A sparse matrix open boundary method for finite element analysis

1989 ◽  
Vol 25 (4) ◽  
pp. 2810-2812 ◽  
Author(s):  
D.A. Lowther ◽  
E.M. Freeman ◽  
B. Forghani
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Sparse Matrix ◽  
Open Boundary ◽  
Element Analysis ◽  
Boundary Method

GPU-Friendly Preconditioners for Efficient 3-D Finite Element Analysis of Thin Structures

2011 ◽  
Author(s):  
Vikalp Mishra ◽  
Krishnan Suresh
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Sparse Matrix ◽  
Grid Method ◽  
Double Precision ◽  
Thin Structures ◽  
Element Analysis ◽  
Dual Representation ◽  
Matrix Vector Multiplication ◽  
Matrix Vector

A serious computational bottle-neck in finite element analysis today is the solution of the underlying system of equations. To alleviate this problem, researchers have proposed the use of graphics programmable units (GPU) for fast iterative solution of such equations. Indeed, researchers have shown that a GPU-implementation of a double-precision sparse-matrix-vector multiplication (that underlies all iterative methods) is approximately an order of magnitude faster than that of an optimized CPU implementation. Unfortunately, fast matrix-vector multiplication alone is insufficient… a good preconditioner is necessary for rapid convergence. Furthermore, most modern preconditioners, such as incomplete Cholesky, are expensive to compute, and cannot be easily ported to the GPU. In this paper, we propose a special class of preconditioners for the analysis of thin structures, such as beams and plates. The proposed preconditioners are developed by combining the multi-grid method, with recently developed dual-representation method for thin structures. It is shown, that these preconditioners are computationally inexpensive, perform better than standard pre-conditioners, and can be easily ported to the GPU.

Finite-Element Analysis of Magnetic Field Problem With Open Boundary Using Infinite Edge Element

2011 ◽  
Vol 47 (5) ◽  
pp. 1194-1197 ◽  
Author(s):  
Satoshi Tamitani ◽  
Tomoaki Takamatsu ◽  
Asuka Otake ◽  
Shinji Wakao ◽  
Akihisa Kameari ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Open Boundary ◽  
Element Analysis ◽  
Field Problem ◽  
Edge Element

Finite Element Analysis in 3D Using the Penalty Boundary Method

2002 ◽  
Author(s):  
Brett W. Clark ◽  
David C. Anderson
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Mesh Generation ◽  
Discretization Error ◽  
Finite Element Models ◽  
Element Analysis ◽  
Hexahedral Elements ◽  
Boundary Method ◽  
Time Required

Traditional methods for applying boundary conditions in finite element analysis require the mesh to conform to the geometry boundaries. This in turn requires complex meshing algorithms for automated mesh generation from CAD geometry, particularly when using quadrilateral and hexahedral elements. The 3D extension of the penalty boundary method (PBM) is presented as a method that significantly reduces the time required generating finite element models because the mesh is not required to conform to the CAD geometry. The PBM employs penalty methods to apply boundary conditions on a simple, regular mesh. The PBM also eliminates discretization error because boundary conditions are applied using CAD geometry directly rather than an approximation of the geometry.

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