Notes on the Schwartz Alternating Method for Partition of Unity FEM

نویسندگان

  • Constantin Bacuta
  • Jiguang Sun
چکیده

We consider discretization on overlapping non-matching grids for elliptic equations by using the Schwartz alternating (SA) method. We investigate also the dependence between the angle of partition of unity (PU) subspaces and the condition number of the stiffness matrix for a model problem. The aim of the paper is to find strategies to choose optimal or quasi-optimal partition of unity set of functions for PU discretizaions for elliptic problems on overlapping non-matching grids.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The generalized product partition of unity for the meshless methods

The partition of unity is an essential ingredient for meshless methods named by GFEM, PUFEM (partition of unity FEM), XFEM(extended FEM), RKPM(reproducing kernel particle method), RPPM(reproducing polynomial particle method), the method of clouds in the literature. There are two popular choices for partition of unity: a piecewise linear FEM mesh and the Shepard-type partition of unity. However,...

متن کامل

Convergence study of the h-adaptive PUM and the hp-adaptive FEM applied to eigenvalue problems in quantum mechanics

In this paper the h-adaptive partition-of-unity method and the hand hp-adaptive finite element method are applied to eigenvalue problems arising in quantum mechanics, namely, the Schrödinger equation with Coulomb and harmonic potentials, and the all-electron Kohn–Sham density functional theory. The partition-of-unity method is equipped with an a posteriori error estimator, thus enabling impleme...

متن کامل

Three-Dimensional SGBEM-FEM Alternating Method for Analyzing Fatigue-Crack Growth in and the Life of Attachment Lugs

In the present paper, stress intensity factor (SIF) analyses and fatigue-crack-growth simulations of corner cracks emanating from loaded pinholes of attachment lugs in structural assemblies are carried out for different load cases. A three-dimensional (3D) symmetric Galerkin boundary-element method (SGBEM) and FEM alternating method is developed to analyze the nonplanar growth of these surface ...

متن کامل

FEM-RBF: A Geometrically Flexible, Efficient Numerical Solution Technique for Partial Differential Equations with Mixed Regularity

1 About This Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 Hybrid FEM-RBF scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.1 One Dimensional Case . . . . . . . . . ....

متن کامل

Solution of Helmholtz problems by knowledge-based FEM

The numerical solution of Helmholtz’ equation at large wavenumber is very expensive if attempted by ”traditional” discretisation methods (FDM, standard Galerkin FEM). For reliable results, the mesh has to be very fine. The bad performance of the traditional FEM for Helmholtz problems can be related to the deterioration of stability of the Helmholtz differential operator at high wavenumber. As a...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008