solvers forchallenging problems in scientific computation and preconditioning has been a more active research area than eitherdirect solution methods A preconditioner is a matrix that effects such a transformation preconditioning attemptsto improve the spectral properties of the coefficient matrix The preconditioned matrix will have a smaller spectralcondition number and eigenvalues clustered around 1 If M is a nonsingular matrix that approximates A then the linear system M 1 Ax M 1 b has the same solution as 1 but may be easier to solve Here M is the preconditioner This System is preconditionedfrom the left but one can also precondition from the right M 1 y b x M 1 y In addition split preconditioning is also possible where the preconditioner is now M M1 M2 Which type ofpreconditioning to use depends on the choice of the iterative method problem characteristics
استاد راهنما :
مهدي تاتاري
استاد داور :
امير هاشمي، رضا مزروعي
