Smoothing factor, order of prolongation and actual multigrid convergence

Smoothing factor, order of prolongation and actual multigrid convergence

We consider the Fourier analysis of multi-grid methods (of Galerkin type) for symmetric positive definite and semi-positive definite linear systems arising from the discretization of scalar partial differential equations (PDEs). We relate the so-called smoothing factor to the actual two-grid convergence rate and also to the convergence rate of the V-cycle multigrid. We derive a two-sided bound ...

Smoothing Factor and Actual Multigrid Convergence

We consider the Fourier analysis of multi-grid methods for symmetric positive definite and semi-positive definite linear systems arising from the discretizations of scalar PDEs. In this framework, the smoothing factor is frequently used to estimate the potential of a multigrid approach. In this paper, the smoothing factor is related to the actual two-grid convergence rate and also to the Vcycle...

A note on optimal multigrid convergence for higher-order FEM

Quadratic and even higher order finite elements are interesting candidates for the numerical solution of partial differential equations (PDEs) due to their improved approximation properties in comparison to linear approaches. The systems of equations that arise from the discretisation of the underlying (elliptic) PDEs are often solved by iterative solvers like preconditioned Krylow-space method...

asymptotic property of order statistics and sample quntile

چکیده: فرض کنید که تابعی از اپسیلون یک مجموع نامتناهی از احتمالات موزون مربوط به مجموع های جزئی براساس یک دنباله از متغیرهای تصادفی مستقل و همتوزیع باشد، و همچنین فرض کنید توابعی مانند g و h وجود دارند که هرگاه امید ریاضی توان دوم x متناهی و امیدریاضی x صفر باشد، در این صورت می توان حد حاصلضرب این توابع را بصورت تابعی از امید ریاضی توان دوم x نوشت. حالت عکس نیز برقرار است. همچنین ما با استفاده...

Analysis of Minimal Residual Smoothing in Multigrid