A Particle-Partition of Unity Method-Part IV: Parallelization

2003 ◽  
pp. 161-192 ◽  
Author(s):  
Michael Griebel ◽  
Marc Alexander Schweitzer
Keyword(s):  
Partition Of Unity ◽  
Partition Of Unity Method

A parallel partition of unity method for the unsteady Stokes equations

2017 ◽  
Vol 27 (9) ◽  
pp. 2105-2114
Author(s):  
Xiaoying Zhao ◽  
Yanren Hou ◽  
Guangzhi Du
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Partition Of Unity ◽  
Time Dependent ◽  
The Finite Element Method ◽  
Partition Of Unity Method ◽  
Content Type ◽  
Standard Galerkin Method ◽  
Unsteady Stokes Equations

Purpose The purpose of this paper is to propose a parallel partition of unity method to solve the time-dependent Stokes problems. Design/methodology/approach This paper solved the time-dependent Stokes equations using the finite element method and the partition of unity method. Findings The proposed method in this paper obtained the same accuracy as the standard Galerkin method, but it, in general, saves time. Originality/value Based on a combination of the partition of unity method and the finite element method, the authors, in this paper, propose a new parallel partition of unity method to solve the unsteady Stokes equations. The idea is that, at each time step, one need to only solve a series of independent local sub-problems in parallel instead of one global problem. Numerical tests show that the proposed method not only reaches the same convergence orders as the fully discrete standard Galerkin method but also saves ample computing time.

The hierarchical finite cell method for problems in structural mechanics

2017 ◽  
Author(s):  
Meysam Joulaian
Keyword(s):  
Integration Method ◽  
Partition Of Unity ◽  
Heterogeneous Material ◽  
High Order ◽  
Partition Of Unity Method ◽  
Finite Cell Method ◽  
Cell Method ◽  
Integration Schemes ◽  
The Moment ◽  
Finite Cell

The finite cell method (FCM) is a combination of the fictitious domain approach and high-order finite elements. This thesis is concerned with the study of the numerical challenges of this method, and it investigates possible approaches to overcome them. Herein, we will introduce and study different numerical integration schemes, such as the adaptive integration method and the moment fitting approach. To improve the convergence behavior of the FCM for problems with heterogeneous material, we will also propose two high-order enrichment strategies based on the hp-d approach and the partition of unity method. Moreover, the application of the FCM will be extended to the simulation of wave propagation problems, employing spectral elements and a novel mass lumping technique. ...

A parallel partition of unity method for the nonstationary Navier-Stokes equations

2017 ◽  
Vol 27 (8) ◽  
pp. 1675-1686 ◽  
Author(s):  
Guangzhi Du ◽  
Liyun Zuo
Keyword(s):  
Stokes Equations ◽  
Partition Of Unity ◽  
Navier Stokes ◽  
Computational Time ◽  
The Finite Element Method ◽  
Partition Of Unity Method ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Content Type ◽  
Standard Galerkin Method

Purpose The purpose of this paper is to propose a parallel partition of unity method (PPUM) to solve the nonstationary Navier-Stokes equations. Design/methodology/approach This paper opted for the nonstationary Navier-Stokes equations by using the finite element method and the partition of unity method. Findings This paper provides one efficient parallel algorithm which reaches the same accuracy as the standard Galerkin method but saves a lot of computational time. Originality/value In this paper, a PPUM is proposed for nonstationary Navier-Stokes. At each time step, the authors only need to solve a series of independent local sub-problems in parallel instead of one global problem.

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